Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #1356 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=g,c^2=f,d^2=e,e^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^23,c^b=cf,d^b=defg,e^b=eg,h^b=h^52,d^c=dg,h^d=h^52202 conjugacy classes — view the full character table.
| maximal subgroup of | #28299349, #28299350, #28299353, … |
| maximal normal subgroup of | #28299349, #28299350, #28299353, … |
| maximal quotient of | #28298216, #28298242, #28298681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19517);