Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic18 |
| Sylow | C32×C9 ⋊ Q8 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88416, C3×#88418, C3×#88423, … |
| maximal normal subgroup of | C3×#88416, C3×#88418, C3×#88423, … |
| maximal quotient of | C32×Dic9⋊C4, C32×C4⋊Dic9, C2×C32×Dic18, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 439);