Order = 4154781481226426191177580544000000 = 241.313.56.72.11.13.17.19.23.31.47.
Mult = 2.
Out = 1.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of B are a, b where a is in class 2C, b is in class 3A, ab has order 55 and ababababbababbabb has order 23.

## Black box algorithms

### Finding generators

Group Algorithm File

### Checking generators (semi-presentations)

Group Semi-presentation File
B 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 55, o(ababababbababbabb) = 23, o(u) = 52, o(au26) = 35, o(v) = 38, o(v19ba) = 8; u = (ababb)2(ab)2(ababb)2, v = (ab)3(abbab)2ab(ababb)2abb 〉〉 Download

## Maximal subgroups

### Maximal subgroups of B

Subgroup Order Index Programs/reps
2.2E6(2):2 306 129 918 735 099 415 756 800 13 571 955 000 Program: Generators
21+22.Co2 354 883 595 661 213 696 000 11 707 448 673 375 Program: Generators
Fi23 4 089 470 473 293 004 800 1 015 970 529 280 000 Program: Generators
29+16.S8(2) 1 589 728 887 019 929 600 2 613 515 747 968 125 Program: Generators
Th 90 745 943 887 872 000 45 784 762 417 152 000 Program: Generators
(22 × F4(2)):2 26 489 012 826 931 200 156 849 238 149 120 000 Program: Generators
22+10+20.(M22:2 × S3) 22 858 846 741 463 040 181 758 140 654 146 875 Program: Generators
[230].L5(2) 10 736 731 045 232 640 386 968 944 618 506 250 Program: Generators
S3 × Fi22:2 774 741 019 852 800 5 362 800 438 804 480 000 Program: Generators
[235].(S5 × L3(2)) 692 692 325 498 880 5 998 018 641 586 846 875
HN:2 546 061 824 000 000 7 608 628 361 513 926 656 Program: Generators
O8+(3):S4 118 852 315 545 600 34 957 513 971 466 240 000
31+8.21+6.U4(2).2 130 606 940 160 31 811 337 714 034 278 400 000 Program: Generators
(32:D8 × U4(3).2.2).2 1 881 169 920 2 208 615 732 717 237 043 200 000
5:4 × HS:2 1 774 080 000 2 341 935 809 673 986 624 716 800 Program: Generators
S4 × 2F4(2) 862 617 600 4 816 481 232 502 590 013 440 000 Program: Generators
[311].(S4 × 2S4) 204 073 344 20 359 256 136 981 938 176 000 000
S5 × M22:2 106 444 800 39 032 263 494 566 443 745 280 000
(S6 × L3(4):2).2 58 060 800 71 559 149 740 038 480 199 680 000
53.L3(5) 46 500 000 89 350 139 381 213 466 476 937 216
51+4.21+4.A5.4 24 000 000 173 115 895 051 101 091 299 065 856 Program: Generators
(S6 × S6).4 2 073 600 2 003 656 192 721 077 445 591 040 000
52:4S4 × S5 288 000 14 426 324 587 591 757 608 255 488 000
L2(49).23 117 600 35 329 774 500 224 712 510 013 440 000
L2(31) 14 880 279 219 185 566 292 082 740 428 800 000
M11 7 920 524 593 621 366 973 003 936 563 200 000
L3(3) 5 616 739 811 517 312 397 826 064 384 000 000
L2(17):2 4 896 848 607 328 681 868 094 603 264 000 000
L2(11):2 1 320 3 147 561 728 201 838 023 619 379 200 000
47:23 1 081 3 843 461 129 719 173 164 826 624 000 000 Program: Generators

