Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1413 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=f,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cf,d^b=def,e^b=eg,h^b=h^52,d^c=dfg,e^d=eg352 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1413, C2×#20272887, #27304450, … |
| maximal normal subgroup of | D53×#1413, C2×#20272887, #27304450, … |
| maximal quotient of | #27271482, #27271500, #27271631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2682);