Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C7×C29×D77 |
| unambiguous semidirect product | C7⋊(C7×D11×C29) |
| unambiguous semidirect product | C11⋊(C7×D7×C29) |
| Fitting, socle, Hall | C72×C11×C29 ⋊ C2 |
| derived | C7×C11 ⋊ C2×C7×C29 |
| Hall | C72×C29 ⋊ D11 |
| Hall | C72×C11 ⋊ C2×C29 |
| Hall | C11×C29 ⋊ C7×D7 |
| Sylow | C72 ⋊ D11×C29 |
| Sylow | C11 ⋊ C7×D7×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C29 | D77 |
| commutator, cosocle, hypocenter | C7×C11 | C2×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C29 | C2 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C7×C29 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4466 |
8120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 27);