Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C9 | A5 |
| commutator, hypocenter | A5 | C2×C9 |
| Frattini, cosocle | C3 | C2×C3×A5 |
| socle, prime radical | C2×C3×A5 | C3 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C2×C9 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 264);