Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊(D53⋊C13) |
| unambiguous semidirect product | ((C3⋊D3)⋊D53)⋊C13 |
| unambiguous semidirect product | (C3⋊(D53⋊C13))⋊D3 |
| Fitting, socle, derived, Hall | C32×C53 ⋊ C22×C13 |
| Hall | C32×C53⋊C13 ⋊ C22 |
| Hall | (C3⋊D3)⋊D53 ⋊ C13 |
| Hall | C53⋊C13 ⋊ D32 |
| Sylow | C53 ⋊ D32×C13 |
| Sylow | C32 ⋊ C2×D53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C53 | C22×C13 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 318 |
Polycyclic presentation:
2^2,13,3^2,53|e^a=e^2,f^a=f^52,d^b=d^2,e^b=e^2,f^c=f^16129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 99);