Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#63633 |
| Fitting | C33×C22⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ #99 |
448 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#806, C3×#10590405, C3×#10590407, … |
| maximal normal subgroup of | C3×D3×#806, C3×#10590405, C3×#10590407, … |
| maximal quotient of | C3×#10589317, C3×#10589318, C3×#10589334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2102);