Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×D9×C29⋊C7 |
| unambiguous semidirect product | C9⋊(C2×C7×C29⋊C7) |
| unambiguous semidirect product | (D9×C29)⋊C72 |
| unambiguous semidirect product | (C7×D9×C29)⋊C7 |
| Fitting | C7×C9×C29 ⋊ C2×C7 |
| derived, Hall | C9×C29 ⋊ C2×C72 |
| Hall | C7×C9×C29⋊C7 ⋊ C2 |
| Hall | D9×C29 ⋊ C72 |
| Sylow | C29 ⋊ C72×D9 |
| Sylow | C9 ⋊ C2×C7×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D9×C29⋊C7 |
| commutator, cosocle, hypocenter | C9×C29 | C2×C72 |
| Frattini | C3 | D3×C7×C29⋊C7 |
| Fitting | C7×C9×C29 | C2×C7 |
| socle | C3×C7×C29 | D3×C7 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C7 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1827 |
462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 52);