Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3229 |
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 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|a^2=g,b^2=e,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^52,f^c=fg526 conjugacy classes — view the full character table.
| maximal subgroup of | #27358141, #27358143, #27358155, … |
| maximal normal subgroup of | #27358141, #27358143, #27358155, … |
| maximal quotient of | #27393572, #27393771, #27394603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15652);