Finite Group DatabasebetaFinite Group Databasebeta| order | 24609 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C631⋊C3 |
| unambiguous semidirect product | C631⋊(C3×C13) |
| Fitting, socle, Hall | C13×C631 ⋊ C3 |
| derived, Sylow | C631 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C631⋊C3 |
| commutator, cosocle, hypocenter | C631 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C631 | C3 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8203 |
2769 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24609, 2);