Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D32⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D32⋊D3 |
| Fitting | C33×C4 ⋊ D4 |
| Sylow | C33 ⋊ C4×D4 |
328 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | (D32⋊D3)⋊C8, #13165176, #13165177, … |
| maximal normal subgroup of | (D32⋊D3)⋊C8, #13165176, #13165177, … |
| maximal quotient of | C8×D32⋊D3, #13166910, #13166911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4279);