Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C3×C7 |
| direct product | C7×C3⋊D3×C29⋊C7 |
| unambiguous semidirect product | C3⋊(D3×C7×C29⋊C7) |
| unambiguous semidirect product | (C3⋊D3×C29)⋊C72 |
| unambiguous semidirect product | (C7×C3⋊D3×C29)⋊C7 |
| Fitting, socle | C32×C7×C29 ⋊ C2×C7 |
| derived, Hall | C32×C29 ⋊ C2×C72 |
| Hall | C32×C7×C29⋊C7 ⋊ C2 |
| Hall | C3⋊D3×C29 ⋊ C72 |
| Sylow | C29 ⋊ C72×C3⋊D3 |
| Sylow | C32 ⋊ C2×C7×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊D3×C29⋊C7 |
| commutator, cosocle, hypocenter | C32×C29 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C29 | C2×C7 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C7 | |
240 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, 113);