Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic90 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic90 |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C9 ⋊ C2×Dic10 |
| Sylow | C5 ⋊ C2×Dic18 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | #13083720, #13083728, #13083741, … |
| maximal normal subgroup of | #13083720, #13083728, #13083741, … |
| maximal quotient of | C4×Dic90, #13084517, #13084518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 175);