Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| direct product | D3×C11⋊D187 |
| unambiguous semidirect product | (D3×C11)⋊D187 |
| unambiguous semidirect product | (D3×C17)⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C3×C112×C17 ⋊ C22 |
| Hall | C112×C17 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D17 |
| Sylow | C112 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×C11⋊D11 |
| Sylow | C17 ⋊ D3×C11⋊D11 |
| Sylow | C3 ⋊ C2×C11⋊D187 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C112×C17 | C22 |
| LCS | G ▷ C3×C112×C17 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6171 |
3090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 100);