Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C11 · Schur multiplier (H2) = C7 |
| Fitting, socle | C7×C11×C29 ⋊ C2×C7 |
| derived, Sylow | C29 ⋊ C2×C72×C11 |
| Hall | C7×C11×C29⋊C7 ⋊ C2 |
| Hall | C7×C29⋊C7 ⋊ C2×C11 |
| Hall | C11×D29 ⋊ C72 |
| Hall | C11×C29 ⋊ C2×C72 |
| Hall | D29 ⋊ C72×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | D29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C2×C72×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C29 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C11 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2233 |
1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 14);