# Group 400.23 downloaded from the LMFDB on 14 November 2025. ## Various presentations of this group are stored in this file: # GPC is polycyclic presentation GPerm is permutation group # GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups # Many characteristics of the group are stored as booleans in a record: # Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, # metacyclic, monomial, nilpotent, perfect, quasisimple, rational, # solvable, supersolvable # The character table is stored as a record chartbl_n_i where n is the order # of the group and i is which group of that order it is. The record is # converted to a character table using ConvertToLibraryCharacterTableNC # Constructions GPC := PcGroupCode(278357045202247695,400); a := GPC.1; b := GPC.2; GPerm := Group( (3,10,6,8,4,9,5,7), (1,2), (11,35,30,25,20,15,34,29,24,19,14,33,28,23,18,13,32,27,22,17,12,31,26,21,16), (3,6,4,5)(7,10,8,9), (11,15,14,13,12)(16,20,19,18,17)(21,25,24,23,22)(26,30,29,28,27)(31,35,34,33,32), (3,4)(5,6)(7,8)(9,10) ); GLFp := Group([[[ Z(401)^22, 0*Z(401) ], [ 0*Z(401), Z(401)^380 ]], [[ Z(401)^200, 0*Z(401) ], [ 0*Z(401), Z(401)^200 ]]]); # Booleans booleans_400_23 := rec( Agroup := true, Zgroup := false, abelian := true, almost_simple := false, cyclic := false, metabelian := true, metacyclic := true, monomial := true, nilpotent := true, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_400_23:=rec(); chartbl_400_23.IsFinite:= true; chartbl_400_23.UnderlyingCharacteristic:= 0; chartbl_400_23.UnderlyingGroup:= GPC; chartbl_400_23.Size:= 400; chartbl_400_23.InfoText:= "Character table for group 400.23 downloaded from the LMFDB."; chartbl_400_23.Identifier:= " C2*C200 "; chartbl_400_23.NrConjugacyClasses:= 400; chartbl_400_23.ConjugacyClasses:= [ of ..., f1, f1*f4*f5^2*f6^2, f4*f5^2*f6^2, f1*f3*f5*f6, f1*f3*f4*f5^3*f6^3, f3*f5*f6, f3*f4*f5^3*f6^3, f6^2, f6^3, f6^4, f6, f2*f5^3, f2*f3*f4*f5*f6^4, f2*f3*f5^4*f6, f2*f4*f6^3, f1*f2*f5^3, f1*f2*f3*f4*f5*f6^4, f1*f2*f3*f5^4*f6, f1*f2*f4*f6^3, f1*f6, f1*f6^4, f1*f6^3, f1*f6^2, f1*f4*f5^2, f1*f4*f5^2*f6^4, f1*f4*f5^2*f6, f1*f4*f5^2*f6^3, f4*f5^2, f4*f5^2*f6^4, f4*f5^2*f6, f4*f5^2*f6^3, f1*f3*f5, f1*f3*f4*f5^3*f6^4, f1*f3*f4*f5^3, f1*f3*f5*f6^4, f1*f3*f4*f5^3*f6, f1*f3*f5*f6^3, f1*f3*f5*f6^2, f1*f3*f4*f5^3*f6^2, f3*f5, f3*f4*f5^3*f6^4, f3*f4*f5^3, f3*f5*f6^4, f3*f4*f5^3*f6, f3*f5*f6^3, f3*f5*f6^2, f3*f4*f5^3*f6^2, f5^2, f5^3*f6^4, f5^4, f5*f6^4, f5*f6, f5^4*f6^3, f5^3*f6, f5^2*f6^3, f5^2*f6^2, f5^3*f6^2, f5^4*f6^2, f5*f6^2, f5*f6^3, f5^4*f6, f5^3*f6^3, f5^2*f6, f5^2*f6^4, f5^3, f5^4*f6^4, f5, f2*f4, f2*f3*f5^4*f6^4, f2*f3*f4*f5, f2*f5^3*f6^4, f2*f3*f5^4, f2*f4*f6^4, f2*f4*f6, f2*f3*f5^4*f6^3, f2*f3*f4*f5*f6, f2*f5^3*f6^3, f2*f5^3*f6, f2*f3*f4*f5*f6^3, f2*f4*f6^2, f2*f3*f5^4*f6^2, f2*f3*f4*f5*f6^2, f2*f5^3*f6^2, f1*f2*f4, f1*f2*f3*f5^4*f6^4, f1*f2*f3*f4*f5, f1*f2*f5^3*f6^4, f1*f2*f3*f5^4, f1*f2*f4*f6^4, f1*f2*f4*f6, f1*f2*f3*f5^4*f6^3, f1*f2*f3*f4*f5*f6, f1*f2*f5^3*f6^3, f1*f2*f5^3*f6, f1*f2*f3*f4*f5*f6^3, f1*f2*f4*f6^2, f1*f2*f3*f5^4*f6^2, f1*f2*f3*f4*f5*f6^2, f1*f2*f5^3*f6^2, f1*f5, f1*f5^4*f6^4, f1*f5^3, f1*f5^2*f6^4, f1*f5^2*f6, f1*f5^3*f6^3, f1*f5^4*f6, f1*f5*f6^3, f1*f5*f6^2, f1*f5^4*f6^2, f1*f5^3*f6^2, f1*f5^2*f6^2, f1*f5^2*f6^3, f1*f5^3*f6, f1*f5^4*f6^3, f1*f5*f6, f1*f5*f6^4, f1*f5^4, f1*f5^3*f6^4, f1*f5^2, f1*f4, f1*f4*f5^4*f6^4, f1*f4*f5, f1*f4*f5^3*f6^4, f1*f4*f5^3, f1*f4*f5*f6^4, f1*f4*f5^4, f1*f4*f6^4, f1*f4*f6, f1*f4*f5^4*f6^3, f1*f4*f5*f6, f1*f4*f5^3*f6^3, f1*f4*f5^3*f6, f1*f4*f5*f6^3, f1*f4*f5^4*f6, f1*f4*f6^3, f1*f4*f6^2, f1*f4*f5^4*f6^2, f1*f4*f5*f6^2, f1*f4*f5^3*f6^2, f4, f4*f5^4*f6^4, f4*f5, f4*f5^3*f6^4, f4*f5^3, f4*f5*f6^4, f4*f5^4, f4*f6^4, f4*f6, f4*f5^4*f6^3, f4*f5*f6, f4*f5^3*f6^3, f4*f5^3*f6, f4*f5*f6^3, f4*f5^4*f6, f4*f6^3, f4*f6^2, f4*f5^4*f6^2, f4*f5*f6^2, f4*f5^3*f6^2, f1*f3, f1*f3*f4*f5^4*f6^4, f1*f3*f4, f1*f3*f5^4*f6^4, f1*f3*f4*f5, f1*f3*