Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊(C9⋊C8) |
| Sylow | C3×C9 ⋊ C22⋊C8 |
172 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|b^2=c,c^2=e,f^3=h,b^a=bd,g^a=g^2,f^b=f^2h^2,h^b=h^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #13137114, #13137115, #13137116, … |
| maximal normal subgroup of | #13137114, #13137115, #13137116, … |
| maximal quotient of | #13134950, #13134951, #13134952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 260);