Question: Please answer it as soon as possible. Abstract Algebra. 5. The set of 24 numbers G = {1, 7,11,13,17,19,23,29,31,37,41,43, 47, 49,53,59,61,67, 71, 73, 77, 79,83,89}

Please answer it as soon as possible. Abstract Algebra.

5. The set of 24 numbers G = {1, 7,11,13,17,19,23,29,31,37,41,43, 47, 49,53,59,61,67, 71, 73, 77, 79,83,89} forms a group under multiplication modulo 90. The orders of these elements are given in the chart below. element 7 11 13 17 19 23 29 31 37 41 43 order 1 12 6 12 4 2 12 6 3 4 6 12 element 47 49 53 59 61 67 71 73 77 79 83 89 order 12 6 4 6 3 12 2 4 12 6 12 2 (5 PTS) Based on this information, express G as an external direct product of cyclic groups with prime- power order. (5 PTS) Now express G as an internal direct product of cyclic groups with prime-power order

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