Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C11×D77 |
| unambiguous semidirect product | (C2×C7)⋊(C7×C11×D11) |
| unambiguous semidirect product | (C2×C11)⋊(C7×C11×D7) |
| Fitting, socle | C2×C72×C112 ⋊ C2 |
| derived | C7×C11 ⋊ C22×C7×C11 |
| Hall | C72×C112 ⋊ C22 |
| Sylow | C112 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ C2×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C11 | D77 |
| commutator, cosocle, hypocenter | C7×C11 | C22×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C112 | C2 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C2×C7×C11 | |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 308 |
6160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 84);