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If a group of order 15 acts on a set of order 22 and there are no fixed points. How many orbits are there?

I know the group action corresponds to a homomorphism from G into $S_{22}$

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    WHatare the possible sizes of the stabilizers?2012-01-08
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    Well stabilizer is a subgroup of G right so 1,3,5 or 15, but if it was 15 then we would have a fixed point which we don't. So 1,3, or 5.2012-01-08
  • 0
    Ok, so what are the possible sizes of the orbits, then?2012-01-08
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    15,5 or 3 so must be 4 orbits of order 3 and 2 of order 5?2012-01-08
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    @user9352 Looks good to me!2012-01-08
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    Indeed. You have just answered your own question. You should write in more detail what you did in the answer box.2012-01-08

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