Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic539 |
| unambiguous semidirect product | C11⋊(C11×Dic49) |
| unambiguous semidirect product | C49⋊(C11×Dic11) |
| derived | C11×C49 ⋊ C4×C11 |
| Hall | C112×C49 ⋊ C4 |
| Sylow | C112 ⋊ Dic49 |
| Sylow | C49 ⋊ C11×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D539 |
| commutator, hypocenter | C11×C49 | C4×C11 |
| Frattini | C2×C7 | C11×D77 |
| Fitting | C2×C112×C49 | C2 |
| socle, prime radical | C2×C7×C112 | D7 |
| cosocle | C2×C11×C49 | C2×C11 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C2×C11 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2156 |
5962 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 20);