Average by Group of Two Conditions

I would like to output the summary statistics (average, maximum, minimum, etc.) for group1 and group2 for the following data frames:I would appreciate it if you could let me know.

Example)
Average value of Group A for Men =
Average value of Men in Group B =
Average value of Group A for Women =
Average value of Group B for Women =

df<-data.frame(age=1:100, group1=c(rep("Men", 50), rep("Women", 50), group2=c(rep("A", 25), rep("B", 25), rep("C", 25), rep("D", 25)))