Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| direct product | C9×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C9 | A5 |
| commutator, hypocenter | A5 | C9 |
| Frattini, cosocle | C3 | C3×A5 |
| socle, prime radical | C3×A5 | C3 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C9 | |
33 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
45 conjugacy classes — view the full character table.
| derived subgroup of | C9⋊S5, D9×A5 |
| maximal subgroup of | C9×S5, C9⋊S5, D9×A5, … |
| maximal normal subgroup of | C9×S5, C9⋊S5, D9×A5, … |
| maximal quotient of | C9×SL(2,𝔽5), C2×C9×A5, C27×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 31);