Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | Q8×C9×D5 |
| Fitting | C5×Q8×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C5 ⋊ C2×Q8×C9 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#4009, #13083998, D5×#3674, … |
| maximal normal subgroup of | C9×#4009, #13083998, D5×#3674, … |
| maximal quotient of | C9×#4033, C9×#4042, C9×#4034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 161);