Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #1338 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^52,c^b=ceg,d^b=dg766 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1338, C2×#20272697, #27293909, … |
| maximal normal subgroup of | D53×#1338, C2×#20272697, #27293909, … |
| maximal quotient of | #27270874, #27270904, #27271005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2492);