For a finite group A and for a finite group G on which A acts, the number of crossed homomorphisms from A to G is a multiple of gcd (|A/B|, |G|) provided that B is a normal subgroup of A such that A/B is cyclic. We prove a character-theoretic version of this fact, which was inspired by a theorem of P. Hall. © 2013, Walter de Gruyter Berlin Boston. All rights reserved.
Karlin, S., & Nirenberg, L. (1967). On a Theorem of P. Nowosad. Journal of Mathematical Analysis and Applications, 17(1), 61–67. https://doi.org/10.1016/0022-247X(67)90165-5