Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#14583752) |
| Fitting, socle, derived, Hall | C32×C13×C53 ⋊ C4 |
| Hall | C13×C53 ⋊ C3⋊Dic3 |
| Hall | C32×C53 ⋊ #261 |
| Hall | C32×C13 ⋊ #6157 |
| Sylow | C53 ⋊ C3⋊(C3⋊#261) |
| Sylow | C13 ⋊ C3⋊(C3⋊#6157) |
| Sylow | C32 ⋊ #14583752 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13×C53 | C4 |
| prime radical, cosocle | C32×D689 | C2 |
| LCS | G ▷ C32×C13×C53 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6201 |
Polycyclic presentation:
2^2,3^2,13,53|a^2=b,c^a=c^2,d^a=d^2,e^a=e^5,f^a=f^30,e^b=e^12,f^b=f^521560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 179);