Finite Group DatabasebetaFinite Group Databasebeta| order | 24492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#10597845⋊C13) |
| unambiguous semidirect product | (C3⋊#10597845)⋊C13 |
| Fitting, socle, derived, Hall | C3×C157 ⋊ C4×C13 |
| Hall | C3×C157⋊C13 ⋊ C4 |
| Hall | C157⋊C13 ⋊ Dic3 |
| Hall | C3⋊#10597845 ⋊ C13 |
| Sylow | C157 ⋊ Dic3×C13 |
| Sylow | C3 ⋊ #10597845⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C157 | C4×C13 |
| prime radical | C3×D157⋊C13 | C2 |
| cosocle | C3×D157 | C2×C13 |
| LCS | G ▷ C3×C157 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,2,3,157|a^2=c,d^a=d^2,e^a=e^28,e^b=e^130,e^c=e^15687 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24492, 35);