Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63653 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#63653 |
| Fitting | C33×D8 ⋊ C2 |
| Sylow | C33 ⋊ D16 |
256 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 256 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) = 144 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#826, C3×#10591024, C3×#10591033, … |
| maximal normal subgroup of | C3×D3×#826, C3×#10591024, C3×#10591033, … |
| maximal quotient of | C3×#10589355, C3×#10589357, C3×#10589385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2122);