Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #1422 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^30,h^b=h^52,h^d=h^52472 conjugacy classes — view the full character table.
| maximal subgroup of | #28299123, #28299124, #28299125, … |
| maximal normal subgroup of | #28299123, #28299124, #28299125, … |
| maximal quotient of | #28299136, #28299144, #28299166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19670);