Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| unambiguous semidirect product | D53⋊#410 |
| Fitting | C2×#41×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#410 |
788 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,c^2=g,b^a=be,e^a=eg,h^a=h^30,f^b=fg,h^d=h^52,h^f=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306523, #28306525, #28306542, … |
| maximal normal subgroup of | #28306523, #28306525, #28306542, … |
| maximal quotient of | D53⋊#1458, D53⋊#1460, D53⋊#1461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21106);