Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#64153 |
| Sylow | C33 ⋊ C4⋊Q8 |
560 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589185, #13145688, #13145744, … |
| maximal normal subgroup of | C3×#10589185, #13145688, #13145744, … |
| maximal quotient of | C3×#10592672, C3×#10592674, C3×#10592675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3866);