Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D5×Dic18 |
| unambiguous semidirect product | (C9×D5)⋊Q8 |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C9 ⋊ Q8×D5 |
| Sylow | C5 ⋊ C2×Dic18 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13083917, #13083920, D5×Dic36, … |
| maximal normal subgroup of | #13083917, #13083920, D5×Dic36, … |
| maximal quotient of | Dic5×Dic18, #13084067, #13084068, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 129);