Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#63969 |
| Sylow | C33 ⋊ #123 |
466 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #13171735, #13171737, #13171738, … |
| maximal normal subgroup of | #13171735, #13171737, #13171738, … |
| maximal quotient of | C3×#10591373, C3×#10591296, C3×#10591299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3261);