Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #2255 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,c^b=cg,h^c=h^52598 conjugacy classes — view the full character table.
| maximal subgroup of | #27298096, #27298097, #27298103, … |
| maximal normal subgroup of | #27298096, #27298097, #27298103, … |
| maximal quotient of | #27300538, #27302129, #27302134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6797);