# what are the sylow 2-subgroups of S5?

• December 1st 2009, 09:12 AM
Louise
what are the sylow 2-subgroups of S5?
what are the sylow 2-subgroups of S5?

i know that s2=15,

but i don't really understand how to list them.

i also need to show they are isomorphic to a sylow 2-subgroup of S4 by showing they fix at least one element in {1,2,3,4,5}

• December 1st 2009, 09:58 AM
tonio
Quote:

Originally Posted by Louise
what are the sylow 2-subgroups of S5?

i know that s2=15,

but i don't really understand how to list them.

i also need to show they are isomorphic to a sylow 2-subgroup of S4 by showing they fix at least one element in {1,2,3,4,5}

$<(12)(34),(1234)\;;\; \left((12)(34)\right)^2=(1234)^4=1\,,\,(12)(34)(12 34)(12)(34)=(1432)>$...do you recognize this group?