Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1322 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^30,d^b=de,h^d=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298096, #28298097, #28298098, … |
| maximal normal subgroup of | #28298096, #28298097, #28298098, … |
| maximal quotient of | #28298108, #28298110, #28298112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19446);