Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1945 |
208 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,b^2=f,c^2=e,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27300709, #27300710, #27300793, … |
| maximal normal subgroup of | #27300709, #27300710, #27300793, … |
| maximal quotient of | #27282627, #27282632, #27282657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5256);