Calculate row-wise maximum

I would like to create a new column, which equals to the maximum value of all columns of that row.

Here is an example:

library(data.table)
data <- data.table(head(iris))
data[ , Species := NULL]
data

   Sepal.Length Sepal.Width Petal.Length Petal.Width
1:          5.1         3.5          1.4         0.2
2:          4.9         3.0          1.4         0.2
3:          4.7         3.2          1.3         0.2
4:          4.6         3.1          1.5         0.2
5:          5.0         3.6          1.4         0.2
6:          5.4         3.9          1.7         0.4

I can't really use the max function here, because it is going to find the maximum value of all columns, e.g., data[, max_value := max(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width)]. What I want is something like this:

   Sepal.Length Sepal.Width Petal.Length Petal.Width max_value
1:          5.1         3.5          1.4         0.2       5.1
2:          4.9         3.0          1.4         0.2       4.9
3:          4.7         3.2          1.3         0.2       4.7
4:          4.6         3.1          1.5         0.2       4.6
5:          5.0         3.6          1.4         0.2       5.0
6:          5.4         3.9          1.7         0.4       5.4