Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D53⋊(Q8⋊C8) |
| Sylow | C53 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^30,d^b=df,h^c=h^52,h^e=h^52316 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊C8×#6157, #28301633, #28301639, … |
| maximal normal subgroup of | Q8⋊C8×#6157, #28301633, #28301639, … |
| maximal quotient of | D53⋊#1271, D53⋊#1272, #28299418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19799);