Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| derived | C7×C29 ⋊ C2×C7×C9 |
| Hall | C7⋊C9×C29⋊C7 ⋊ C2 |
| Hall | C7×D29⋊C7 ⋊ C9 |
| Hall | C7×C29⋊C7 ⋊ C2×C9 |
| Hall | D29 ⋊ C7×C7⋊C9 |
| Sylow | C29 ⋊ C2×C7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D29⋊C7 |
| commutator, hypocenter | C7×C29 | C2×C7×C9 |
| Fitting, socle, cosocle | C3×C7×C29 | C2×C3×C7 |
| prime radical | C3×C7×D29⋊C7 | C3 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1827 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 46);