Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3160 |
356 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 157 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=e,c^2=f,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27279405, #27279406, #27279408, … |
| maximal normal subgroup of | #27279405, #27279406, #27279408, … |
| maximal quotient of | #27384503, #27387422, #27388652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15020);