ANCOVA full multiplicative model.

So i have 3 covariates and one categorical predictor with two levels(group), obviously along with a continuous response.
How would i code the full multiplicative model for an ancova taking into account all interactions.
Would it be something like this or am i on the wrong track.

model <- lm(responsevariable ~ covariate1group + covariate2group + covariate3*group)

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