Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1849 |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,b^2=d,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cg,h^b=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27271515, #27278480, #27278481, … |
| maximal normal subgroup of | #27271515, #27278480, #27278481, … |
| maximal quotient of | #27277839, #27277842, #27277844, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4684);