Finite Group DatabasebetaFinite Group Databasebeta| order | 24492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C157⋊C3)⋊C13) |
| unambiguous semidirect product | (C22⋊(C157⋊C3))⋊C13 |
| unambiguous semidirect product | (C157⋊C13)⋊A4 |
| Fitting, socle, derived, Hall | C22×C157 ⋊ C3×C13 |
| Hall | C22×C157⋊C13 ⋊ C3 |
| Hall | C157⋊C13 ⋊ A4 |
| Hall | C22⋊(C157⋊C3) ⋊ C13 |
| Sylow | C157 ⋊ A4×C13 |
| Sylow | C22 ⋊ (C157⋊C3)⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C157 | C3×C13 |
| LCS | G ▷ C22×C157 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3,13,2^2,157|c^a=d,d^a=cd,e^a=e^12,e^b=e^13068 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24492, 37);