Order = 145926144000 = 214.33.53.7.13.29.
Mult = 2.
Out = 1.

## Porting notes

Porting incomplete.

## Standard generators

Standard generators of Ru are a, b where a is in class 2B, b is in class 4A and ab has order 13.

Standard generators of 2.Ru are preimages A, B where B is in class +4A and AB has order 13. Alternatively: AB has order 13 and ABABB has order 29.

## Black box algorithms

### Finding generators

Group Algorithm File
Ru

### Checking generators (semi-presentations)

Group Semi-presentation File
Ru 〈〈 a, b | o(a) = 2, o(b) = 4, o(ab) = 13, o(abb) = 14, o(ababb) = 29 〉〉 Download

## Representations

### Representations of Ru

• View detailed report.
• Permutation representations:
Number of points ID Generators Description Link
4060StdDetails
• Matrix representations
Char Ring Dimension ID Generators Description Link
2GF(2)28StdDetails
2GF(2)376StdDetails
2GF(2)1246StdDetails
Char Ring Dimension ID Generators Description Link
3GF(9)378StdDetails
3GF(3)406StdDetails
3GF(3)783StdDetails
Char Ring Dimension ID Generators Description Link
5GF(5)133StdDetails
5GF(5)273StdDetails
5GF(5)378StdDetails
5GF(5)783StdDetails
Char Ring Dimension ID Generators Description Link
7GF(49)378StdDetails
7GF(7)406StdDetails
7GF(7)782StdDetails
Char Ring Dimension ID Generators Description Link
13GF(13)378StdDetails
13GF(13)406StdDetails
13GF(13)783StdDetails
Char Ring Dimension ID Generators Description Link
29GF(29)378StdDetails
29GF(29)406StdDetails
29GF(29)783StdDetails

## Maximal subgroups

### Maximal subgroups of Ru

Subgroup Order Index Programs/reps
2F4(2) = 2F4(2)'.2 Program: Generators
Program: Generators
26.U3(3).2 Program: Generators
Program: Generators
(22 × Sz(8)):3 Program: Generators
Program: Generators
23+8:L3(2) Program: Generators
Program: Generators
U3(5):2 Program: Generators
Program: Generators
21+4+6.S5 Program: Generators
Program: Generators
L2(25).22 Program: Generators
Program: Generators
A8 Program: Generators
Program: Generators
L2(29) Program: Generators
Program: Generators
Program: Generators
52:4.S5 Program: Generators
Program: Generators
3.A6.22 Program: Generators
Program: Generators
51+2:[25] Program: Generators
Program: Generators
L2(13):2 Program: Generators
Program: Generators
A6.22 Program: Generators
Program: Generators
5:4 × A5 Program: Generators
Program: Generators
Program: Generators

## Conjugacy classes

### Conjugacy classes of Ru

Conjugacy class Centraliser order Power up Class rep(s)
1A145 926 144 000
2A245 760 4A 4B 4C 4D 6A 8A 8B 8C 10A 12A 12B 16A 16B 20A 20B 20C 24A 24B
2B116 480 10B 14A 14B 14C 26A 26B 26C
3A2 160 6A 12A 12B 15A 24A 24B
4A7 680 8A 12A 20A 24A 24B
4B3 840 12B 20B 20C
4C1 024 8B 16A 16B
4D512 8C
5A1 000 10A 20A 20B 20C
5B300 10B 15A
6A48 12A 12B 24A 24B
7A28 14A 14B 14C
8A96 24A 24B
8B64 16A 16B
8C32 babbabababbababbabbababbabbabbabbabababbababbabb
10A40 20A 20B 20C
10B20 abbabababbababbabbababbabbbbabbabababbababbabbababbabbabb
12A24 24A 24B
12B12 abababbababbabb
13A52 26A 26B 26C
14A28 14B5 14C3
14B28 14A3 14C5
14C28 14A5 14B3
15A15 ababbababbabb
16A16 16B3 babbabababbababbabbababbabb
16B16 16A3
20A20 abababbabb
20B20 20C3
20C20 20B3
24A24 24B7
24B24 24A7 abbabababbababbabb
26A52 26B7 26C3
26B52 26A3 26C7 bababbabb
26C52 26A7 26B3
29A29 29B2 ababb
29B29 29A2
14A-C abb
20B-C abbabababbababbabbababbabb