Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×(C22⋊C9)⋊Q8 |
163 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #13146263, #13146269, #13146273, … |
| maximal normal subgroup of | #13146263, #13146269, #13146273, … |
| maximal quotient of | C3×#10589488, C3×#10589491, C3×#10589493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2301);