Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊AGL(1,𝔽53) |
| unambiguous semidirect product | C3⋊(C3×AGL(1,𝔽53)) |
| unambiguous semidirect product | (C3⋊#6157)⋊(C3×C13) |
| unambiguous semidirect product | (C3×C3⋊#6157)⋊C13 |
| Fitting, socle, Hall | C32×C53 ⋊ C4×C13 |
| derived | C3×C53 ⋊ C3×C4×C13 |
| Hall | C32×C53⋊C13 ⋊ C4 |
| Hall | C3×C3⋊#6157 ⋊ C13 |
| Hall | C53⋊C13 ⋊ C3×Dic3 |
| Sylow | C53 ⋊ C3×Dic3×C13 |
| Sylow | C32 ⋊ AGL(1,𝔽53) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊AGL(1,𝔽53) |
| commutator, hypocenter | C3×C53 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C53 | C4×C13 |
| prime radical | C32×D53⋊C13 | C2 |
| cosocle | C3×D53 | C2×C3×C13 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 318 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 96);