Finite Group DatabasebetaFinite Group Databasebeta| order | 24531 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17×C37 · Schur multiplier (H2) = C1 |
| direct product | C17×C37×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C17×C37) |
| unambiguous semidirect product | (C13×C17)⋊(C3×C37) |
| Fitting, socle, Hall | C13×C17×C37 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C17×C37 |
| Hall | C13×C37 ⋊ C3×C17 |
| Hall | C13×C17 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C37 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C17×C37 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C37 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C17×C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8177 |
4403 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24531, 3);