Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #1738 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^30,h^f=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306529, #28306531, #28306532, … |
| maximal normal subgroup of | #28306529, #28306531, #28306532, … |
| maximal quotient of | #28300171, #28300174, #28300181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20203);