Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D45 |
| Fitting | C5×Q8×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C9 ⋊ Q8×D5 |
| Sylow | C5 ⋊ Q8×D9 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13084270, #13084275, #13084278, … |
| maximal normal subgroup of | #13084270, #13084275, #13084278, … |
| maximal quotient of | #13084535, #13084536, #13084537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 181);