Some supercharacter theories of a certain group of order 6n

In this paper, we are going to obtain some normal supercharacter theories of a group of order 6n with the presentation U6n = a, b: a^2n = b³ = 1, a^−1 ba = b^−1 in special cases. We will also prove that the automorphic supercharacter theories of this group can be computed with the other methods