Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1319 |
134 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 34 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=d,b^2=g,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^30,c^b=cg,d^b=deg,h^b=h^52,d^c=dg,h^d=h^52442 conjugacy classes — view the full character table.
| maximal subgroup of | #28299027, #28299028, #28299029, … |
| maximal normal subgroup of | #28299027, #28299028, #28299029, … |
| maximal quotient of | #28298099, #28298107, #28298190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19441);