Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#896 |
| Fitting | C33×C4⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ C22⋊Q8 |
548 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#896, C3×#10594615, C3×#10594365, … |
| maximal normal subgroup of | C3×D3×#896, C3×#10594615, C3×#10594365, … |
| maximal quotient of | C32×#4667, C32×#4646, C32×#4652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3732);