ANU p-Quotient Program Version 1.2 running with workspace 1000000 on wilton Fri Apr 22 10:18:46 EST 1994 Standard Presentation Menu ----------------------------- 1. Supply start information 2. Compute standard presentation to supplied class 3. Save presentation to file 4. Display presentation 5. Set print level for construction 6. Compare two presentations stored in files 7. Call p-Quotient menu 8. Exit from program Select option: 1 Lower exponent-2 central series for G Group: G to lower exponent-2 central class 1 has order 2^2 Group: G to lower exponent-2 central class 2 has order 2^4 Class 2 2-quotient and its 2-covering group computed in 0.00 seconds Select option: 2 Enter output file name for group information: Standard Standardise presentation to what class? 10 Input the number of automorphisms: 3 Now enter the data for automorphism 1 Input 4 exponents for image of pcp generator 1: 1 0 0 1 Input 4 exponents for image of pcp generator 2: 0 1 0 0 Now enter the data for automorphism 2 Input 4 exponents for image of pcp generator 1: 1 0 0 0 Input 4 exponents for image of pcp generator 2: 0 1 0 1 Now enter the data for automorphism 3 Input 4 exponents for image of pcp generator 1: 1 1 1 0 Input 4 exponents for image of pcp generator 2: 0 1 1 1 PAG-generating sequence for automorphism group? 1 Starting group has order 2^4; its automorphism group order is at most 96 The standard presentation for the class 3 2-quotient is Group: G #1;2 to lower exponent-2 central class 3 has order 2^6 Non-trivial powers: .1^2 = .4 .2^2 = .5 .3^2 = .6 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 Its automorphism group has order at most 384 Computing standard presentation for class 3 took 0.15 seconds The standard presentation for the class 4 2-quotient is Group: G #1;1 to lower exponent-2 central class 4 has order 2^7 Non-trivial powers: .1^2 = .4 .2^2 = .5 .3^2 = .6 .7 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 [ .4, .3 ] = .7 [ .5, .1 ] = .7 Its automorphism group has order at most 1536 Computing standard presentation for class 4 took 0.08 seconds The standard presentation for the class 5 2-quotient is Group: G #1;2 to lower exponent-2 central class 5 has order 2^9 Non-trivial powers: .1^2 = .4 .2^2 = .5 .3^2 = .6 .7 .5^2 = .8 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 .8 [ .4, .3 ] = .7 .8 [ .5, .1 ] = .7 [ .5, .3 ] = .9 [ .5, .4 ] = .8 [ .6, .1 ] = .9 [ .6, .2 ] = .9 [ .7, .1 ] = .8 [ .7, .2 ] = .9 Its automorphism group has order at most 6144 Computing standard presentation for class 5 took 0.15 seconds The standard presentation for the class 6 2-quotient is Group: G #1;2 to lower exponent-2 central class 6 has order 2^11 Non-trivial powers: .1^2 = .4 .2^2 = .5 .11 .3^2 = .6 .7 .10 .11 .5^2 = .8 .11 .6^2 = .10 .7^2 = .10 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 .8 .10 [ .4, .3 ] = .7 .8 .10 .11 [ .5, .1 ] = .7 [ .5, .3 ] = .9 .11 [ .5, .4 ] = .8 .10 [ .6, .1 ] = .9 [ .6, .2 ] = .9 .10 .11 [ .6, .3 ] = .11 [ .6, .4 ] = .11 [ .7, .1 ] = .8 [ .7, .2 ] = .9 [ .7, .3 ] = .11 [ .7, .4 ] = .10 [ .8, .1 ] = .10 [ .9, .1 ] = .11 Its automorphism group has order at most 98304 Computing standard presentation for class 6 took 0.17 seconds The standard presentation for the class 7 2-quotient is Group: G #1;3 to lower exponent-2 central class 7 has order 2^14 Non-trivial powers: .1^2 = .4 .2^2 = .5 .11 .13 .3^2 = .6 .7 .10 .11 .12 .13 .14 .5^2 = .8 .11 .6^2 = .10 .14 .7^2 = .10 .12 .8^2 = .12 .9^2 = .12 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 .8 .10 .12 .13 [ .4, .3 ] = .7 .8 .10 .11 [ .5, .1 ] = .7 [ .5, .2 ] = .14 [ .5, .3 ] = .9 .11 .14 [ .5, .4 ] = .8 .10 .12 [ .6, .1 ] = .9 .12 .13 .14 [ .6, .2 ] = .9 .10 .11 .12 [ .6, .3 ] = .11 .12 [ .6, .4 ] = .11 .12 [ .6, .5 ] = .13 .14 [ .7, .1 ] = .8 [ .7, .2 ] = .9 [ .7, .3 ] = .11 .12 [ .7, .4 ] = .10 .12 [ .7, .5 ] = .12 .13 [ .8, .1 ] = .10 [ .8, .2 ] = .14 [ .8, .3 ] = .12 [ .8, .4 ] = .12 [ .9, .1 ] = .11 [ .9, .2 ] = .13 [ .9, .3 ] = .14 [ .9, .4 ] = .13 [ .10, .1 ] = .12 [ .10, .2 ] = .12 [ .11, .1 ] = .13 [ .11, .2 ] = .14 Its automorphism group has order at most 786432 Computing standard presentation for class 7 took 0.21 seconds The standard presentation for the class 8 2-quotient is Group: G #1;3 to lower exponent-2 central class 8 has order 2^17 Non-trivial powers: .1^2 = .4 .2^2 = .5 .11 .13 .17 .3^2 = .6 .7 .10 .11 .12 .13 .14 .17 .5^2 = .8 .11 .6^2 = .10 .14 .16 .7^2 = .10 .12 .8^2 = .12 .15 .9^2 = .12 .17 .10^2 = .15 .11^2 = .15 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 .8 .10 .12 .13 .15 [ .4, .3 ] = .7 .8 .10 .11 .15 [ .5, .1 ] = .7 [ .5, .2 ] = .14 .16 [ .5, .3 ] = .9 .11 .14 [ .5, .4 ] = .8 .10 .12 [ .6, .1 ] = .9 .12 .13 .14 .15 .16 .17 [ .6, .2 ] = .9 .10 .11 .12 [ .6, .3 ] = .11 .12 [ .6, .4 ] = .11 .12 [ .6, .5 ] = .13 .14 .17 [ .7, .1 ] = .8 [ .7, .2 ] = .9 [ .7, .3 ] = .11 .12 .16 .17 [ .7, .4 ] = .10 .12 .15 [ .7, .5 ] = .12 .13 [ .7, .6 ] = .15 .16 .17 [ .8, .1 ] = .10 [ .8, .2 ] = .14 [ .8, .3 ] = .12 .15 [ .8, .4 ] = .12 .15 [ .9, .1 ] = .11 [ .9, .2 ] = .13 .17 [ .9, .3 ] = .14 .15 .16 .17 [ .9, .4 ] = .13 .15 [ .9, .5 ] = .16 [ .10, .1 ] = .12 [ .10, .2 ] = .12 .17 [ .10, .3 ] = .15 [ .10, .4 ] = .15 [ .11, .1 ] = .13 [ .11, .2 ] = .14 [ .11, .3 ] = .16 .17 [ .11, .4 ] = .15 [ .12, .1 ] = .15 [ .13, .1 ] = .15 [ .13, .2 ] = .16 [ .14, .1 ] = .17 Its automorphism group has order at most 25165824 Computing standard presentation for class 8 took 0.28 seconds The standard presentation for the class 9 2-quotient is Group: G #1;3 to lower exponent-2 central class 9 has order 2^20 Non-trivial powers: .1^2 = .4 .2^2 = .5 .11 .13 .17 .3^2 = .6 .7 .10 .11 .12 .13 .14 .17 .20 .5^2 = .8 .11 .19 .20 .6^2 = .10 .14 .16 .18 .7^2 = .10 .12 .8^2 = .12 .15 .9^2 = .12 .17 .20 .10^2 = .15 .18 .11^2 = .15 .20 .12^2 = .18 .13^2 = .18 .14^2 = .18 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 .8 .10 .12 .13 .15 .18 [ .4, .3 ] = .7 .8 .10 .11 .15 .19 [ .5, .1 ] = .7 [ .5, .2 ] = .14 .16 [ .5, .3 ] = .9 .11 .14 .18 .19 [ .5, .4 ] = .8 .10 .12 [ .6, .1 ] = .9 .12 .13 .14 .15 .16 .17 .19 [ .6, .2 ] = .9 .10 .11 .12 .19 [ .6, .3 ] = .11 .12 .18 .19 .20 [ .6, .4 ] = .11 .12 .18 .19 .20 [ .6, .5 ] = .13 .14 .17 .18 .19 .20 [ .7, .1 ] = .8 [ .7, .2 ] = .9 [ .7, .3 ] = .11 .12 .16 .17 .18 .19 .20 [ .7, .4 ] = .10 .12 .15 [ .7, .5 ] = .12 .13 .18 [ .7, .6 ] = .15 .16 .17 .19 .20 [ .8, .1 ] = .10 [ .8, .2 ] = .14 [ .8, .3 ] = .12 .15 .19 .20 [ .8, .4 ] = .12 .15 .18 [ .8, .5 ] = .18 .20 [ .9, .1 ] = .11 [ .9, .2 ] = .13 .17 .18 .20 [ .9, .3 ] = .14 .15 .16 .17 [ .9, .4 ] = .13 .15 .20 [ .9, .5 ] = .16 [ .9, .6 ] = .18 .19 .20 [ .9, .7 ] = .18 .19 .20 [ .10, .1 ] = .12 [ .10, .2 ] = .12 .17 .18 .19 [ .10, .3 ] = .15 .20 [ .10, .4 ] = .15 .18 [ .11, .1 ] = .13 [ .11, .2 ] = .14 [ .11, .3 ] = .16 .17 .19 [ .11, .4 ] = .15 .20 [ .11, .5 ] = .18 .20 [ .12, .1 ] = .15 [ .12, .3 ] = .18 [ .12, .4 ] = .18 [ .13, .1 ] = .15 .18 .20 [ .13, .2 ] = .16 [ .13, .3 ] = .18 .19 [ .13, .4 ] = .18 [ .14, .1 ] = .17 [ .14, .2 ] = .20 [ .14, .3 ] = .18 [ .14, .4 ] = .20 [ .15, .1 ] = .18 [ .15, .2 ] = .18 [ .16, .1 ] = .19 [ .17, .1 ] = .20 [ .17, .2 ] = .18 Its automorphism group has order at most 402653184 Computing standard presentation for class 9 took 0.45 seconds The standard presentation for