Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#407 ⋊ C2 |
| Sylow | C53 ⋊ #1785 |
584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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,c^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27276583, #27276587, #27276589, … |
| maximal normal subgroup of | #27276583, #27276587, #27276589, … |
| maximal quotient of | #27275424, #27275428, #27275438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4436);