Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×D32×Q8 |
| Fitting | C33×Q8 ⋊ C22 |
| Sylow | C33 ⋊ C22×Q8 |
750 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593471, C3×#10593472, #13167248, … |
| maximal normal subgroup of | C3×#10593471, C3×#10593472, #13167248, … |
| maximal quotient of | C3×D3×#887, C3×#10594363, C3×D3×#896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4512);