Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 198 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=g,f^2=g,b^a=be,e^a=eg,h^a=h^30,f^b=fg,d^c=dg,h^f=h^52301 conjugacy classes — view the full character table.
| maximal subgroup of | #28311812, #28311814, #28311820, … |
| maximal normal subgroup of | #28311812, #28311814, #28311820, … |
| maximal quotient of | #28314000, #28314001, #28314003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21122);