Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3117 |
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^c=dg,f^c=fg,h^d=h^52526 conjugacy classes — view the full character table.
| maximal subgroup of | #27356684, #27356686, #27356706, … |
| maximal normal subgroup of | #27356684, #27356686, #27356706, … |
| maximal quotient of | #27384152, #27387131, #27387150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14676);