Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#63955 |
| Sylow | C33 ⋊ #117 |
458 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #13156979, #13156981, C3×#10590405, … |
| maximal normal subgroup of | #13156979, #13156981, C3×#10590405, … |
| maximal quotient of | C3×#10591223, C3×#10591053, C3×#10591056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3247);