Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D9×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | D9×A5 |
| unambiguous semidirect product | C9⋊(C2×A5) |
| Fitting | C9 ⋊ C2×A5 |
| derived | C9×A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C9×A5 | C2 |
| Frattini | C3 | D3×A5 |
| Fitting, cosocle | C9 | C2×A5 |
| socle | C3×A5 | D3 |
| LCS | G ▷ C9×A5 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 45 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | A5×SL(2,𝔽8) |
| maximal quotient of | D9×SL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 263);