Order = 319979520 =
2^{15}.3^{2}.5.7.31.

Mult = 1.

Out = 1.

## Porting notes

Porting complete, but handling of notes is unsatisfactory.## Standard generators

Standard generators of 2^{5}.L_{5}(2) are
*a*, *b* where *a* has order 2, *b* has
order 5, *a**b* has order 21,
*a**b**a**b**b* has order 10,
*a**b**a**b**a**b**b**b**b*
has order 28 and
*a**b**a**b**a**b**b**b**a**b**b*
has order 5.

### Notes

- (2
^{5}.L_{5}(2)) These generators map onto standard generators of L_{5}(2).

## Presentations

Group | Presentation | Link |
---|---|---|

2^{5}.L_{5}(2) |
〈 a, b |
a^{2} = b^{5} =
(ab)^{21} =
[a,b^{2}]^{4} =
[a,b^{−2}ab^{−2}][a,b]^{3}
=
(ababab^{−2})^{2}(abab^{−1}ab)^{2}(ab^{−1})^{2}
= 1 〉 |
Details |

## Representations

### Representations
of 2^{5}.L_{5}(2)

- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 7440 a Std Details 7440 b Std Details 7440 c Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 248 Std Details 2 GF(2) 69 a Std Details 3 GF(3) 248 Std Details 5 GF(5) 248 Std Details 7 GF(7) 248 Std Details 31 GF(31) 248 Std Details

## Miscellaneous Notes

Group | Category | Note |
---|---|---|

2^{5}.L_{5}(2) |
Group theoretic trivia. | There is just one class of involutions of
2^{5}.L_{5}(2) not in the normal
2^{5} and it maps onto class 2A of
L_{5}(2). |