Abstract Algebra - Isomorphism

1. Feb 26, 2014

jz0101

1. Show that S42 contains multiple subgroups that are isomorphic to S41.
Choose one such subgroup H and find σ1,....,σ42 such that

How can you solve this?? I am confused if anyone can help me to solve this!!

2. Feb 26, 2014

haruspex

What, in words, does S42 represent?

3. Feb 26, 2014

kduna

I'll assume you already identified a subgroup $H$ that is isomorphic to $S_{41}$. Think about the cosets of $H$. How many are there? (If this is a hard question, try looking over a proof of Lagrange's Theorem).

4. Feb 26, 2014

jz0101

@kduna: I am studying by myself reading book. Now I saw this question which I wanted to know how to solve this question.