Nope.
For example, if in_c = 10, out_c = 20, in_w = 64, in_h = 64, group=10, each input channel (whose shape is (64,64,in_c//group=1)) will have independently filter (whose shape for example is (5,5,1)), the two will be convoluted to (60,60,1). so here group=10 will generate (60,60,group). If out_c = group=10, this will just be the resulting output. But if out_c is the multiple of group like 20, 30, etc, there will be out_c//group feature map concatenating to (60,60,out_c), the total filter parameter = group * (5, 5, in_c//group) * (out_c//group) = 5 * 5 * in_c * (out_c//group). All of weights are different instead of sharing. This op is used in depthwise seperable convolution like MobileNet. When we want to seperate depth, group=in_c is what we want.