Suzuki Sporadic Group - Suzuki Chain

Suzuki Chain

The Suzuki chain or Suzuki tower is the following tower of rank 3 permutation groups from (Suzuki 1969), each of which is the point stabilizer of the next.

• G₂(2) = U(3, 3) · 2 has a rank 3 action on 36 = 1 + 14 + 21 points with point stabilizer PSL(3, 2) · 2
• J₂ · 2 has a rank 3 action on 100 = 1 + 36 + 63 points with point stabilizer G₂(2)
• G₂(4) · 2 has a rank 3 action on 416 = 1 + 100 + 315 points with point stabilizer J₂ · 2
• Suz · 2 has a rank 3 action on 1782 = 1 + 416 + 1365 points with point stabilizer G₂(4) · 2