Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊AGL(1,𝔽53) |
| unambiguous semidirect product | (C9⋊#6157)⋊C13 |
| Fitting, derived, Hall | C9×C53 ⋊ C4×C13 |
| Hall | C9×C53⋊C13 ⋊ C4 |
| Hall | C9⋊#6157 ⋊ C13 |
| Hall | C53⋊C13 ⋊ Dic9 |
| Sylow | C53 ⋊ C13×Dic9 |
| Sylow | C9 ⋊ AGL(1,𝔽53) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C53 | C4×C13 |
| Frattini | C3 | C3⋊AGL(1,𝔽53) |
| socle | C3×C53 | Dic3×C13 |
| prime radical | C3×D53⋊C13 | D3 |
| cosocle | C9×D53 | C2×C13 |
| LCS | G ▷ C9×C53 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 477 |
Polycyclic presentation:
2,13,2,3,53,3|a^2=c,d^3=f^2,d^a=d^2f,e^a=e^30,f^a=f^2,e^b=e^16,e^c=e^52165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 19);