Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×D3×Q16 |
| Fitting | C33×Q16 ⋊ C2 |
| Sylow | C33 ⋊ C2×Q16 |
432 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#828, C3×D3×#829, C3×#10591045, … |
| maximal normal subgroup of | C3×D3×#828, C3×D3×#829, C3×#10591045, … |
| maximal quotient of | C32×#4792, C32×#4793, C32×#4795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3753);