Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×Dic18 |
| unambiguous semidirect product | (C2×C9)⋊(C5×Q8) |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C9 ⋊ C2×C5×Q8 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | #13083719, #13083727, #13083740, … |
| maximal normal subgroup of | #13083719, #13083727, #13083740, … |
| maximal quotient of | C4×C5×Dic18, C5×#63431, C5×#63432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 165);