  $\lambda$-graph systems are labeled Bratteli diagram with shift operations.
They present subshifts. Their matrix presentations are called symbolic matrix
systems. We define skew products of $\lambda$-graph systems and study
extensions of subshifts by finite groups. We prove that two canonical symbolic
matrix systems are $G$-strong shift equivalent if and only if their presented
subshifts are $G$-conjugate. $G$-equivalent classes of subshifts are classified
by the cohomology classes of their associated skewing functions.
