Finite Group DatabasebetaFinite Group Databasebeta| order | 24586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C2×C647⋊C19 |
| unambiguous semidirect product | (C2×C647)⋊C19 |
| Fitting, socle, Hall | C2×C647 ⋊ C19 |
| derived, Sylow | C647 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C647⋊C19 |
| commutator, cosocle, hypocenter | C647 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C647 | C19 |
| LCS | G ▷ C647 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1294 |
106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24586, 2);