Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1321 |
112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^30,c^b=cg,d^b=deg,h^b=h^52,d^c=dg,h^d=h^52442 conjugacy classes — view the full character table.
| maximal subgroup of | #28299015, #28299016, #28299017, … |
| maximal normal subgroup of | #28299015, #28299016, #28299017, … |
| maximal quotient of | #28298097, #28298099, #28298101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19445);