Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#64224 |
| Sylow | C33 ⋊ AGL(1,ℤ/8) |
262 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #13165226, #13165227, #13165232, … |
| maximal normal subgroup of | #13165226, #13165227, #13165232, … |
| maximal quotient of | C3×#10593351, C3×#10593356, C3×#10593360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4246);