Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | Q8×C3⋊D15 |
| Fitting | C32×C5×Q8 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×Q8 |
| Sylow | C32 ⋊ Q8×D5 |
| Sylow | C5 ⋊ Q8×C3⋊D3 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13086387, #13086988, #13086994, … |
| maximal normal subgroup of | #13086387, #13086988, #13086994, … |
| maximal quotient of | #13088156, #13088157, #13088158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 755);