1. ## Direct Prodcuts

The group S3 (+) Z2 is isomorphic to one of the following groups: Z12, Z6 (+) Z2 , A4, D6. Determine which one by elimination. Please Help!!! which one is isomorphic.??

2. Originally Posted by spitz34
The group S3 (+) Z2 is isomorphic to one of the following groups: Z12, Z6 (+) Z2 , A4, D6. Determine which one by elimination. Please Help!!! which one is isomorphic.??
the first two groups are abelian and $A_4$ has no element of order 6. thus the answer is $D_6.$ how hard was that?!!! now try to find an isomorphism from $S_3 \oplus \mathbb{Z}_2$ to $D_6.$