Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C7 |
| direct product | C11×C11⋊#5997 |
| unambiguous semidirect product | C11⋊(C11×#5997) |
| Fitting, socle, Hall | C72×C112 ⋊ C4 |
| derived | C72×C11 ⋊ C4×C11 |
| Sylow | C112 ⋊ #5997 |
| Sylow | C72 ⋊ C11×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C11⋊#5997 |
| commutator, hypocenter | C72×C11 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C72×C112 | C4 |
| prime radical | C112×C7⋊D7 | C2 |
| cosocle | C11×C7⋊D7 | C2×C11 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C11 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
1606 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 60);