Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#64157 |
| Sylow | C33 ⋊ #131 |
532 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590221, #13157238, C3×#10591675, … |
| maximal normal subgroup of | C3×#10590221, #13157238, C3×#10591675, … |
| maximal quotient of | C3×#10592696, C3×#10592698, C3×#10592699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3870);