Finite Group DatabasebetaFinite Group Databasebeta| order | 24586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D647⋊C19 |
| unambiguous semidirect product | (C647⋊C19)⋊C2 |
| Fitting, socle, derived, Sylow | C647 ⋊ C2×C19 |
| Hall | C647⋊C19 ⋊ C2 |
| Hall | D647 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C647 | C2×C19 |
| LCS | G ▷ C647 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 647 |
Polycyclic presentation:
2,19,647|c^a=c^646,c^b=c^10455 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24586, 1);