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1) a) Let G=S8. Show H={(1),(154)(326)(78),(154)(326),(145)(362),(145)(362)(78),(78)} is a subgroup of G. b) Find the orbits of 1,2,3,4,5,6,7,8 in H. c) Find the stabilizers of 1,2,3,4,5,6,7,8

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1) a) Let G=S8. Show H={(1),(154)(326)(78),(154)(326),(145)(362),(145)(362)(78),(78)} is a subgroup of G. b) Find the orbits of 1,2,3,4,5,6,7,8 in H. c) Find the stabilizers of 1,2,3,4,5,6,7,8 in H

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