Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#6233 |
| Fitting | C22×C32×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ D4 |
235 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88658, C3×#88662, C3×D9×#67, … |
| maximal normal subgroup of | C3×#88658, C3×#88662, C3×D9×#67, … |
| maximal quotient of | C3×#88534, C3×#88536, C3×#88543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 492);