How to run Cox proportional Hazard model for each group in R?
The fact that you supplied GROUP as a covariate, you are getting 9 coefficients as one of the ten levels is used as the reference level.

If you would like to fit one model per group (and in this scenario you would not be correcting for GROUP), you should first split your data frame and fit your models on the resulting list's elements:

lapply(split(DF, DF$GROUP),
       function(x) coxph(serve_object ~ age + Smoking + Diabetes, data = DF))


Example with the mtcars data set when grouped by number of cylinders, cyl having values of 4, 6 or 8:

&gt; lapply(split(mtcars, mtcars$cyl),
+        function(x) lm(disp ~ hp, data = x))
$`4`

Call:
lm(formula = disp ~ hp, data = x)

Coefficients:
(Intercept)           hp  
    59.0369       0.5579  


$`6`

Call:
lm(formula = disp ~ hp, data = x)

Coefficients:
(Intercept)           hp  
   290.9178      -0.8799  


$`8`

Call:
lm(formula = disp ~ hp, data = x)

Coefficients:
(Intercept)           hp  
   320.2083       0.1572