Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4×C5×C3⋊D3 |
| Fitting | C2×C32×C4×C5 ⋊ C2 |
| derived, Sylow | C32 ⋊ C22×C4×C5 |
| Hall | C32×C5 ⋊ C22×C4 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #13084724, C5×#63557, #13084890, … |
| maximal normal subgroup of | #13084724, C5×#63557, #13084890, … |
| maximal quotient of | C4×C5×#634, C42×C5×C3⋊D3, C5×#64081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 740);