Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3387 |
326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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=eg,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^52,f^c=fg757 conjugacy classes — view the full character table.
| maximal subgroup of | #27373649, #27373651, #27373664, … |
| maximal normal subgroup of | #27373649, #27373651, #27373664, … |
| maximal quotient of | #27400737, #27400748, #27402410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17440);