Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C2 |
| derived, Hall | C22×C53 ⋊ C9×C13 |
| Hall | C22×C53⋊C13 ⋊ C9 |
| Hall | C22⋊C9×C53 ⋊ C13 |
| Sylow | C53 ⋊ C13×C22⋊C9 |
| Sylow | C22 ⋊ C9×C53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×C53⋊C13 |
| commutator, hypocenter | C22×C53 | C9×C13 |
| Fitting, socle, cosocle | C22×C3×C53 | C3×C13 |
| prime radical | C22×C3×C53⋊C13 | C3 |
| LCS | G ▷ C22×C53 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 954 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 21);