|P| = 60480 = 2^6 * 3^3 * 5^1 * 7^1 ; Sylow orders: {2: 64, 3: 27, 5: 5, 7: 7}
centraliser orders |C_P(x)| by element order: {2: [192], 3: [27, 63, 180], 4: [16], 5: [15], 6: [12], 7: [21], 15: [15], 21: [21]}
max |C_P(x)| over x != 1: 192
max |C_P(x)| over x in Q with phi(x) != 1: 192
largest element order: 21
M = 240 ; all of the above are < 240 : True
