Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×GO+(4,𝔽2)⋊C4 |
| unambiguous semidirect product | GO+(4,𝔽2)⋊(C3×C4) |
| Sylow | C33 ⋊ #102 |
142 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×GO+(4,𝔽2)⋊C4, #89091⋊C4, #13180142, … |
| maximal normal subgroup of | D3×GO+(4,𝔽2)⋊C4, #89091⋊C4, #13180142, … |
| maximal quotient of | C3×GO+(4,𝔽2)⋊C8, C3×#10593155, C3×#10593156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4062);