Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#469 ⋊ C2 |
| Sylow | C53 ⋊ #3309 |
404 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^52,h^d=h^52445 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3309, C2×#20286716, #28260850, … |
| maximal normal subgroup of | D53×#3309, C2×#20286716, #28260850, … |
| maximal quotient of | #27399612, #27400480, #27401221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16511);