Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #1373 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^521708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271554, #27271555, #27271557, … |
| maximal normal subgroup of | #27271554, #27271555, #27271557, … |
| maximal quotient of | #27270832, #27270834, #27270976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2586);