Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic5×3−1+2 |
| unambiguous semidirect product | (C9×Dic5)⋊C3 |
| Hall | C5×3−1+2 ⋊ C4 |
| Sylow | C5 ⋊ C4×3−1+2 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×#170, 3−1+2⋊#170, #67077⋊C3, … |
| maximal normal subgroup of | 3−1+2×#170, 3−1+2⋊#170, #67077⋊C3, … |
| maximal quotient of | 3−1+2×#168, C2×Dic5×3−1+2, Dic5×C32⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 15);