Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#63914 |
| Sylow | C33 ⋊ #127 |
586 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590037, #13154979, #13155903, … |
| maximal normal subgroup of | C3×#10590037, #13154979, #13155903, … |
| maximal quotient of | C3×#10590352, C3×#10590354, C3×#10590353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3206);