Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×Q8×C22⋊C9 |
| Sylow | C22×Q8 ⋊ C3×C9 |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589518, C3×#10589519, #13147051, … |
| maximal normal subgroup of | C3×#10589518, C3×#10589519, #13147051, … |
| maximal quotient of | C3×C4⋊C4×C22⋊C9, C3×#557⋊C9, C3×Q8×Q8⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2534);