Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C53 ⋊ C4 |
| Sylow | C53 ⋊ AGL(1,ℤ/16) |
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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=e,c^2=efg,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^30,d^b=dfg,e^b=eg,f^b=fg,d^c=dg,h^c=h^23,h^e=h^52166 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20291125, D53⋊AGL(1,ℤ/16), #28328405, … |
| maximal normal subgroup of | C2×#20291125, D53⋊AGL(1,ℤ/16), #28328405, … |
| maximal quotient of | #28310057, #28310059, #28310067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20920);