undefined columns selected in plm() function

I had a weird problem in plm() function. Below is the code:

library(data.table)
library(tidyverse)
library(plm)


#Data Generation
n <- 500
set.seed(75080)

z   <- rnorm(n)
w   <- rnorm(n)
x   <- 5*z + 50
y   <- -100*z+ 1100 + 50*w
y   <- 10*round(y/10)
y   <- ifelse(y<200,200,y)
y   <- ifelse(y>1600,1600,y)
dt1 <- data.table('id'=1:500,'sat'=y,'income'=x,'group'=rep(1,n))

z   <- rnorm(n)
w   <- rnorm(n)
x   <- 5*z + 80
y   <- -80*z+ 1200 + 50*w
y   <- 10*round(y/10)
y   <- ifelse(y<200,200,y)
y   <- ifelse(y>1600,1600,y)
dt2 <- data.table('id'=501:1000,'sat'=y,'income'=x,'group'=rep(2,n))

z   <- rnorm(n)
w   <- rnorm(n)
x   <- 5*z + 30
y   <- -120*z+ 1000 + 50*w
y   <- 10*round(y/10)
y   <- ifelse(y<200,200,y)
y   <- ifelse(y>1600,1600,y)
dt3 <- data.table('id'=1001:1500,'sat'=y,'income'=x,'group'=rep(3,n))

dtable <- merge(dt1    ,dt2, all=TRUE)
dtable <- merge(dtable ,dt3, all=TRUE)


# Model 
dtable_p <- pdata.frame(dtable, index = "group")

mod_1 <- plm(sat ~ income, data = dtable_p,model = "pooling")

Error in [.data.frame(x, , which) : undefined columns selected

I checked all possibilities but I can not figure out why it gives me an error. the columns'names are correct, why R said undefined columns??? Thank you!

Follow up: I add another data set test as the @StupidWolf use to prove

data("Produc", package = "plm")
form <- log(gsp) ~ log(pc) 
Produc$group <-  Produc$region
pProduc <- pdata.frame(Produc, index = "group")

Produc$group <- rep(1:48, each = 17)

summary(plm(form, data = pProduc, model = "pooling"))
>Error in `[.data.frame`(x, , which) : undefined columns selected