Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×(C13⋊C3)⋊D53 |
| unambiguous semidirect product | (D3×C13⋊C3)⋊D53 |
| unambiguous semidirect product | (D3×C53)⋊(D13⋊C3) |
| unambiguous semidirect product | (D3×D689)⋊C3 |
| Fitting, socle, derived | C3×C13×C53 ⋊ C22×C3 |
| Hall | C3×C13⋊C3×C53 ⋊ C22 |
| Hall | C13×C53 ⋊ C2×C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C2×D53 |
| Sylow | C53 ⋊ D3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C53 | C22×C3 |
| LCS | G ▷ C3×C13×C53 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2067 |
570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 125);