print "Conway's simple group co3 on 276 letters. ";
print "Order: 495 766 656 000 = 2^10 * 3^7 * 5^3 * 7 * 11 * 23 ";
print "Base: 1,2,3,4,8,5; Basic Orbits: 276 * 275 * 162 * 105 * 64 * 6 ";
print "Stabilizer of set [1,2,...,23] is Mathieu group M23 ";
print "Stabilizer of set [1,2,...,100] is Higman-Sims group HS ";
print "Group G";
G := PermutationGroup<276 |
    \[     1,  24,   2,   5,   7,   6,   4, 189, 184, 190, 183, 192,
191, 181, 182, 196, 194, 195, 193, 188, 186, 185, 187,   3,  26,  27,  25,
 28,  49,  50,  51,  52,  57,  58,  59,  60,  55,  56,  53,  54,  47,  48,
 45,  46, 208, 207, 206, 205, 200, 199, 198, 197, 202, 201, 204, 203, 226,
225, 228, 227, 121, 122, 123, 124, 127, 128, 125, 126, 138, 137, 139, 140,
118, 117, 120, 119, 131, 132, 130, 129, 134, 133, 136, 135,  91,  90,  87,
 88, 100,  98,  97,  99,  93,  94,  89,  92,  85,  86,  96,  95, 107, 108,
105, 106, 115, 116, 113, 114, 109, 110, 111, 112, 101, 102, 103, 104, 173,
174, 175, 176, 172, 171, 169, 170, 160, 159, 158, 157, 179, 180, 177, 178,
167, 168, 165, 166, 161, 162, 164, 163,  22,  23,  11,   9,  19,  16,  18,
 17,  10,   8,  20,  21,  13,  14,  15,  12,  66,  65,  68,  67,  70,  69,
 72,  71,  84,  83,  82,  81,  63,  64,  62,  61,  74,  73,  76,  75,  77,
 78,  80,  79, 154, 155, 143, 144, 141, 152, 142, 151, 150, 149, 153, 156,
145, 148, 147, 146,  32,  31,  30,  29,  40,  39,  38,  37,  42,  41,  44,
 43, 232, 236, 239, 233, 231, 241, 244, 237, 242, 235, 229, 234, 240, 243,
230, 238,  34,  33,  36,  35, 264, 270, 271, 266, 263, 273, 274, 268, 267,
276, 272, 261, 265, 269, 262, 275, 255, 258, 250, 245, 249, 257, 252, 259,
246, 254, 248, 256, 247, 253, 251, 260, 221, 222, 212, 219, 214, 209, 216,
210, 217, 223, 213, 211, 220, 218, 215, 224],
    \[   117,  78,   3, 167, 148,  12,  33, 181, 136,  20,  31,  56,
 35, 193, 240, 152, 137, 134, 231, 132, 130, 199, 118,  86,  71, 112, 263,
198,  17, 224, 155, 140, 250,  40, 187, 244, 153, 176, 165,  47, 150, 256,
 49, 259, 114,  55, 248, 175,  52, 154, 210, 220, 223, 205,  18, 214, 188,
232, 212,  29,  19, 228,  80,  72, 236, 186,  44, 271, 273, 267,   8, 206,
164, 102,  75, 183, 226, 113,  82, 275, 251,  45, 109, 157,  85,  92,  38,
238,   4, 262,  95, 159,  74, 253, 104, 161,  84,  94,  42, 100, 101, 103,
 93, 108, 105, 268, 269,  91,  83, 270,   2,  70, 111,  79,  81,  98, 120,
197,   9, 125, 143,  54, 123, 119,   1, 122, 127, 221, 129,  58, 190, 178,
211,  46, 200, 124,  60,  57, 151,  50,   7, 121, 146, 144, 234, 142, 179,
174, 247, 145, 131,  59,  37,  32, 213, 156, 173, 252,  24, 160, 107,  99,
260, 246, 158,  89, 166, 115, 276,   5, 217, 254,  97, 170, 149, 249,  68,
 10, 265,  90,  25, 184, 258, 208, 169, 106, 264, 274, 222, 139, 216,  67,
 51,  27, 255, 242, 201,  62, 189, 135,  23, 207, 203, 204, 126, 219,  53,
227, 209,  14, 133,  16,  11,   6, 241,  15,  69,  30,  64,  43, 128,  22,
202, 266, 239, 196, 182,  28,  73, 230, 233,  21,  61,  41, 194,  65,  63,
 88,  36, 191, 110,  77,  76, 225, 180, 229,  48,  34,  87, 141, 168,  39,
116, 172, 195, 162, 177, 243, 192, 163, 147, 245, 235,  13, 261, 218,  26,
 66,  96, 215, 257, 185, 171, 138, 237, 272]>;
AssertAttribute(G, "Order", 2^10 * 3^7 * 5^3 * 7 * 11 * 23);
