Need the help for $ \large \sqsubset $ and $\large \sqsupset $

Question

I need \sqsubset and \sqsupset in larger size. That means $ \sqsubset G_n \sqsupset $ for the purpose of completely lies in side the text within the interval of that open and closed space.

Answer 1

Something like

The symbols are obtained through these definitions (need graphicx package):

\newcommand{\bigsqsubset}{\mathrel{\text{\scalebox{1.5}{$\sqsubset$}}}}
\newcommand{\bigsqsupset}{\mathrel{\text{\scalebox{1.5}{$\sqsupset$}}}}

MWE:

\documentclass{article}

\usepackage{amsmath,amssymb}
\usepackage{graphicx}

\newcommand{\bigsqsubset}{\mathrel{\text{\scalebox{1.5}{$\sqsubset$}}}}
\newcommand{\bigsqsupset}{\mathrel{\text{\scalebox{1.5}{$\sqsupset$}}}}

\begin{document}

$ \bigsqsubset  G_n \bigsqsupset $

\end{document} 

Answer 2

I'm not sure what's the meaning of this, but you can try with relsize:

\documentclass{article}
\usepackage{amssymb,relsize}

\newcommand{\fancybrackets}[1]{%
  \mathopen{\mathlarger{\mathlarger{\sqsubset}}}%
  #1%
  \mathclose{\mathlarger{\mathlarger{\sqsupset}}}%
}

\begin{document}

$\fancybrackets{G_{n}}$

\end{document}