Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1848 |
220 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,b^2=d,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^30,h^b=h^52,h^f=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298693, #28298708, #28298712, … |
| maximal normal subgroup of | #28298693, #28298708, #28298712, … |
| maximal quotient of | #28303579, #28303580, #28303586, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20451);