Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D11×C7⋊D77 |
| unambiguous semidirect product | (C7×D11)⋊D77 |
| unambiguous semidirect product | (C11×D11)⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C112 ⋊ C22 |
| Sylow | C112 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C112 | C22 |
| LCS | G ▷ C72×C112 | |
| UCS | C1 | |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1078 |
1897 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 78);