Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #121×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1874 |
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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=f,b^2=dfg,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^23,d^b=dg,f^b=fg,h^b=h^30,h^f=h^52220 conjugacy classes — view the full character table.
| maximal subgroup of | #28302502, #28302503, #28302506, … |
| maximal normal subgroup of | #28302502, #28302503, #28302506, … |
| maximal quotient of | #28303892, #28303893, #28303894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20497);