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7,872,3560,3158,3823,1645,2083,573,1232,2988,626,1735,1482,2918,3001,698,969,1405,2470,2683,2628,2592,1443,921,2543,3545,1233,1127,1749,718,36,535,1925,2242,3791,2235,652,2521,330,3475,3224,717,2997,3380,2549,2949,1570,2289,1164,3373,748,244,2158,1871,860,2254,1429,1401,2865,2290,682,2227,2313,586,1062,1116,557,3916,3606,3783,3392,3460,3080,2253,3114,3455,3162,2106,2439,2593,1389,1078,1489,3720,2687,1524,755,2113,2068,2002,704,3356,1456,2165,1713,2571,170,1151,714,3332,290,919,2851,2093,2721,2146,3583,2701,2523,3269,2339,133,2558,3378,1395,734,1452,2109,2200,678,231,3705,780,223,2940,1503,1317,214,3503,1596,514,2340,2085,3867,4039,2786,3506,389,1133,1678,197,1928,2473,3044,1034,3152,4066,130,2274,1178,4045,3707,3641,2688,1835,2376,18,230,2246,2931,361)(8,827,542,1130,806,2195,1082,44,740,670,1056,1610,1909,3288,2495,1698,1100,4020,321,2883,947,1087,1792,3624,834,83,1514,3193,4074,2343,854,3845,3471,3879,1438,108,3302,1268,2155,3748,2480,4081,3872,2677,2269,253,2881,3683,469,3782,3671,803,650,1669,3662,3618,3654,2813,512,1313,1101,142,3208,363,370,1781,3860,873,830,545,1266,2815,1492,2205,1789,1522,2304,1770,3148,3046,399,1157,3212,727,1541,3504,747,4001,3350,2669,3880,3857,410,3251,1936,521,2152,1384,1355,3726,4051,1888,3192,3134,1915,1670,3323,3282,519,2090,3483,2631,1619,3696,879,3390,3494,2622,751,4016,611,3052,2959,1652,2187,862,1285,1368,1874,2204,3749,1740,689,3479,2916,3801,2468,2899,1399,2312,3747,1765,2030,3325,179,507,1996,2040,2324,1262,875,2782,1372,592,2070,342,3075,2514,338,3647,3207,3082,448,1601,1440,3670,1474,2392,709,3463,3825,2066,401,1246,3691,1234,2608,3339,1449,2504,3882,4059,3109,281,2749,914,3365,2769,2280,2824,1988,1566,1949,2179,516,3210,3810,2333,889,318,1976,1982,3427,1158,3342,1861,425,1003,2716,3160,2043,3612,987,2214,2896,1992,1898,3727,3811,1916,1308,2637,4092,3413,1194,1468,2712,2400,3764,927,613,81,2019,3753,1018,703,1994,2818,3132,1920,3476,900,2110,2353,2328,3031,2322,2781,4073,2454,79,2052,668,2228,2037,1336,758,2868,1031,1090,3950,1718,738,1288,306,649,3064,1533,1282,1167,1330,2063,3343,2509,3530,3925,843,3690,3273)(9,868,2977,1274,906,240,3568,804,1537,3851,2167,3397,624,500,1967,2597,3195)(12,812,2710,859,1347,1574,2674,2046,2735,226,2620,378,2919,1889,895,3933,857,3819,3774,2519,3964,2689,2399,2099,2054,1220,3918,1435,2603,2199,3484,3875,4069,3992,1991,1172,2548,2933,3868,1423,3969,2151,3582,1077,719,1855,2742,2210,3188,840,3679,3366,237,483,3382,3863,2096,3328,3076,765,2774,3341,4095,3549,1745,3955,579,3320,1955,1822,404,1065,1036,136,1964,824,3462,1758,558,2536,3528,1757,667,206,3352,3913,1007,3228,3669,3887,311,2680,2308,2130,1852,457)(17,977,2139,2550,2720,3953,724,385,1901,234,2164,2895,712,3344,1550,3904,836,1865,3128,1540,616,815,241,1343,933,1924,2373,3354,2546,377,3538,446,422,628,3623,2668,3140,3186,3776,2629,1962,1445,3945,3136,1975,1984,3607,1301,2960,1703,2267,3532,359,591,1904,3168,3580,2074,1990,1154,1531,46,2756,594,536,2953,1191,2023,2845,1606,1839,451,2028,982,3581,4019,2301,1623,697,2793,700,794,60,855,2684,3688,2800,3766,1447,1496,376,1316,1957,2506,2053,3635,3929,187,3878,3666,1047,1872,2129,1410,1428,1966,2217,277,757,3525,3638,354,3615,2794,3090,1558,3286,677,1721,3979,4031,1591,2889,171,672,2596,3491,3962,1412,1699,2481,453,1269,2264,1345,2633,3048,2501,1254,205,1465,3026,3163,4022,3848,3937,816,2951,1287,1457,1486,1935,1027,2034,1032,3078,1202,3807,838,2463,3146,1180,2022,1248,2600,248,1702,1917,104,2395,2746,655,4036,2862,4047,1851,3689,98,2397,3490,3041,2575,1644,681,131,2193,3088,1593,1879,647,3019,3719,2105,856,908,151,3159,1650,307,1595,3007,848,2937,2