Could someone help me on this problem?
I want to figure out which of the following groups is isomorphic to
. The following groups are
I know
has order 6, so the given group has order 48/6=8. I tried to list the elements of this factor group which has order 8, but I was unable to do so since I don't know how to pick the representatives from
so that they will give 5 distinct elements (I know
is the identity in this factor group). I know
is cyclic, so if I can show that the factor group has no element of order 8, then I can eliminate
. I also know every non-identity element of
has order 2, so if I can show that the factor group has an element of order 4, then I should be able to finish. Any help is appreciated.