2 The following Cayley table is for \(G\), a group of order 6. The identity element is \(e\) and the group is generated by the elements \(a\) and \(b\).
| G | \(e\) | \(а\) | \(a ^ { 2 }\) | \(b\) | \(a b\) | \(\mathrm { a } ^ { 2 } \mathrm {~b}\) |
| \(e\) | \(e\) | \(а\) | \(a ^ { 2 }\) | \(b\) | \(a b\) | \(\mathrm { a } ^ { 2 } \mathrm {~b}\) |
| \(a\) | \(а\) | \(a ^ { 2 }\) | \(e\) | \(a b\) | \(\mathrm { a } ^ { 2 } \mathrm {~b}\) | \(b\) |
| \(a ^ { 2 }\) | \(a ^ { 2 }\) | \(e\) | \(a\) | \(\mathrm { a } ^ { 2 } \mathrm {~b}\) | \(b\) | \(a b\) |
| \(b\) | b | \(\mathrm { a } ^ { 2 } \mathrm {~b}\) | \(a b\) | \(e\) | \(a ^ { 2 }\) | \(a\) |
| \(a b\) | \(a b\) | b | \(\mathrm { a } ^ { 2 } \mathrm {~b}\) | \(a\) | \(e\) | \(a ^ { 2 }\) |
| \(\mathrm { a } ^ { 2 } \mathrm {~b}\) | \(\mathrm { a } ^ { 2 } \mathrm {~b}\) | \(a b\) | b | \(a ^ { 2 }\) | \(a\) | \(e\) |
- List all the proper subgroups of \(G\).
- State another group of order 6 to which \(G\) is isomorphic.