Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊AGL(1,𝔽53)) |
| unambiguous semidirect product | (C3⋊(C3⋊#6157))⋊C13 |
| Fitting, socle, derived, Hall | C32×C53 ⋊ C4×C13 |
| Hall | C32×C53⋊C13 ⋊ C4 |
| Hall | C3⋊(C3⋊#6157) ⋊ C13 |
| Hall | C53⋊C13 ⋊ C3⋊Dic3 |
| Sylow | C53 ⋊ C13×C3⋊Dic3 |
| Sylow | C32 ⋊ AGL(1,𝔽53) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C53 | C4×C13 |
| prime radical | C32×D53⋊C13 | C2 |
| cosocle | C32×D53 | C2×C13 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 477 |
Polycyclic presentation:
2,13,2,3^2,53|a^2=c,d^a=d^2,e^a=e^2,f^a=f^30,f^b=f^16,f^c=f^52165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 101);