Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#823 |
| Fitting | C33×M16 ⋊ C2 |
| Sylow | C33 ⋊ #100 |
356 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590987, C3×#10590989, C3×#10590997, … |
| maximal normal subgroup of | C3×#10590987, C3×#10590989, C3×#10590997, … |
| maximal quotient of | C32×#4464, C32×#4468, C32×#4485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2078);