Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×3−1+2⋊C4 |
| unambiguous semidirect product | 3−1+2⋊(C4×C5) |
| unambiguous semidirect product | Dic9⋊(C3×C5) |
| unambiguous semidirect product | (C5×Dic9)⋊C3 |
| derived | C9 ⋊ C3×C4×C5 |
| Hall | C5×3−1+2 ⋊ C4 |
| Sylow | 3−1+2 ⋊ C4×C5 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #67077⋊C3, #67079⋊C3, D5×3−1+2⋊C4, … |
| maximal normal subgroup of | #67077⋊C3, #67079⋊C3, D5×3−1+2⋊C4, … |
| maximal quotient of | C5×3−1+2⋊C8, C2×C5×3−1+2⋊C4, C5×#66316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 19);