Order = 448345497600 = 213.37.52.7.11.13.
Mult = 6.
Out = 2.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of Suz are a, b where a is in class 2B, b is in class 3B, ab has order 13 and ababb has order 15.

Standard generators of 2.Suz are preimages A, B where B has order 3 and AB has order 13.

Standard generators of 3.Suz are preimages A, B where A has order 2 and AB has order 13.

Standard generators of 6.Suz are preimages A, B where A has order 4, B has order 3 and AB has order 13.

Standard generators of Suz:2 are c, d where c is in class 2C, d is in class 3B and cd has order 28.

Standard generators of 2.Suz:2 are preimages C, D where D has order 3.

Standard generators of 3.Suz:2 are preimages C, D where D is in class +3B. Alternatively: CDCDD has order 7.

Standard generators of 6.Suz:2 are preimages C, D where D has order 3 and CDCDD has order 7.

Standard generators of 6.Suz:2 (type b) are preimages C, D where D has order 3 and CDCDD has order 14.

## Automorphisms

Group Automorphism Order in Out(G) Description
Suz Outer automorphism u 2 a maps to aabab
b maps to babbabb
(No program)
Suz Outer automorphism v 2 a maps to a
b maps to bababbab
(No program)

(Suz) If c' = u15 and d'=b then (c',d') is conjugate to (c,d).

(Suz) v is in class 8H and ((babv)7, baba) is conjugate to (c,d).

## Black box algorithms

### Finding generators

Group Algorithm File
Suz
Suz:2

### Checking generators (semi-presentations)

Group Semi-presentation File
Suz 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 13, o(ababb) = 15, o(abababb) = 12 〉〉 Download
Suz:2 〈〈 c, d | o(c) = 2, o(d) = 3, o(cd) = 28, o(cdcdcddcdd) = 7 〉〉 Download

## Representations

### Representations of 2.Suz

• View detailed report.
• Permutation representations:
Number of points ID Generators Description Link
65520StdDetails
• Matrix representations
Char Ring Dimension ID Generators Description Link
3GF(3)12StdDetails
3GF(3)208StdDetails
3GF(3)352StdDetails

### Representations of 6.Suz

• View detailed report.
• Permutation representations:
Number of points ID Generators Description Link
196560StdDetails
• Matrix representations
Char Ring Dimension ID Generators Description Link
5GF(25)12aStdDetails
7GF(7)12aStdDetails
13GF(13)12aStdDetails

## Maximal subgroups

### Maximal subgroups of Suz

Subgroup Order Index Programs/reps
G2(4) 251 596 800 1 782Program: Standard generators
32.U4(3).23' 19 595 520 22 880Program: Generators
U5(2) 13 685 760 32 760Program: Standard generators
21+6.U4(2) 3 317 760 135 135Program: Generators
35:M11 1 924 560 232 960Program: Generators mapping onto standard generators
J2:2 1 209 600 370 656Program: Generators
24+6:3A6 1 105 920 405 405Program: Generators
(A4 × L3(4)):2 483 840 926 640Program: Generators
22+8:(A5 × S3) 368 640 1 216 215Program: Generators
M12:2 190 080 2 358 720Program: Standard generators
32+4:2.(A4 × 22).2 139 968 3 203 200Program: Generators
(A6 × A5).2 43 200 10 378 368Program: Generators
(A6 × 32:4).2 25 920 17 297 280Program: Generators
L3(3):2 11 232 39 916 800Program: Standard generators
L3(3):2 11 232 39 916 800Program: Standard generators
L2(25) 7 800 57 480 192Program: Generators
A7 2 520 177 914 880Program: Generators

### Maximal subgroups of Suz:2

Subgroup Order Index Programs/reps
Suz 448 345 497 600 2Program: Standard generators
G2(4):2 503 193 600 1 782Program: Generators
Program: Generators
32.U4(3).22 39 191 040 22 880Program: Generators
U5(2):2 27 371 520 32 760Program: Standard generators
21+6.U4(2).2 6 635 520 135 135Program: Generators mapping onto standard generators
Program: Generators
35:(M11 × 2) 3 849 120 232 960Program: Generators mapping onto standard generators
J2:2 × 2 2 419 200 370 656Program: Generators mapping onto standard generators
Program: Generators
24+6:3.S6 2 211 840 405 405Program: Generators mapping onto standard generators
Program: Generators
(A4 × L3(4):2):2 967 680 926 640Program: Generators
22+8:(S5 × S3) 737 280 1 216 215Program: Generators
M12:2 × 2 380 160 2 358 720Program: Generators mapping onto standard generators
Program: Generators
32+4:2.(S4 × D8) 279 936 3 203 200Program: Generators
(PGL2(9) × A5).2 86 400 10 378 368Program: Generators mapping onto standard generators
Program: Generators
(A6 × 32:8).2 51 840 17 297 280Program: Generators mapping onto standard generators
L2(25):2 15 600 57 480 192Program: Generators
S7 5 040 177 914 880Program: Standard generators
Program: Generators

