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In page Sylow theorems:

"

TheoremIf K is a Sylow p-subgroup of G, and n p = | Cl ( K ) | {\displaystyle n_{p}=|\operatorname {Cl} (K)|} is finite, then every Sylow p-subgroup is conjugate to K, and n p 1   ( m o d   p ) {\displaystyle n_{p}\equiv 1\ (\mathrm {mod} \ p)} .[citation needed]