Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D53⋊#421 |
| Fitting | C2×#41×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^30,e^b=eg,h^d=h^52,h^f=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306621, #28306623, #28306627, … |
| maximal normal subgroup of | #28306621, #28306623, #28306627, … |
| maximal quotient of | D53⋊#1478, D53⋊#1479, D53⋊#1477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21137);