Unrealistic coefficients when comparing two count samples with glm poisson

Unrealistic coefficients when comparing two count samples with glm poisson

I would like to test the significance of the difference in mean between two independent count samples. I'm doing this with a GLM poisson in R, as shown in the code below:

a=c(0,0,0,0,0,0,0,0,0,0)
b=c(1,2,0,1,1,2,0,1,0,2)

c=data.frame(sp=c(a,b),grp=c(rep('A',10),rep('B',10)))

summary(glm(sp~grp,data=c,family=poisson))

Call:
glm(formula = sp ~ grp, family = poisson, data = c)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-1.41421  -0.00006  -0.00006   0.00000   0.87897  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)    -20.3     4914.8  -0.004    0.997
grpB            20.3     4914.8   0.004    0.997

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 22.1807  on 19  degrees of freedom
Residual deviance:  8.3178  on 18  degrees of freedom
AIC: 28.159

Number of Fisher Scoring iterations: 18

As you can see, the coefficient values are not reflecting reality. I noticed that this happened because group "A" has mean=0. In this way, I would like to know if there is any way to fix this problem in glm, or if there is any other better method to test my hypothesis.