Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C27 ⋊ C4⋊Q8 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=d,c^2=d,f^3=g,g^3=h,c^a=ce,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=cd144 conjugacy classes — view the full character table.
| maximal subgroup of | #13133973, #13134257, #13134293, … |
| maximal normal subgroup of | #13133973, #13134257, #13134293, … |
| maximal quotient of | #13134477, #13134479, #13134480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 160);