Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#914 |
| Fitting | C33×SD16 ⋊ C2 |
| Sylow | C33 ⋊ AGL(1,ℤ/8) |
488 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#914, C3×#10594740, C3×#10594744, … |
| maximal normal subgroup of | C3×D3×#914, C3×#10594740, C3×#10594744, … |
| maximal quotient of | C32×#4786, C32×#4764, C32×#4766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3750);