the class 10 2-quotient is Group: G #1;4 to lower exponent-2 central class 10 has order 2^24 Non-trivial powers: .1^2 = .4 .2^2 = .5 .11 .13 .17 .24 .3^2 = .6 .7 .10 .11 .12 .13 .14 .17 .20 .21 .22 .5^2 = .8 .11 .19 .20 .21 .6^2 = .10 .14 .16 .18 .22 .23 .24 .7^2 = .10 .12 .21 .22 .24 .8^2 = .12 .15 .9^2 = .12 .17 .20 .22 .23 .10^2 = .15 .18 .11^2 = .15 .20 .24 .12^2 = .18 .21 .13^2 = .18 .24 .14^2 = .18 .23 .15^2 = .21 .17^2 = .21 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 .8 .10 .12 .13 .15 .18 .21 [ .4, .3 ] = .7 .8 .10 .11 .15 .19 .21 .22 [ .5, .1 ] = .7 [ .5, .2 ] = .14 .16 .21 .23 .24 [ .5, .3 ] = .9 .11 .14 .18 .19 .21 .23 [ .5, .4 ] = .8 .10 .12 .21 .22 .24 [ .6, .1 ] = .9 .12 .13 .14 .15 .16 .17 .19 .21 .22 .23 [ .6, .2 ] = .9 .10 .11 .12 .19 .21 .23 [ .6, .3 ] = .11 .12 .18 .19 .20 .21 .22 [ .6, .4 ] = .11 .12 .18 .19 .20 .24 [ .6, .5 ] = .13 .14 .17 .18 .19 .20 .21 [ .7, .1 ] = .8 [ .7, .2 ] = .9 [ .7, .3 ] = .11 .12 .16 .17 .18 .19 .20 .21 .22 [ .7, .4 ] = .10 .12 .15 [ .7, .5 ] = .12 .13 .18 [ .7, .6 ] = .15 .16 .17 .19 .20 .22 [ .8, .1 ] = .10 [ .8, .2 ] = .14 .23 [ .8, .3 ] = .12 .15 .19 .20 .22 .24 [ .8, .4 ] = .12 .15 .18 [ .8, .5 ] = .18 .20 .21 [ .9, .1 ] = .11 [ .9, .2 ] = .13 .17 .18 .20 .23 .24 [ .9, .3 ] = .14 .15 .16 .17 .23 .24 [ .9, .4 ] = .13 .15 .20 .24 [ .9, .5 ] = .16 .23 [ .9, .6 ] = .18 .19 .20 .22 .24 [ .9, .7 ] = .18 .19 .20 .22 .24 [ .10, .1 ] = .12 [ .10, .2 ] = .12 .17 .18 .19 .24 [ .10, .3 ] = .15 .20 .22 [ .10, .4 ] = .15 .18 .21 [ .10, .5 ] = .21 .24 [ .11, .1 ] = .13 [ .11, .2 ] = .14 [ .11, .3 ] = .16 .17 .19 .21 [ .11, .4 ] = .15 .20 .21 .24 [ .11, .5 ] = .18 .20 .21 [ .11, .6 ] = .21 .22 .24 [ .11, .7 ] = .21 .22 .24 [ .12, .1 ] = .15 [ .12, .2 ] = .23 [ .12, .3 ] = .18 .21 [ .12, .4 ] = .18 .21 [ .13, .1 ] = .15 .18 .20 .21 [ .13, .2 ] = .16 [ .13, .3 ] = .18 .19 .21 [ .13, .4 ] = .18 .24 [ .13, .5 ] = .22 [ .14, .1 ] = .17 [ .14, .2 ] = .20 .21 .23 [ .14, .3 ] = .18 .23 [ .14, .4 ] = .20 .21 [ .14, .5 ] = .23 [ .15, .1 ] = .18 [ .15, .2 ] = .18 [ .15, .3 ] = .21 [ .15, .4 ] = .21 [ .16, .1 ] = .19 [ .16, .2 ] = .22 [ .16, .3 ] = .23 [ .16, .4 ] = .22 [ .17, .1 ] = .20 [ .17, .2 ] = .18 .21 .24 [ .17, .3 ] = .21 .23 [ .17, .4 ] = .24 [ .18, .1 ] = .21 [ .19, .1 ] = .22 [ .19, .2 ] = .23 [ .20, .1 ] = .24 [ .20, .2 ] = .23 Its automorphism group has order at most 25769803776 Computing standard presentation for class 10 took 0.46 seconds