Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3237 |
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 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|a^2=g,b^2=e,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^52,c^b=ceg,f^c=fg754 conjugacy classes — view the full character table.
| maximal subgroup of | #27281342, #27281344, #27285124, … |
| maximal normal subgroup of | #27281342, #27281344, #27285124, … |
| maximal quotient of | #27393615, #27393855, #27394665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15724);