The Sylow Theorems · Superchallenge problem

$GL(2,\mathbb Z_{11})$ has order $13200$. The normalizer of a Sylow $11$-subgroup (the upper-triangular matrices with $1$'s on the diagonal) is the group of all upper-triangular invertible matrices, of order $1100$. How many Sylow $11$-subgroups does $GL(2,\mathbb Z_{11})$ have?