Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #2166 |
122 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^30,c^b=cg,e^b=eg,e^c=eg,h^c=h^52,h^e=h^52448 conjugacy classes — view the full character table.
| maximal subgroup of | #28298594, #28298595, #28298597, … |
| maximal normal subgroup of | #28298594, #28298595, #28298597, … |
| maximal quotient of | #28310449, #28310511, #28310768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20884);