The isovalent-substituted iron-pnictide superconductor SrFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ ($x$=0.35) has a slightly higher optimum critical temperature than the similar system BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$, and its parent compound SrFe$_{2}$As$_{2}$ has a much higher Neel temperature than BaFe$_{2}$As$_{2}$. We have studied the band structure and the Fermi surfaces of optimally-doped SrFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ by angle-resolved photoemission spectroscopy (ARPES). Three holelike Fermi surfaces (FSs) around (0,0) and two electronlike FSs around ($pi$,$pi$) have been observed as in the case of BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$. Measurements with different photon energies have revealed that one of the hole FSs is more strongly warped along the $k_{z}$ direction than the corresponding one in BaFe(As$_{1-x}$P$_{x}$)$_{2}$, while the electron FSs are almost cylindrical unlike corrugated ones in BaFe(As$_{1-x}$P$_{x}$)$_{2}$. Comparison of the ARPES data with first-principles band-structure calculation revealed that the quasiparticle mass renormalization factors are different not only between bands of different orbital character but also between the hole and electron FSs of the same orbital character. By examining nesting conditions between the hole and electron FSs, we conclude that magnetic interactions between FeAs layers rather than FS nesting play an important role in stabilizing the antiferromagnetic order. The insensitivity of superconductivity to the FS nesting can be explained if only the $d_{xy}$ and/or $d_{xz/yz}$ orbitals are active in inducing superconductivity or if FS nesting is not important for superconductivity.
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