2 The set \(S = \{ a , b , c , d \}\) under the binary operation * forms a group \(G\) of order 4 with the following operation table.
| \(*\) | \(a\) | \(b\) | \(c\) | \(d\) |
| \(a\) | \(d\) | \(a\) | \(b\) | \(c\) |
| \(b\) | \(a\) | \(b\) | \(c\) | \(d\) |
| \(c\) | \(b\) | \(c\) | \(d\) | \(a\) |
| \(d\) | \(c\) | \(d\) | \(a\) | \(b\) |
- Find the order of each element of \(G\).
- Write down a proper subgroup of \(G\).
- Is the group \(G\) cyclic? Give a reason for your answer.
- State suitable values for each of \(a , b , c\) and \(d\) in the case where the operation \(*\) is multiplication of complex numbers.