The set 1411141619262931344144 is a group under multiplicati

The set [1,4,11,14,16,19,26,29,31,34,41,44] is a group under multiplication mod 45. Give the isomorphism class for this group. That is, write G as a direct product of prime-power order. Defend/Explain your answer please.

Solution

A prime power is a positive integer power of a single prime number and 1 is not count as prime number

prime power is 2,3, (4=2^2),5,7,(8=2^3),(9=3^3),11,13,(16=2^4),17,19,23,(25=5^2),(27=3^3),29,31,(32=2^5),37,41,43

so the isomorphism class of the group [1,4,11,14,16,19,26,29,31,34,41,44] under multiplication Mod 45

is [4,11,16,19,29,31,41]