Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C9×#638 |
| Fitting | C22×C32×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ D4 |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#3804, D3×C9×#67, #13048697, … |
| maximal normal subgroup of | C9×#3804, D3×C9×#67, #13048697, … |
| maximal quotient of | C9×#3750, C9×#3752, C9×#3753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 493);