Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #64155⋊C3 |
| Fitting | C2×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C22⋊Q8 |
297 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 297 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,c^a=ce,g^a=g^2,h^a=h^2,c^b=cf,g^d=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13140907, #13140908, #13140909, … |
| maximal normal subgroup of | #13140907, #13140908, #13140909, … |
| maximal quotient of | #10592677⋊C3, #10592671⋊C3, #10592681⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1639);