f5^3*f6^4, f1*f3*f5^2, f1*f3*f4*f5^2*f6^4, f1*f3*f4*f5^2, f1*f3*f5^2*f6^4, f1*f3*f5^3, f1*f3*f4*f5*f6^4, f1*f3*f5^4, f1*f3*f4*f6^4, f1*f3*f4*f5^4, f1*f3*f6^4, f1*f3*f6, f1*f3*f4*f5^4*f6^3, f1*f3*f4*f6, f1*f3*f5^4*f6^3, f1*f3*f4*f5*f6, f1*f3*f5^3*f6^3, f1*f3*f5^2*f6, f1*f3*f4*f5^2*f6^3, f1*f3*f4*f5^2*f6, f1*f3*f5^2*f6^3, f1*f3*f5^3*f6, f1*f3*f4*f5*f6^3, f1*f3*f5^4*f6, f1*f3*f4*f6^3, f1*f3*f4*f5^4*f6, f1*f3*f6^3, f1*f3*f6^2, f1*f3*f4*f5^4*f6^2, f1*f3*f4*f6^2, f1*f3*f5^4*f6^2, f1*f3*f4*f5*f6^2, f1*f3*f5^3*f6^2, f1*f3*f5^2*f6^2, f1*f3*f4*f5^2*f6^2, f3, f3*f4*f5^4*f6^4, f3*f4, f3*f5^4*f6^4, f3*f4*f5, f3*f5^3*f6^4, f3*f5^2, f3*f4*f5^2*f6^4, f3*f4*f5^2, f3*f5^2*f6^4, f3*f5^3, f3*f4*f5*f6^4, f3*f5^4, f3*f4*f6^4, f3*f4*f5^4, f3*f6^4, f3*f6, f3*f4*f5^4*f6^3, f3*f4*f6, f3*f5^4*f6^3, f3*f4*f5*f6, f3*f5^3*f6^3, f3*f5^2*f6, f3*f4*f5^2*f6^3, f3*f4*f5^2*f6, f3*f5^2*f6^3, f3*f5^3*f6, f3*f4*f5*f6^3, f3*f5^4*f6, f3*f4*f6^3, f3*f4*f5^4*f6, f3*f6^3, f3*f6^2, f3*f4*f5^4*f6^2, f3*f4*f6^2, f3*f5^4*f6^2, f3*f4*f5*f6^2, f3*f5^3*f6^2, f3*f5^2*f6^2, f3*f4*f5^2*f6^2, f2, f2*f3*f4*f5^4*f6^4, f2*f3, f2*f4*f5^4*f6^4, f2*f3*f4, f2*f5^4*f6^4, f2*f5, f2*f3*f4*f5^3*f6^4, f2*f3*f5, f2*f4*f5^3*f6^4, f2*f4*f5, f2*f3*f5^3*f6^4, f2*f5^2, f2*f3*f4*f5^2*f6^4, f2*f3*f5^2, f2*f4*f5^2*f6^4, f2*f4*f5^2, f2*f3*f5^2*f6^4, f2*f3*f4*f5^2, f2*f5^2*f6^4, f2*f3*f5^3, f2*f4*f5*f6^4, f2*f4*f5^3, f2*f3*f5*f6^4, f2*f3*f4*f5^3, f2*f5*f6^4, f2*f5^4, f2*f3*f4*f6^4, f2*f4*f5^4, f2*f3*f6^4, f2*f3*f4*f5^4, f2*f6^4, f2*f6, f2*f3*f4*f5^4*f6^3, f2*f3*f6, f2*f4*f5^4*f6^3, f2*f3*f4*f6, f2*f5^4*f6^3, f2*f5*f6, f2*f3*f4*f5^3*f6^3, f2*f3*f5*f6, f2*f4*f5^3*f6^3, f2*f4*f5*f6, f2*f3*f5^3*f6^3, f2*f5^2*f6, f2*f3*f4*f5^2*f6^3, f2*f3*f5^2*f6, f2*f4*f5^2*f6^3, f2*f4*f5^2*f6, f2*f3*f5^2*f6^3, f2*f3*f4*f5^2*f6, f2*f5^2*f6^3, f2*f3*f5^3*f6, f2*f4*f5*f6^3, f2*f4*f5^3*f6, f2*f3*f5*f6^3, f2*f3*f4*f5^3*f6, f2*f5*f6^3, f2*f5^4*f6, f2*f3*f4*f6^3, f2*f4*f5^4*f6, f2*f3*f6^3, f2*f3*f4*f5^4*f