Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#63964 |
| Sylow | C33 ⋊ C22⋊Q8 |
450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13171825, #13171834, #13171841, … |
| maximal normal subgroup of | #13171825, #13171834, #13171841, … |
| maximal quotient of | C3×#10591327, C3×#10591331, C3×#10591343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3256);