Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×3−1+2 |
| unambiguous semidirect product | C5⋊(C22×3−1+2) |
| unambiguous semidirect product | (C2×C5)⋊(C2×3−1+2) |
| unambiguous semidirect product | (C2×C9×D5)⋊C3 |
| Fitting | C2×C5×3−1+2 ⋊ C2 |
| Hall | C5×3−1+2 ⋊ C22 |
| Sylow | C5 ⋊ C22×3−1+2 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×3−1+2⋊C4, #67082⋊C3, #67083⋊C3, … |
| maximal normal subgroup of | D5×3−1+2⋊C4, #67082⋊C3, #67083⋊C3, … |
| maximal quotient of | 3−1+2×Dic10, C4×D5×3−1+2, 3−1+2×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 64);