Das, BireswarBireswarDasThakkar, DharaDharaThakkar2026-03-132026-03-132026-01-010097-539710.1137/24M1685353https://repository.iitgn.ac.in/handle/IITG2025/34798The minimal faithful permutation degree 𝜇⁡(𝐺) of a finite group 𝐺 is the smallest integer 𝑚 for which there is an injective homomorphism 𝜙 from 𝐺 to 𝑆𝑚. The main result of this paper is a randomized polynomial-time algorithm for computing the minimal faithful permutation degree groups without abelian normal subgroups. Additionally, we show that: 1. For any primitive permutation group 𝐺, 𝜇⁡(𝐺) can be computed in quasi-polynomial time. 2. For a group 𝐺 given by its Cayley table, 𝜇⁡(𝐺) can be computed in DSPACE⁡(log3⁡|𝐺|).en-USMinimal faithful permutation representationPermutation group algorithmsComputational group theorySemisimple groupsArticle1095-7111WOS:001707066900003