Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D9×Dic10 |
| unambiguous semidirect product | (C5×D9)⋊Q8 |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C9 ⋊ C2×Dic10 |
| Sylow | C5 ⋊ Q8×D9 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#677, #13084029, D9×Dic20, … |
| maximal normal subgroup of | D9×#677, #13084029, D9×Dic20, … |
| maximal quotient of | Dic9×Dic10, #13084074, #13084076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 125);