Finite Group DatabasebetaFinite Group Databasebeta| order | 10075 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C13 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C13×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C52×C13 |
| Hall | C13×C31 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C52×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C13 | |
32 conjugacy classes of subgroups.
715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10075, 4);