Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D53⋊#356 |
| Sylow | C53 ⋊ C2×#356 |
240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 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,b^2=g,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^30,d^b=dg,e^b=efg,h^c=h^52,e^d=eg,h^e=h^52208 conjugacy classes — view the full character table.
| maximal subgroup of | #28299215, #28299247, #28299275, … |
| maximal normal subgroup of | #28299215, #28299247, #28299275, … |
| maximal quotient of | D53⋊#1319, D53⋊#1325, #28308080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20799);