Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C11 |
| direct product | C7×C7⋊#92150 |
| unambiguous semidirect product | C7⋊(C7×#92150) |
| Fitting, socle, Hall | C72×C112 ⋊ C4 |
| derived | C7×C112 ⋊ C4×C7 |
| Sylow | C112 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#92150 |
| commutator, hypocenter | C7×C112 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C112 | C4 |
| prime radical | C72×C11⋊D11 | C2 |
| cosocle | C7×C11⋊D11 | C2×C7 |
| LCS | G ▷ C7×C112 | |
| UCS | C1 ◁ C7 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
1540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 64);