Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #131 |
206 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 63 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:
2^5,3^3|c^2=d,d^2=e,f^3=h,b^a=be,g^a=g^2,c^b=ce,f^b=f^2h^2,h^b=h^2126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63464, #13149745, #13149748, … |
| maximal normal subgroup of | D3×#63464, #13149745, #13149748, … |
| maximal quotient of | #13138113, #13138116, #13138121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 775);