Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #6654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#6663 |
| Hall | C32×C5 ⋊ Q16 |
| Sylow | C32 ⋊ #689 |
| Sylow | C5 ⋊ C3×Dic12 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6663, #13085714, #13085715, … |
| maximal normal subgroup of | D3×#6663, #13085714, #13085715, … |
| maximal quotient of | C3×#90973, C3×#90975, C3×#90988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 212);