Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×Dic3×#67 |
| Sylow | C33 ⋊ C4×D4 |
550 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#3804, Dic3×#3805, #13171735, … |
| maximal normal subgroup of | Dic3×#3804, Dic3×#3805, #13171735, … |
| maximal quotient of | C3×Dic3×Dic3⋊C4, C3×#10591262, C3×#10591305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3264);