Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic18 |
| Sylow | C92 ⋊ Q8 |
75 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #13046366, #13046368, #13046369, … |
| maximal normal subgroup of | #13046366, #13046368, #13046369, … |
| maximal quotient of | C9×Dic9⋊C4, C9×C4⋊Dic9, C2×C9×Dic18, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 105);