Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#14583754⋊C3) |
| unambiguous semidirect product | (C3⋊#14583754)⋊C3 |
| Fitting, socle, derived | C3×C13×C53 ⋊ C3×C4 |
| Hall | C3×C13⋊C3×C53 ⋊ C4 |
| Hall | C13×C53 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ Dic53 |
| Sylow | C53 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×Dic159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C53 | C3×C4 |
| prime radical | C3×C53×D13⋊C3 | C2 |
| cosocle | C3×D13×C53 | C2×C3 |
| LCS | G ▷ C3×C13×C53 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2067 |
Polycyclic presentation:
2,3,2,3,13,53|a^2=c,d^a=d^2,e^a=e^5,f^a=f^52,e^b=e^3,e^c=e^12645 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 120);