## Conjugacy classes

### Conjugacy classes of B

Conjugacy class Centraliser order Power up Class rep(s)
1A 4 154 781 481 226 426 191 177 580 544 000 000
2A 306 129 918 735 099 415 756 800 6A 6B 6D 10A 14A 14B 18A 18B 22A 26B 30A 30B 34B 34C 38A 42A 42B 66A 70A
2B 354 883 595 661 213 696 000 4A 4B 4C 4D 4F 4G 6C 6G 8A 8B 8C 8D 8E 8F 8H 8I 8L 10B 10D 12A 12B 12C 12D 12E 12G 12H 12I 12K 12L 12M 12O 14D 16A 16B 16C 16D 16E 16F 18C 20A 20B 20C 20D 20E 20F 20I 22B 24A 24B 24C 24D 24E 24F 24G 24K 24M 28A 28B 28C 28D 30D 30G 30H 32A 32B 32C 32D 36A 36B 40A 40B 40C 40D 44A 46A 46B 48A 48B 56A 56B 60A 60B
2C 26 489 012 826 931 200 4I 6F 6K 10C 12T 14C 18F 20H 26A 30C 34A 42C 52A
2D 11 689 182 992 793 600 4E 4H 4J 6E 6H 6I 6J 8G 8J 8K 8M 8N 10E 10F 12F 12J 12N 12P 12Q 12R 12S 14E 16G 16H 18D 18E 20G 20J 24H 24I 24J 24L 24N 28E 30E 30F 36C 40E 60C
3A 387 370 509 926 400 6A 6B 6C 6E 6F 6H 12A 12C 12D 12E 12G 12H 12I 12J 12L 12P 15A 21A 24A 24B 24C 24D 24E 24G 24I 24J 30A 30B 30C 30D 30E 33A 39A 42A 42B 42C 48A 48B 60A 60B 66A
3B 65 303 470 080 6D 6G 6I 6J 6K 9A 9B 12B 12F 12K 12M 12N 12O 12Q 12R 12S 12T 15B 18A 18B 18C 18D 18E 18F 24F 24H 24K 24L 24M 24N 27A 30F 30G 30H 36A 36B 36C 60C
4A 372 051 542 016 000 12C 20A 20B 20C 28C 44A 60A
4B 109 586 090 557 440 8B 8C 8E 12A 12B 12D 20D 24A 24B 24C 24D 28A 36A 40A 40B 40C
4C 202 937 204 736 8A 8D 8F 8H 12G 12M 16A 16B 16C 16D 16E 16F 24E 24F 24G 24K 28B 32A 32B 32C 32D 48A 48B 56A 56B
4D 190 253 629 440 12E 12H 12K 20E 28D 36B 60B
4E 95 126 814 720 8G 8J 12F 12J 12N 20G 24H 24I 24J 28E 36C 40E 60C
4F 24 159 191 040 8I 12I 12O 20I 24M
4G 6 039 797 760 8L 12L 20F 40D
4H 301 989 888 8K 8M 12P 12Q 12S 16G 16H 24L
4I 143 769 600 12T 20H 52A
4J 125 829 120 8N 12R 20J 24N
5A 443 520 000 10A 10B 10C 10E 15A 20A 20C 20D 20E 20F 20H 30A 30B 30C 30D 30E 35A 40A 40B 40C 40D 55A 60A 60B 70A
5B 6 000 000 10D 10F 15B 20B 20G 20I 20J 25A 30F 30G 30H 40E 60C
6A 110 361 968 640 30B 42B 66A
6B 6 270 566 400 30A 42A
6C 318 504 960 12A 12C 12D 12E 12G 12H 12I 12L 24A 24B 24C 24D 24E 24G 30D 48A 48B 60A 60B
6D 40 310 784 18A 18B
6E 19 906 560 30E
6F 17 418 240 30C 42C
6G 14 929 920 12B 12K 12M 12O 18C 24F 24K 24M 30G 30H 36A 36B
6H 10 616 832 12J 12P 24I 24J
6I 9 953 280 12F 12Q 12R 24H 24L 24N 30F 60C
6J 497 664 12N 12S 18D 18E 36C
6K 373 248 12T 18F
7A 564 480 14A 14B 14C 14D 14E 21A 28A 28B 28C 28D 28E 35A 42A 42B 42C 56A 56B 70A
8A 396 361 728 24E 24F 56A 56B
8B 11 796 480 24A 40A
8C 11 796 480 24B 40B
8D 6 291 456 16A 16B 16E 24G 48A 48B
8E 5 898 240 24C 24D 40C
8F 1 572 864 24K
8G 1 474 560 24H 24I 40E
8H 524 288 16C 16D 16F 32A 32B 32C 32D
8I 196 608 24M
8J 98 304 24J
8K 98 304 16G 24L
8L 81 920 40D
8M 32 768 16H
8N 12 288 24N
9A 17 496 18E 27A 36C
9B 11 664 18A 18B 18C 18D 18F 36A 36B
10A 403 200 30A 30B 70A
10B 76 800 20A 20C 20D 20E 20F 30D 40A 40B 40C 40D 60A 60B
10C 28 800 20H 30C
10D 24 000 20B 20I 30G 30H
10E 19 200 30E
10F 9 600 20G 20J 30F 40E 60C
11A 1 320 22A 22B 33A 44A 55A 66A
12A 3 981 312 Omitted owing to length.
12B 746 496 36A
12C 737 280 60A
12D 663 552 24A 24B 24C 24D
12E 276 480 60B
12F 138 240 24H 60C
12G 73 728 24E 24G 48A 48B
12H 55 296 Omitted owing to length.
12I 36 864 abababbababbabababbababbabababababbababbabbabbababb
12J 27 648 24I 24J
12K 20 736 36B
12L 18 432 Omitted owing to length.
12M 13 824 24F 24K
12N 10 368 36C
12O 9 216 24M
12P 9 216 Omitted owing to length.
12Q 9 216 24L
12R 1 536 24N
