Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C3×C42×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #126 |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=d,c^2=e,f^3=h,b^a=be,c^a=cde,f^a=f^2h^2,g^a=g^2,h^a=h^2222 conjugacy classes — view the full character table.
| maximal subgroup of | #13147505, #13147508, #13147514, … |
| maximal normal subgroup of | #13147505, #13147508, #13147514, … |
| maximal quotient of | #13143689, #13143691, #13143693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1680);