Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C9×#67 |
| Fitting | C22×C32×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ D4 |
235 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88663, C3×#88662, C9×#3804, … |
| maximal normal subgroup of | C3×#88663, C3×#88662, C9×#3804, … |
| maximal quotient of | C3×C9×Dic3⋊C4, C3×C9×(C2×D3)⋊C4, C3×C9×#213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 460);