Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #6652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#6661 |
| Hall | C32×C5 ⋊ Q16 |
| Sylow | C32 ⋊ #689 |
| Sylow | C5 ⋊ C3×#216 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6661, #13085708, #13085710, … |
| maximal normal subgroup of | D3×#6661, #13085708, #13085710, … |
| maximal quotient of | C3×#90970, C3×#90972, C3×#90989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 210);