Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic18⋊C9 |
| unambiguous semidirect product | (C9⋊C9)⋊Q8 |
| Sylow | C9⋊C9 ⋊ Q8 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3^3|a^2=d,b^2=d,c^3=e,f^3=g,b^a=bd,f^a=f^2g^2,g^a=g^2,f^c=fg^293 conjugacy classes — view the full character table.
| maximal subgroup of | Dic36⋊C9, #3664⋊C9, #3672⋊C9, … |
| maximal normal subgroup of | Dic36⋊C9, #3664⋊C9, #3672⋊C9, … |
| maximal quotient of | (Dic9⋊C4)⋊C9, C4⋊(Dic9⋊C9), C2×Dic18⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 114);