Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D7×C29⋊C7 |
| unambiguous semidirect product | C7⋊(C2×C11×C29⋊C7) |
| unambiguous semidirect product | (D7×C29)⋊(C7×C11) |
| unambiguous semidirect product | (C11×D7×C29)⋊C7 |
| Fitting, socle | C7×C11×C29 ⋊ C2×C7 |
| derived | C7×C29 ⋊ C2×C7×C11 |
| Hall | C7×C11×C29⋊C7 ⋊ C2 |
| Hall | C7×C29⋊C7 ⋊ C2×C11 |
| Hall | C11×C29 ⋊ C7×D7 |
| Sylow | C29 ⋊ C7×C11×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D7×C29⋊C7 |
| commutator, cosocle, hypocenter | C7×C29 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C29 | C2×C7 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C11 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2233 |
605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 18);