The set G = {1, 9, 31, 39, 41, 49, 71, 79} is a group under multiplicati modulo 80, with the group table below. 31 39 41 49 71 79 1 9 31 39 41 49 71 79 9 1 39 31 49 41 79 71 elism 8 31 39 1 9 71 79 41 49 9 71 49 41 ildsitusmilib to uoitiatab sul 39 31 9 1 79 41 49 71 79 1 9 31 39 49 41 79 71 9 1 39 31 71 79 41 49 31 39 1 9 79 71 49 41 39 3191 X80 1 9 1 9 31 39 41 49 71 79 Jest noarismo dis tesT of ide hastalog dosa te aldeia od guies piec interval (a) How many elements of order 2 does G have? (b) State a standard group isomorphic to G. (c) Write down all the distinct left cosets of the subgroup N = {1,31} in G. [S] 110 $-a (d) Explain why N is a normal subgroup of G. (e) Write down the group table of the quotient group G/N.

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