group PGL(3,4): 60480 elements on 21 points; built in 0.1s
element list is a group (closed, generated by 6 random elements): True
element orders: {1: 1, 2: 315, 3: 4832, 4: 3780, 5: 8064, 6: 10080, 7: 5760, 15: 16128, 21: 11520}
|Q| = 2880, index 21; |phibar(Q)| = 60; |T| = 60
Q closed and phibar(q1 q2) = phibar(q1) phibar(q2) for all pairs in Q x Q: True
|ker phibar| = 48; orders in the kernel: {1: 1, 2: 15, 3: 32}
T closed under multiplication: True
orders in T: {1: 1, 2: 15, 3: 20, 5: 24} ; orders in phibar(Q): {1: 1, 2: 15, 3: 20, 5: 24}
Q-orbit of point 1 has length 20 (2-transitive iff 20 )
|Q_t| by order of t: {2: [192], 3: [144], 5: [240]}  M = 240  |P|/M = 252  = k * MinSubDeg(H) with k = 21 , MinSubDeg(H) = |Q|/M = 12
orbit lengths of phi(Q) on T minus 1 (non-trivial subdegrees of H): [12, 12, 15, 20]
total time 0.8s
