Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #63508⋊C3 |
| Fitting | C2×Q8×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C22⋊Q8 |
241 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^3,3,2^2,3^2|b^2=f,c^2=f,g^3=h,c^a=ce,g^a=g^2h^2,h^a=h^2,c^b=cf,g^d=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #10588485⋊C3, #10588487⋊C3, #10588491⋊C3, … |
| maximal normal subgroup of | #10588485⋊C3, #10588487⋊C3, #10588491⋊C3, … |
| maximal quotient of | #10588658⋊C3, #10588652⋊C3, #10588662⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1646);