Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×C5×D9 |
| Fitting | C2×C4×C5×C9 ⋊ C2 |
| derived, Sylow | C9 ⋊ C22×C4×C5 |
| Hall | C5×C9 ⋊ C22×C4 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D9)⋊#168, C5×(C2×D9)⋊C8, C2×D9×#168, … |
| maximal normal subgroup of | (C2×D9)⋊#168, C5×(C2×D9)⋊C8, C2×D9×#168, … |
| maximal quotient of | C4×C5×Dic18, C42×C5×D9, C5×#63434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 166);