Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C9⋊S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C9⋊S5 |
| unambiguous semidirect product | A5⋊D9 |
| Fitting | C9 ⋊ S5 |
| derived | C9×A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C9×A5 | C2 |
| Frattini | C3 | ΓL(2,𝔽4) |
| Fitting | C9 | S5 |
| socle | C3×A5 | D3 |
| LCS | G ▷ C9×A5 | |
| UCS | C1 | |
69 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Permutation generators:
(1,9,6,3,8,5,2,7,4)(10,14,13,12,11);(1,2)(4,7)(5,9)(6,8)(12,14)27 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 262);