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^30,h^b=h^52,h^d=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28299123, #28299124, #28299125, … |
| maximal normal subgroup of | #28299123, #28299124, #28299125, … |
| maximal quotient of | #28298182, #28298184, #28298325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19546);