350,1048,3888,314,2186,800,2730,3095,291,452,1739,313,1903,188,1771,2884,3990,641,1674,3963,2999,3337,2651,1707,651,134,2728,1476,3984,3822,3701,2319,3393,4010,4018,1426,990,494,1165,665,283,1532,1631,3721,3056,3543,2524,4043,2410,3061,1732,1014,1012,153,2946,867,1400,2907,3537,1869,2995,224)(25,3837,1173,2004,997,220,2698,1512,1088,1752,1086,1067,1045,2976,4049,1375,405,3309,1006,984,3991,725,888,3716,1589,2168,3646,3408,2643,1907,309,3272,733,560,2690,3050,3255,1190,2278,2048,928,335,2184,3305,3622,880,3557,1793,962,2484,3466,195,1349,1734,2258,570,2051)(102,157,3799,1899,119,3611,993,1367,3266,995,1296,1119,2727,1695,2288,2279,1413,124,566,1862,2303,2719,1113,3591,686,1729,1099,1913,1184,2378,2544,2891,1255,1795,851,1693,3485)(986,3686,3440,1215,1586,2069,2121,4061)(3767,3830)


The automorphism group is generated by

1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1
1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0
0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0
1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1
1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0
1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0
0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1
1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1
1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1
1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0
1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1
1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0
1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0
0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1
1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1
0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1
1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1
1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0
1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1
0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0
1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0
0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1
0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0
1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0
0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1
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572,1425,4000,2007,3750)(778,3656,3794,3433,1026,2822,3633)(786,2000,1875,908,2760,3051,2436)(787,945,2762,2173,1628,3796,2284)(788,1146,3516,2231,3635,1050,2055)(789,3043,2315,2524,3001,3111,1325)(792,3544,2904,2958,2281,3821,1976)(794,3026,3482,1195,1935,3739,2551)(799,2412,2485,1011,1483,1496,4087)(800,2657,1665,2648,1444,892,1651)(801,805,2011,3252,3594,1553,3358)(804,3435,1877,1799,3429,2735,2724)(808,3002,2842,3710,2314,2610,2116)(812,2840,3074,3249,3615,3414,1200)(813,1224,2946,1225,1412,3574,2887)(814,1142,2520,3134,1898,2441,1381)(820,937,3901,3072,3495,1107,3255)(823,979,1320,2673,4083,2695,2928)(827,1776,2394,1234,1398,3565,2087)(831,2141,3889,1435,2908,2047,3222)(832,2703,2126,2856,3368,1269,2552)(847,1552,2218,858,1558,4017,3022)(848,2357,2736,899,867,2788,2649)(852,1154,2484,1460,3938,1507,2381)(857,3658,2826,1434,2099,1283,1587)(864,2676,3063,2387,1532,2050,2317)(874,4048,977,3440,2588,3742,2431)(887,3972,2725,2658,1916,1825,2363)(897,1945,2329,1840,2574,3619,1870)(898,1315,3582,3251,1384,3351,3971)(903,2114,1331,1555,1047,3580,1472)(904,1582,2354,3867,2751,1274,2176)(909,3999,1085,2949,2489,3737,2370)(911,3936,3655,1747,2997,3823,1046)(913,4046,2136,2696,4009,2797,4075)(914,2753,2996,1932,1882,2242,2304)(916,4082,2591,3610,989,3398,2599)(920,3857,2496,3212,1287,935,3020)(930,3462,2122,3760,1182,3087,3525)(934,3809,1