Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊(C3⋊(D53⋊C13)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊(D53⋊C13)) |
| unambiguous semidirect product | (C2×C53⋊C13)⋊(C3⋊D3) |
| unambiguous semidirect product | (C2×C3⋊D159)⋊C13 |
| Fitting, socle | C2×C32×C53 ⋊ C2×C13 |
| derived, Hall | C32×C53 ⋊ C22×C13 |
| Hall | C32×C53⋊C13 ⋊ C22 |
| Hall | C2×C3⋊D159 ⋊ C13 |
| Hall | C53⋊C13 ⋊ C2×C3⋊D3 |
| Sylow | C53 ⋊ C2×C13×C3⋊D3 |
| Sylow | C32 ⋊ C2×D53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊(D53⋊C13)) |
| commutator, cosocle, hypocenter | C32×C53 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C53 | C2×C13 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 954 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 107);