Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×D32⋊C8 |
| unambiguous semidirect product | D32⋊(C3×C8) |
| Sylow | C33 ⋊ C22⋊C8 |
200 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D32⋊C8, #13165143, #13165144, … |
| maximal normal subgroup of | D3×D32⋊C8, #13165143, #13165144, … |
| maximal quotient of | C3×D32⋊C16, C3×#10590013, C3×#10590014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2700);