Select option: 4 Group: G #1;4 to lower exponent-2 central class 10 has order 2^24 Non-trivial powers: .1^2 = .4 .2^2 = .5 .11 .13 .17 .24 .3^2 = .6 .7 .10 .11 .12 .13 .14 .17 .20 .21 .22 .5^2 = .8 .11 .19 .20 .21 .6^2 = .10 .14 .16 .18 .22 .23 .24 .7^2 = .10 .12 .21 .22 .24 .8^2 = .12 .15 .9^2 = .12 .17 .20 .22 .23 .10^2 = .15 .18 .11^2 = .15 .20 .24 .12^2 = .18 .21 .13^2 = .18 .24 .14^2 = .18 .23 .15^2 = .21 .17^2 = .21 Non-trivial commutators: [ .2, .1 ] = .3 [ .3, .1 ] = .5 [ .3, .2 ] = .6 [ .4, .2 ] = .5 .6 .7 .8 .10 .12 .13 .15 .18 .21 [ .4, .3 ] = .7 .8 .10 .11 .15 .19 .21 .22 [ .5, .1 ] = .7 [ .5, .2 ] = .14 .16 .21 .23 .24 [ .5, .3 ] = .9 .11 .14 .18 .19 .21 .23 [ .5, .4 ] = .8 .10 .12 .21 .22 .24 [ .6, .1 ] = .9 .12 .13 .14 .15 .16 .17 .19 .21 .22 .23 [ .6, .2 ] = .9 .10 .11 .12 .19 .21 .23 [ .6, .3 ] = .11 .12 .18 .19 .20 .21 .22 [ .6, .4 ] = .11 .12 .18 .19 .20 .24 [ .6, .5 ] = .13 .14 .17 .18 .19 .20 .21 [ .7, .1 ] = .8 [ .7, .2 ] = .9 [ .7, .3 ] = .11 .12 .16 .17 .18 .19 .20 .21 .22 [ .7, .4 ] = .10 .12 .15 [ .7, .5 ] = .12 .13 .18 [ .7, .6 ] = .15 .16 .17 .19 .20 .22 [ .8, .1 ] = .10 [ .8, .2 ] = .14 .23 [ .8, .3 ] = .12 .15 .19 .20 .22 .24 [ .8, .4 ] = .12 .15 .18 [ .8, .5 ] = .18 .20 .21 [ .9, .1 ] = .11 [ .9, .2 ] = .13 .17 .18 .20 .23 .24 [ .9, .3 ] = .14 .15 .16 .17 .23 .24 [ .9, .4 ] = .13 .15 .20 .24 [ .9, .5 ] = .16 .23 [ .9, .6 ] = .18 .19 .20 .22 .24 [ .9, .7 ] = .18 .19 .20 .22 .24 [ .10, .1 ] = .12 [ .10, .2 ] = .12 .17 .18 .19 .24 [ .10, .3 ] = .15 .20 .22 [ .10, .4 ] = .15 .18 .21 [ .10, .5 ] = .21 .24 [ .11, .1 ] = .13 [ .11, .2 ] = .14 [ .11, .3 ] = .16 .17 .19 .21 [ .11, .4 ] = .15 .20 .21 .24 [ .11, .5 ] = .18 .20 .21 [ .11, .6 ] = .21 .22 .24 [ .11, .7 ] = .21 .22 .24 [ .12, .1 ] = .15 [ .12, .2 ] = .23 [ .12, .3 ] = .18 .21 [ .12, .4 ] = .18 .21 [ .13, .1 ] = .15 .18 .20 .21 [ .13, .2 ] = .16 [ .13, .3 ] = .18 .19 .21 [ .13, .4 ] = .18 .24 [ .13, .5 ] = .22 [ .14, .1 ] = .17 [ .14, .2 ] = .20 .21 .23 [ .14, .3 ] = .18 .23 [ .14, .4 ] = .20 .21 [ .14, .5 ] = .23 [ .15, .1 ] = .18 [ .15, .2 ] = .18 [ .15, .3 ] = .21 [ .15, .4 ] = .21 [ .16, .1 ] = .19 [ .16, .2 ] = .22 [ .16, .3 ] = .23 [ .16, .4 ] = .22 [ .17, .1 ] = .20 [ .17, .2 ] = .18 .21 .24 [ .17, .3 ] = .21 .23 [ .17, .4 ] = .24 [ .18, .1 ] = .21 [ .19, .1 ] = .22 [ .19, .2 ] = .23 [ .20, .1 ] = .24 [ .20, .2 ] = .23 Select option: 0 Exiting from ANU p-Quotient Program Total user time in seconds is 2.02