Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#836 |
| Sylow | C33 ⋊ #101 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10589182, C3×#10589183, C3×#10589184, … |
| maximal normal subgroup of | C3×#10589182, C3×#10589183, C3×#10589184, … |
| maximal quotient of | C32×#4528, C32×#4530, C32×#4543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2091);