Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×#634 |
| 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 | C9×#3716, C9×#3719, #13047659, … |
| maximal normal subgroup of | C9×#3716, C9×#3719, #13047659, … |
| maximal quotient of | C9×#3750, C9×C4⋊(C3⋊Dic3), C2×C9×#634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 470);