Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C72×C29 ⋊ C2×C32 |
| Hall | ΓL(1,𝔽8)2×C29 ⋊ C2 |
| Hall | C72×D29 ⋊ C32 |
| Sylow | C72 ⋊ C32×D29 |
| Sylow | C29 ⋊ C2×ΓL(1,𝔽8)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C29 | C2×C32 |
| LCS | G ▷ C72×C29 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 609 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 100);