6, f2*f6^3, f2*f6^2, f2*f3*f4*f5^4*f6^2, f2*f3*f6^2, f2*f4*f5^4*f6^2, f2*f3*f4*f6^2, f2*f5^4*f6^2, f2*f5*f6^2, f2*f3*f4*f5^3*f6^2, f2*f3*f5*f6^2, f2*f4*f5^3*f6^2, f2*f4*f5*f6^2, f2*f3*f5^3*f6^2, f2*f5^2*f6^2, f2*f3*f4*f5^2*f6^2, f2*f3*f5^2*f6^2, f2*f4*f5^2*f6^2, f1*f2, f1*f2*f3*f4*f5^4*f6^4, f1*f2*f3, f1*f2*f4*f5^4*f6^4, f1*f2*f3*f4, f1*f2*f5^4*f6^4, f1*f2*f5, f1*f2*f3*f4*f5^3*f6^4, f1*f2*f3*f5, f1*f2*f4*f5^3*f6^4, f1*f2*f4*f5, f1*f2*f3*f5^3*f6^4, f1*f2*f5^2, f1*f2*f3*f4*f5^2*f6^4, f1*f2*f3*f5^2, f1*f2*f4*f5^2*f6^4, f1*f2*f4*f5^2, f1*f2*f3*f5^2*f6^4, f1*f2*f3*f4*f5^2, f1*f2*f5^2*f6^4, f1*f2*f3*f5^3, f1*f2*f4*f5*f6^4, f1*f2*f4*f5^3, f1*f2*f3*f5*f6^4, f1*f2*f3*f4*f5^3, f1*f2*f5*f6^4, f1*f2*f5^4, f1*f2*f3*f4*f6^4, f1*f2*f4*f5^4, f1*f2*f3*f6^4, f1*f2*f3*f4*f5^4, f1*f2*f6^4, f1*f2*f6, f1*f2*f3*f4*f5^4*f6^3, f1*f2*f3*f6, f1*f2*f4*f5^4*f6^3, f1*f2*f3*f4*f6, f1*f2*f5^4*f6^3, f1*f2*f5*f6, f1*f2*f3*f4*f5^3*f6^3, f1*f2*f3*f5*f6, f1*f2*f4*f5^3*f6^3, f1*f2*f4*f5*f6, f1*f2*f3*f5^3*f6^3, f1*f2*f5^2*f6, f1*f2*f3*f4*f5^2*f6^3, f1*f2*f3*f5^2*f6, f1*f2*f4*f5^2*f6^3, f1*f2*f4*f5^2*f6, f1*f2*f3*f5^2*f6^3, f1*f2*f3*f4*f5^2*f6, f1*f2*f5^2*f6^3, f1*f2*f3*f5^3*f6, f1*f2*f4*f5*f6^3, f1*f2*f4*f5^3*f6, f1*f2*f3*f5*f6^3, f1*f2*f3*f4*f5^3*f6, f1*f2*f5*f6^3, f1*f2*f5^4*f6, f1*f2*f3*f4*f6^3, f1*f2*f4*f5^4*f6, f1*f2*f3*f6^3, f1*f2*f3*f4*f5^4*f6, f1*f2*f6^3, f1*f2*f6^2, f1*f2*f3*f4*f5^4*f6^2, f1*f2*f3*f6^2, f1*f2*f4*f5^4*f6^2, f1*f2*f3*f4*f6^2, f1*f2*f5^4*f6^2, f1*f2*f5*f6^2, f1*f2*f3*f4*f5^3*f6^2, f1*f2*f3*f5*f6^2, f1*f2*f4*f5^3*f6^2, f1*f2*f4*f5*f6^2, f1*f2*f3*f5^3*f6^2, f1*f2*f5^2*f6^2, f1*f2*f3*f4*f5^2*f6^2, f1*f2*f3*f5^2*f6^2, f1*f2*f4*f5^2*f6^2]; chartbl_400_23.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400]; chartbl_400_23.ComputedPowerMaps:= [ , [1, 1, 1, 1, 4, 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E(200)^11, E(200)^67, -1*E(200)^51, E(200)^51, E(200)]]; ConvertToLibraryCharacterTableNC(chartbl_400_23);