Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#64265 |
233 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 233 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593223, C3×#10593226, C3×#10593232, … |
| maximal normal subgroup of | C3×#10593223, C3×#10593226, C3×#10593232, … |
| maximal quotient of | C3×#10593620, C3×#10593622, C3×C4⋊(C3⋊#226), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4425);