Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#64418⋊C3 |
| unambiguous semidirect product | #64418⋊(C3×C29) |
| unambiguous semidirect product | (C29×#64418)⋊C3 |
| Fitting, socle, Hall | C72×C29 ⋊ C3×D3 |
| derived | #3862 ⋊ C2×C3×C29 |
| Hall | ΓL(1,𝔽8)2×C29 ⋊ C2 |
| Hall | ΓL(1,𝔽8)2 ⋊ C2×C29 |
| Sylow | C72 ⋊ C3×D3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #64418⋊C3 |
| commutator, cosocle, hypocenter | #3862 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C72×C29 | C3×D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C29 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 406 |
580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 98);