The center of 2"I" is the subgroup { ±1 }, so that the inner automorphism group is isomorphic to "I". The full automorphism group is isomorphic to "S"5 (the symmetric group on 5 letters), just as for formula_6 - any automorphism of 2"I" fixes the non-trivial element of the center (formula_7), hence descends to an automorphism of "I," and conversely, any automorphism of "I" lifts to an automorphism of 2"I," since the lift of generators of "I" are generators of 2"I" (different lifts give the same automorphism).