Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3105 |
454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^d=h^52532 conjugacy classes — view the full character table.
| maximal subgroup of | #27356415, #27356417, #27356437, … |
| maximal normal subgroup of | #27356415, #27356417, #27356437, … |
| maximal quotient of | #27384092, #27387024, #27387072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14552);