Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D77×C29⋊C7 |
| unambiguous semidirect product | C7⋊(D11×C29⋊C7) |
| unambiguous semidirect product | C11⋊(D7×C29⋊C7) |
| unambiguous semidirect product | (C29×D77)⋊C7 |
| Fitting, socle, derived | C7×C11×C29 ⋊ C2×C7 |
| Hall | C7×C11×C29⋊C7 ⋊ C2 |
| Hall | C7×C29⋊C7 ⋊ D11 |
| Hall | C11×C29 ⋊ C7×D7 |
| Sylow | C29 ⋊ C7×D77 |
| Sylow | C11 ⋊ D7×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C29 | C2×C7 |
| LCS | G ▷ C7×C11×C29 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2233 |
440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 20);