Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #108 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=c,c^2=e,d^2=e,f^3=h,b^a=bd,f^a=f^2h^2,g^a=g^2,h^a=h^2,d^b=de144 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#822, #13139069, D3×#63381, … |
| maximal normal subgroup of | D9×#822, #13139069, D3×#63381, … |
| maximal quotient of | #13135786, #13135787, #13135935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 522);