Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×D112 |
| unambiguous semidirect product | (C11×D11)⋊(C2×C72) |
| unambiguous semidirect product | (C11⋊D11)⋊(C2×C72) |
| Fitting, socle, Hall | C72×C112 ⋊ C22 |
| derived, Sylow | C112 ⋊ C22×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D112 |
| commutator, cosocle, hypocenter | C112 | C22×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C112 | C22 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C72 | |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1078 |
2401 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 63);