Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2083 |
230 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 93 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=e,b^2=d,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,f^c=fg,h^c=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27273128, #27273130, #27273135, … |
| maximal normal subgroup of | #27273128, #27273130, #27273135, … |
| maximal quotient of | #27288998, #27289003, #27289018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5981);