Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×A4⋊Q8 |
| unambiguous semidirect product | A4⋊(C32×Q8) |
300 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593178, C3×#10593180, C3×#10593185, … |
| maximal normal subgroup of | C3×#10593178, C3×#10593180, C3×#10593185, … |
| maximal quotient of | C32×#5386, C32×#5389, C32×#5391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4408);