The set G = {1, 5, 7, 11, 25, 29, 31, 35} is a group under multiplication modulo 48, with the group table below. X48 1 5 7 11 25 29 31 35 1 1 5 7 11 25 29 31 35 ст 5 5 25 35 7 29 1 11 31 7 7 35 1 29 31 11 25 5 11 11 7 29 25 35 31 5 1 25 25 29 31 35 1 5 7 11 29 29 1 11 31 5 25 35 7 31 31 11 25 5 7 35 1 29 35 35 31 5 1 11 7 29 25 (a) How many elements of order 2 does G have? (b) State a standard group isomorphic to G, briefly justifying your answer. (c) Write down all the distinct left cosets of the subgroup N = {1,7} in G. (d) Justify the statement that N is a normal subgroup of G. (e) Write down the group table of the quotient group G/N. (f) State a standard group isomorphic to G/N.

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