how many 2-sylow's subgroups are there in group of order 72. please explain

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- May 13th 2012, 07:04 AMsaravananbsno. of subgroups
how many 2-sylow's subgroups are there in group of order 72. please explain

- May 13th 2012, 12:53 PMDevenoRe: no. of subgroups
72 = 2

^{3}*3^{2}, so the 2-sylow subgroups are of order 8.

the number of such subgroups is congruent to 1 mod 2, and is a divisor of 72. so the only possibilities are odd divisors of 72: 1,3 or 9.