## Conjugacy classes

### Conjugacy classes of Suz

Conjugacy class Centraliser order Power up Class rep(s)
1A448 345 497 600
2A3 317 760 4A 4B 4C 6A 6B 6C 6D 8A 8B 8C 10A 12A 12B 12C 12E 18A 18B 20A 24A
2B161 280 4D 6E 10B 12D 14A
3A9 797 760 6A 12A 12C 15C 21A 21B 24A
3B34 992 6B 6C 6D 9A 9B 12B 12E 18A 18B
3C3 240 6E 12D 15A 15B
4A46 080 8A 12A 12B 20A 24A
4B3 072 8B 12E
4C1 536 8C 12C
4D288 12D
5A1 800 10A 15A 15B 20A
5B300 10B 15C
6A3 456 12A 12C 24A
6B1 296 6C5 18A 18B
6C1 296 6B5 18A 18B
6D432 12B 12E
6E72 12D
7A84 14A 21A 21B
8A192 24A
8B64 abababbababbabb
8C32 abababbababb
9A54 9B2 18A 18B
9B54 9A2 18A 18B
10A40 20A
10B20 abababababbababbabb
11A11 abababababbababbabbababbababababbababbabb
12A288 24A
12B72 abababb
12C48 abababbabababababbababbabb
12D36 ababbababababbababbabb
12E24 abababbabababbababbabb
13A13 13B2
13B13 13A2
14A28 ababababbababbabb
15A45 15B2
15B45 15A2
15C15 ababababababbababbabb
18A18 18B5
18B18 18A5
20A20 abababbababbabbabababbabababababbababbabb
21A21 21B2
21B21 21A2
24A24 ababababababbababbabbababababbabababbababb
13A-B ab
15A-B ababb
18A-B ababababbabababbababb
21A-B ababababb

### Conjugacy classes of Suz:2

Conjugacy class Centraliser order Power up Class rep(s)
1A896 690 995 200
2A6 635 520 4A 4B 4C 6A 6B 6C 8A 8B 8C 10A 12A 12B 12C 12E 18A 20A 24A 4E 8D 8E 8F 8G 8H 12F 12G 16A 24B 24C 24D 24E 24F 40A 40B
2B322 560 4D 6D 10B 12D 14A 4F 12H 28A
3A19 595 520 6A 12A 12C 15B 21A 24A 6E 12F 24B 24C 24F 30A
3B69 984 6B 6C 9A 12B 12E 18A 6F 12G 24D 24E
3C6 480 6D 12D 15A 6G 6H 12H
4A92 160 8A 12A 12B 20A 24A 8D 8E 8F 8G 24B 24C 24D 24E 40A 40B
4B6 144 8B 12E 16A
4C3 072 8C 12C 8H 24F
4D576 12D
5A3 600 10A 15A 20A 10D 40A 40B
5B600 10B 15B 10C 10E 30A
6A6 912 12A 12C 24A 12F 24B 24C 24F
6B1 296 18A
6C864 12B 12E 12G 24D 24E
6D144 12D 12H
7A168 14A 21A 14B 28A
8A384 24A
8B128 16A
8C64
9A54 18A
10A80 20A 40A 40B
10B40
11A22 22A
12A576 24A 24B 24C
12B144 24D 24E
12C96 24F
12D72
12E48
13A13
14A56 28A
15A45
15B30 30A
18A18
20A40 40A 40B
21A21
24A48
2C2 419 200 6E 6G 10C 10D 14B 30A
2D380 160 6F 6H 10E 22A
4E4 608 12F 12G
4F1 344 12H 28A
6E4 320 30A
6F216
6G144
6H144
8D46 080 24B 24D 40A 40B
8E3 072 24C
8F768 24E
8G256
8H192 24F
10C600 30A
10D100
10E40
12F288
12G72
12H24
14B28
16A16
22A22
24B288
24C96
24D72
24E24
24F24
28A28
30A30
40A40 40B7
40B40 40A7