Finite Group DatabasebetaFinite Group Databasebeta| order | 24492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×#10597845⋊C13 |
| unambiguous semidirect product | (C3×#10597845)⋊C13 |
| Fitting, socle, Hall | C3×C157 ⋊ C4×C13 |
| derived, Sylow | C157 ⋊ C3×C4×C13 |
| Hall | C3×C157⋊C13 ⋊ C4 |
| Hall | C157⋊C13 ⋊ C3×C4 |
| Hall | C3×#10597845 ⋊ C13 |
| Hall | #10597845 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10597845⋊C13 |
| commutator, hypocenter | C157 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C157 | C4×C13 |
| prime radical | C3×D157⋊C13 | C2 |
| cosocle | D157 | C2×C3×C13 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24492, 34);