Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic561 |
| unambiguous semidirect product | C3⋊(C11×Dic187) |
| unambiguous semidirect product | C11⋊(C11×Dic51) |
| derived | C3×C11×C17 ⋊ C4×C11 |
| Hall | C3×C112×C17 ⋊ C4 |
| Hall | C112×C17 ⋊ Dic3 |
| Hall | C3×C112 ⋊ Dic17 |
| Sylow | C112 ⋊ Dic51 |
| Hall | C3×C17 ⋊ C11×Dic11 |
| Sylow | C17 ⋊ C11×Dic33 |
| Sylow | C3 ⋊ C11×Dic187 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D561 |
| commutator, hypocenter | C3×C11×C17 | C4×C11 |
| Frattini | C2 | C11×D561 |
| Fitting, socle, prime radical | C2×C3×C112×C17 | C2 |
| cosocle | C2×C3×C11×C17 | C2×C11 |
| LCS | G ▷ C3×C11×C17 | |
| UCS | C1 ◁ C2×C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2244 |
6204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 38);