I have generated counts using featurecounts for each sample (replicate) of each group and then merged it which looks like the following

Gene_id A_1  A_2  A_3  B_1  B_2  B_3  C_1  C_2  C_3  C_4  B_4  C_5  D_1  D_2  D_3  B_5 
gene1    1     2    3   4    5    6    7    8    9    1    2    3     4    5    6   7 
gene2    9     8    7   6    5    4    3    2    1    2    3    4     5    6    7   8  
..... 
...... 
geneN    8    1    7   6     5    3    3    2    1    2    5    4     5    7    6   1  

I need to do the differential gene expression analysis of groups A-B, A-C, and A-D. My EdgeR script looks like this

df <- read.table("count.txt", header=TRUE, row.names = 1)
group <- factor(c("A", "A", "A", "B", "B", "B", "C", "C", "C", "C", "B", "C", "D", "D", "D", "B"))
group <- relevel(group, ref="A")
dgList <- DGEList(counts=df, group=group)
dgList <- calcNormFactors(dgList)
dgList <- estimateCommonDisp(dgList,verbose=TRUE)
dgList <- estimateGLMTagwiseDisp(dgList)
design = model.matrix(~group)
fit <- glmFit(dgList, design)

for (x in 2:4) { 
  lrt <- glmLRT(fit, coef=x)
  edgeR_result <- topTags(lrt, n=100)
  write.table(edgeR_result, file="result.tsv", quote=FALSE, append=TRUE)
}

For my real dataset, I have 25 groups i.e. DGE analysis of 1st group will be done with other 24 groups (pairwise) , so my for loop has (x in 2:24). I just wanted to check if I am doing it correctly. For grouping, I am currently doing it manually i.e. checking the first line of the count.txt file and typing "A", "A"...."B" in the 2nd line. Is there a syntax in R to make the grouping and reference automatically from the header of count file?

I am doing RNA-Seq analysis using EdgeR for the first time, so any help would be appreciated.