Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3×C9 ⋊ SD32 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=cde,c^2=de,d^2=e,f^3=h,b^a=bc,c^a=cd,d^a=de,g^a=g^2,f^b=f^2h^2,h^b=h^287 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#800, #13136978, #13136990, … |
| maximal normal subgroup of | D9×#800, #13136978, #13136990, … |
| maximal quotient of | #13134995, #13134998, #13135055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 210);