Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D53⋊#430 |
| Sylow | C53 ⋊ C2×#430 |
460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 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,b^2=e,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^30,c^b=cg,h^d=h^52,h^f=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306991, #28306995, #28307004, … |
| maximal normal subgroup of | #28306991, #28306995, #28307004, … |
| maximal quotient of | D53⋊#1565, #28316087, #28316089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21170);