Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#63647 |
| Fitting | C2×C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ C22⋊C8 |
388 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590643, C3×#10590665, C3×#10590686, … |
| maximal normal subgroup of | C3×#10590643, C3×#10590665, C3×#10590686, … |
| maximal quotient of | C3×#10589325, C3×#10589322, C3×#10589334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2116);