12S 1 152 ababbabababbababababbababbabb
12T 864 ababababbababababbababbabababbababb
13A 312 26A 26B 39A 52A
14A 564 480 42A 70A
14B 4 704 42B
14C 4 704 42C
14D 1 792 28A 28B 28C 28D 56A 56B
14E 1 792 28E
15A 3 600 30A 30B 30C 30D 30E 60A 60B
15B 120 30F 30G 30H 60C
16A 12 288 48A
16B 12 288 48B
16C 2 048 32A 32B
16D 2 048 32C 32D
16E 2 048 aababbabababababbababbabbabbababbabbababababbababb
16F 1 024 ababbababababbababbabbabb
16G 256 abababababbababbabbabbab
16H 256 Omitted owing to length.
17A 68 34A 34B 34C
18A 1 296 abababababbababbabbabbababababababbababbabbabbababbabb
18B 648 Omitted owing to length.
18C 432 36A 36B
18D 432 aabababababbababbabbabbababbabbababababbababbabb
18E 216 36C
18F 216 abababbababb
19A 38 38A
20A 38 400 60A
20B 4 000 Omitted owing to length.
20C 3 200 Omitted owing to length.
20D 2 560 40A 40B 40C
20E 960 60B
20F 640 40D
20G 480 40E 60C
20H 400 abababbabababbababbabababbababb
20I 160 ababababbababbababababbababbabbababababbababbabb
20J 80
21A 252 42A 42B 42C
22A 132 66A
22B 88 44A
23A 46 23B5 46A 46B
23B 46 23A5 46A 46B
24A 2 304 abababbabababababbababbabbabbababababbababababbababb
24B 2 304 Omitted owing to length.
24C 2 304 Omitted owing to length.
24D 2 304 Omitted owing to length.
24E 2 304 ababbabababbabababbababb
24F 1 728 ababbababbabababbabababbababb
24G 768 48A 48B
24H 576 Omitted owing to length.
24I 576 abababbabababbababbababababbababbabb
24J 192 abababbabababbababbabababbab
24K 192 abababababbababbabababbab
24L 192 abababbababababbababbabababbababababababbababbabbabb
24M 96 abababbababababbababbabababbabababababbababbabbabb
24N 96 bababababbababbabababababbababbabbabb
25A 25 ababababbabababbab
26A 104 52A
26B 52 ababababbabababbababb
27A 27 abababbababbababababbababbabb
28A 448 aabababbababbabababababbababbabbabbababbabbababbab
28B 448 56A 56B
28C 224 abababbababbabababbababbababababbababb
28D 224 Omitted owing to length.
28E 112 abababbabababababbababbabb
30A 3 600 Omitted owing to length.
30B 360 aabababbabababbabababababbababbabbabbababbabbababb
30C 360 Omitted owing to length.
30D 240 60A 60B
30E 240 abababbababbabababbababababbab
30F 120 60C
30G 60 30H7
30H 60 30G7
31A 31 31B3
31B 31 31A3
32A 128 32B3
32B 128 32A3
32C 128 32D5
32D 128 32C5
33A 66 66A
34A 68 ababababbababbabababababbababbabbabb
34B 68 34C3 abababbabababbab
34C 68 34B3
35A 70 70A
36A 216 Omitted owing to length.
36B 72 abababbababbabababababbababbabbabb
36C 36 ababbabababbababbabababbab
38A 38 ababababbababbababababbababbabb
39A 39 ababababbababababbababbabb
40A 320 Omitted owing to length.
40B 320 abababbabababababbababbabbababababbababbabb
40C 160 Omitted owing to length.
40D 80 ababb
40E 40 ababababbababababbababb
42A 252 Omitted owing to length.
42B 84 aabababababbababbabbabbababababababbababbabbabbababbabb
42C 84 abababbababababababbababbabbabbababb
44A 44 abababbabababababbababb
46A 46 46B5 abababababbababbabbabb
46B 46 46A5
47A 47 47B5 abababbababababbababb
47B 47 47A5
48A 96 ababababbab
48B 96 ababababbababbabbabbabababababbababbabbabbababb
52A 52 ababbababbababababbababb
55A 55 ab
56A 112 56B5 ababbababababbababbabababbababb
56B 112 56A5
60A 120 abbababababbababbabbabababb
60B 120 abababababbababbabbabbababbababababbababbabababababbababbabbabb
60C 60 ababababbababababbab
66A 66 abababbabababababbababbabbababababbababb
70A 70 abababababbababbabababbababb
30G-H abababababbababbabbabababbab
31A-B ababababbababb
32A-B abababababbababb
32C-D ababababababbababbabbabbababb