Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C2×C11 |
| Fitting, socle, Hall | C22×C112×C17 ⋊ C3 |
| derived, Hall | C22×C112 ⋊ C3×C17 |
| Hall | C112×C17 ⋊ A4 |
| Sylow | C112 ⋊ A4×C17 |
| Hall | C22×C17 ⋊ C112⋊C3 |
| Sylow | C22 ⋊ C17×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C22⋊(C112⋊C3) |
| commutator, cosocle, hypocenter | C22×C112 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C22×C112×C17 | C3 |
| LCS | G ▷ C22×C112 | |
| UCS | C1 ◁ C17 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1122 |
2788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 102);