Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C32×C53 ⋊ C2×C13 |
| derived | C3×C53 ⋊ C22×C3×C13 |
| Hall | C32×C53⋊C13 ⋊ C22 |
| Hall | C2×C3×D159 ⋊ C13 |
| Hall | C53⋊C13 ⋊ C2×C3×D3 |
| Hall | C32×C53 ⋊ C22×C13 |
| Sylow | C53 ⋊ C2×C3×D3×C13 |
| Sylow | C32 ⋊ C2×D53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊(D53⋊C13) |
| commutator, cosocle, hypocenter | C3×C53 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C53 | C2×C13 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C2×C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 636 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 105);