Finite Group DatabasebetaFinite Group Databasebeta| order | 24492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22551027 |
| Fitting, socle, derived, Hall | C3×C13×C157 ⋊ C4 |
| Hall | C13×C157 ⋊ Dic3 |
| Hall | C3×C157 ⋊ #261 |
| Sylow | C157 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ #10597845 |
| Sylow | C13 ⋊ C3⋊#10597845 |
| Sylow | C3 ⋊ #22551027 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C157 | C4 |
| prime radical, cosocle | C3×D2041 | C2 |
| LCS | G ▷ C3×C13×C157 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13,157|a^2=b,c^a=c^2,d^a=d^5,e^a=e^129,d^b=d^12,e^b=e^1561536 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24492, 95);