Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C32×#638 |
| Fitting | C22×C34 ⋊ C2 |
| Sylow | C34 ⋊ D4 |
728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#3804, C32×D3×#67, C3×#89031, … |
| maximal normal subgroup of | C32×#3804, C32×D3×#67, C3×#89031, … |
| maximal quotient of | C32×#3750, C32×#3752, C32×#3753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 688);