Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2061 |
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=d,b^2=d,c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,h^b=h^52,e^c=eg,h^c=h^52754 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2061, C2×#20276064, #27412201, … |
| maximal normal subgroup of | D53×#2061, C2×#20276064, #27412201, … |
| maximal quotient of | #27288499, #27288504, #27288514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5859);