891,3642,2999,3168,3426)(938,1029,1838,3208,1771,1476,3085)(940,2280,2343,2913,3843,2578,1905)(942,2659,2939,3614,1548,1591,1581)(943,973,1048,2722,1677,1432,3198)(944,2073,2802,2057,3671,2948,970)(956,3873,3024,1417,1101,3622,2783)(957,3161,2708,2492,2875,2234,2065)(958,3229,1986,1329,2960,2491,3410)(960,3013,2584,2545,3363,3360,3693)(961,2342,3481,2859,2103,1775,3402)(963,1769,3829,3346,1527,1859,3922)(965,1340,1638,2903,1403,3155,1973)(967,1852,1092,3973,2143,3187,1528)(968,2082,3181,1018,1390,1839,1328)(980,1065,2139,2259,2969,2559,2462)(983,3230,4081,3874,2430,3322,992)(984,4027,3985,2309,3508,3299,1773)(985,1118,3929,2791,3647,4050,3079)(990,1786,3559,1676,1199,1718,2770)(995,1920,2631,1931,2625,1073,3291)(998,1715,2411,3839,3474,3687,2827)(1007,2390,1588,3870,1957,3383,2869)(1031,3062,2759,2288,1710,1570,1036)(1032,3082,3708,3419,1896,3349,2564)(1033,2743,2064,3792,2069,2603,3321)(1034,2278,3506,2120,3617,2961,1333)(1042,3492,3490,2839,3866,2668,2721)(1044,3044,3804,3480,1952,2919,1830)(1045,3850,3466,3391,1521,2418,3361)(1068,4052,4085,2023,1348,3446,2504)(1074,1397,1494,1194,3030,1904,4010)(1087,1103,3125,1832,1978,4069,2701)(1099,3341,3852,3031,2013,3403,2981)(1104,3911,1518,2311,3512,3530,1546)(1108,2204,1277,1918,1751,3138,1535)(1116,2618,3698,2926,3520,1344,2248)(1117,2526,1354,3485,3080,3628,1246)(1120,3918,1649,1322,3878,3820,3746)(1123,1402,1459,1685,3825,2003,3902)(1126,2106,3385,3685,3265,2191,3588)(1155,3840,2146,1167,2487,3862,1990)(1168,2358,2230,1516,1724,2857,2154)(1171,3477,2935,2528,3788,3099,1701)(1172,2131,3858,3987,1726,2741,2274)(1180,2833,1943,2307,2341,1448,2286)(1184,2752,3029,1489,2112,3303,2166)(1185,4047,3522,3916,2502,2590,3292)(1201,1600,2888,1219,1784,3330,3302)(1209,2570,1733,2808,3728,1925,3743)(1212,1278,3994,3434,2211,1298,1249)(1223,3182,1783,3162,3133,1884,3096)(1238,3596,2962,3392,2754,3468,2406)(1241,2885,1347,1583,2084,3637,2889)(1247,4028,2257,3733,3286,1370,3195)(1250,2189,3259,2076,2348,3394,1908)(1251,1646,4071,1958,1295,2640,1761)(1262,3603,2442,3205,3548,2710,3569)(1264,3597,2633,3515,1894,2898,3786)(1270,3983,2327,3060,2006,3841,3769)(1285,1404,3010,2652,2914,1864,3919)(1296,2351,1851,1590,2078,2541,2460)(1307,3664,2174,3956,2206,4043,2155)(1308,2194,1802,1506,2034,3287,2902)(1317,2337,2910,2731,2107,2862,1405)(1349,1886,3354,1946,2864,2096,2301)(1353,3598,1608,2763,2775,1375,3754)(1366,1607,3779,2456,3634,2205,2678)(1416,3775,2186,2323,2719,3311,3802)(1430,3640,3120,2795,4030,3900,2080)(1431,2706,1455,3101,2750,3216,3413)(1438,2882,2238,3103,3089,2330,4086)(1445,3352,1980,2398,3572,3436,3023)(1454,1611,3118,2765,3071,2463,3992)(1458,4044,1889,3196,1750,1837,4063)(1466,3536,1981,3028,2884,3312,3453)(1471,2834,1912,2202,3651,3149,1953)(1475,2683,3496,3908,2162,1534,3907)(1487,1970,3199,2236,4005,3763,2063)(1549,3493,3171,2771,1556,2052,3217)(1554,3905,3632,4014,3144,3405,2850)(1585,2733,2053,2400,2403,1624,3135)(1602,3093,1610,3106,4022,2621,2409)(1605,3933,3108,2193,3715,2715,3169)(1626,2824,2448,3053,1797,1679,2450)(1640,2895,1874,2214,3707,2415,2049)(1673,2977,2529,3962,2811,1961,2932)(1681,2509,2438,2402,3568,3200,2565)(1711,1930,2806,2680,2215,3276,3946)(1743,3513,3660,2865,2088,3904,1993)(1796,2768,2630,2607,3069,3847,2407)(1822,1899,3777,3551,3215,2092,3494)(1867,1967,2198,4026,2587,2711,3609)(1868,1903,3523,2241,3782,2757,3189)(1876,3542,2058,2952,3676,2075,2321)(1926,3054,3538,3718,3563,3749,2597)(1965,2794,3808,2988,3925,2388,2148)(2097,2229,2446,2171,2269,3768,3566)(2240,3661,3741,3545,3298,3397,2644)(2246,3555,2804,4006,2918,3709,3370)(2297,2916,3500,3993,3674,3778,4031)

The automorphism group has order
28672