Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3 |
| direct product | C32×AGL(1,𝔽53) |
| unambiguous semidirect product | #6157⋊(C32×C13) |
| unambiguous semidirect product | (C3×#6157)⋊(C3×C13) |
| unambiguous semidirect product | (C32×#6157)⋊C13 |
| Fitting, socle, Hall | C32×C53 ⋊ C4×C13 |
| derived, Sylow | C53 ⋊ C32×C4×C13 |
| Hall | C32×C53⋊C13 ⋊ C4 |
| Hall | C32×#6157 ⋊ C13 |
| Hall | C53⋊C13 ⋊ C32×C4 |
| Hall | #6157 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | AGL(1,𝔽53) |
| commutator, hypocenter | C53 | C32×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C53 | C4×C13 |
| prime radical | C32×D53⋊C13 | C2 |
| cosocle | D53 | C2×C32×C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 477 |
477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 95);