Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C3⋊AGL(1,𝔽13) |
| unambiguous semidirect product | C3⋊(C53×AGL(1,𝔽13)) |
| unambiguous semidirect product | (C3⋊#261)⋊(C3×C53) |
| unambiguous semidirect product | (C53×C3⋊#261)⋊C3 |
| Fitting, socle | C3×C13×C53 ⋊ C3×C4 |
| derived | C3×C13 ⋊ C3×C4×C53 |
| Hall | C3×C13⋊C3×C53 ⋊ C4 |
| Hall | C13×C53 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ C4×C53 |
| Sylow | C13 ⋊ C3×Dic3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C3⋊AGL(1,𝔽13) |
| commutator, hypocenter | C3×C13 | C3×C4×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C53 | C3×C4 |
| prime radical | C3×C53×D13⋊C3 | C2 |
| cosocle | C3×D13 | C2×C3×C53 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C53 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2067 |
1113 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 117);