# Group 9600.cc downloaded from the LMFDB on 27 June 2026. 
 
## 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 
GPerm := Group( (2,4,3,5), (2,4,3,5)(6,9,8,10,7), (6,9,7,10), (2,3)(4,5), (1,11)(2,4,3,5)(6,8,7,9,10)(12,13,14), (2,5,3,4)(6,7)(9,10), (2,4,3,5)(6,8,9,7)(11,14) );

 
# Booleans 
booleans_9600_cc := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := false,
supersolvable := false); 

 
# Character Table 
chartbl_9600_cc:=rec(); 
chartbl_9600_cc.IsFinite:= true; 
chartbl_9600_cc.UnderlyingCharacteristic:= 0; 
chartbl_9600_cc.UnderlyingGroup:= GPerm;
chartbl_9600_cc.Size:= 9600;
chartbl_9600_cc.InfoText:= "Character table for group 9600.cc downloaded from the LMFDB."; 
chartbl_9600_cc.Identifier:= " C4*F5*S5 "; 
chartbl_9600_cc.NrConjugacyClasses:= 140; 
chartbl_9600_cc.ConjugacyClasses:= [(), (2,3)(4,5), (7,9)(8,10), (2,3)(4,5)(7,9)(8,10), (1,11), (1,11)(2,3)(4,5), (1,11)(2,3)(4,5)(13,14), (1,13)(11,12), (1,11)(2,3)(4,5)(6,7)(9,10), (1,12)(6,10)(8,9), (1,14)(2,3)(4,5)(6,8)(7,10)(12,13), (1,14)(6,10)(8,9)(12,13), (12,13,14), (2,4,3,5), (2,5,3,4), (2,5,3,4)(7,10,9,8), (2,4,3,5)(7,8,9,10), (6,10,8,7), (6,7,8,10), (2,3)(4,5)(6,10,7,9), (2,3)(4,5)(6,9,7,10), (2,4,3,5)(6,10)(8,9), (2,5,3,4)(6,10)(8,9), (2,4,3,5)(7,10,9,8), (2,5,3,4)(7,8,9,10), (1,11)(2,5,3,4), (1,11)(2,4,3,5), (2,4,3,5)(11,12)(13,14), (2,5,3,4)(11,12)(13,14), (1,14,13,12), (1,11,13,12)(2,3)(4,5), (1,14,11,13)(2,5,3,4), (1,13,11,14)(2,4,3,5), (1,11)(2,5,3,4)(6,9)(7,8), (1,11)(2,4,3,5)(6,9)(7,8), (1,11)(6,9,7,10), (1,11)(6,10,7,9), (1,11)(2,4,3,5)(7,8,9,10), (1,11)(2,5,3,4)(7,10,9,8), (1,11)(2,3)(4,5)(6,10,7,9), (1,11)(2,3)(4,5)(6,9,7,10), (1,11)(2,5,3,4)(6,9,7,10), (1,11)(2,4,3,5)(6,10,7,9), (7,8,9,10)(11,12)(13,14), (7,10,9,8)(11,12)(13,14), (2,3)(4,5)(7,8,9,10)(11,12)(13,14), (2,3)(4,5)(7,10,9,8)(11,12)(13,14), (2,4,3,5)(7,8,9,10)(11,12)(13,14), (2,5,3,4)(7,10,9,8)(11,12)(13,14), (2,4,3,5)(7,9)(8,10)(11,12)(13,14), (2,5,3,4)(7,9)(8,10)(11,12)(13,14), (2,4,3,5)(7,10,9,8)(11,12)(13,14), (2,5,3,4)(7,8,9,10)(11,12)(13,14), (1,11,13,12)(2,3)(4,5)(7,9)(8,10), (6,10)(8,9)(11,13,14,12), (1,12,14,13)(2,5,3,4)(6,7,8,10), (1,13,14,12)(2,4,3,5)(6,10,8,7), (1,13,11,14)(2,5,3,4)(6,8)(7,10), (1,14,11,13)(2,4,3,5)(6,8)(7,10), (1,11,12,14)(2,4,3,5)(7,10,9,8), (1,14,12,11)(2,5,3,4)(7,8,9,10), (1,13,14,12)(6,9,10,8), (1,12,14,13)(6,8,10,9), (1,13,11,12)(2,3)(4,5)(6,8,10,9), (1,12,11,13)(2,3)(4,5)(6,9,10,8), (6,9,8,10,7), (1,14,13,12,11), (1,14,13,12,11)(6,9,8,10,7), (1,11)(12,14,13), (1,11)(2,3)(4,5)(12,14,13), (2,3)(4,5)(12,13,14), (1,11)(2,3)(4,5)(6,7)(9,10)(12,13,14), (6,7)(9,10)(12,14,13), (2,3)(4,5)(7,9)(8,10)(12,13,14), (1,12)(6,10)(8,9)(11,14,13), (2,3)(4,5)(6,10,9,7,8), (1,12,14,11,13)(2,3)(4,5), (1,11)(6,8,7,9,10), (1,11)(2,3)(4,5)(6,8,7,9,10), (1,11)(2,3)(4,5)(6,7,10,8,9)(13,14), (1,13)(6,8,7,9,10)(12,14), (1,12,14,11,13)(2,3)(4,5)(6,10,9,7,8), (1,14,12,11,13)(6,8)(7,10), (1,14,13,11,12)(2,3)(4,5)(7,9)(8,10), (2,4,3,5)(12,14,13), (2,5,3,4)(12,13,14), (1,11)(2,4,3,5)(12,14,13), (1,11)(2,5,3,4)(12,13,14), (1,11)(2,4,3,5)(6,9)(7,8)(12,13,14), (1,11)(2,5,3,4)(6,9)(7,8)(12,14,13), (1,11)(6,10,7,9)(12,13,14), (1,11)(6,9,7,10)(12,14,13), (2,4,3,5)(7,8,9,10)(12,14,13), (2,5,3,4)(7,10,9,8)(12,13,14), (1,11)(2,5,3,4)(7,10,9,8)(12,13,14), (1,11)(2,4,3,5)(7,8,9,10)(12,14,13), (1,11)(2,3)(4,5)(6,9,7,10)(12,14,13), (1,11)(2,3)(4,5)(6,10,7,9)(12,13,14), (1,11)(2,4,3,5)(6,10,7,9)(12,13,14), (1,11)(2,5,3,4)(6,9,7,10)(12,14,13), (2,3)(4,5)(6,9,7,10)(12,14,13), (2,3)(4,5)(6,10,7,9)(12,13,14), (6,10,7,9)(11,14,13), (6,9,7,10)(11,13,14), (1,12,13)(2,4,3,5)(6,10,7,9), (1,13,12)(2,5,3,4)(6,9,7,10), (2,4,3,5)(7,9)(8,10)(12,13,14), (2,5,3,4)(7,9)(8,10)(12,14,13), (6,10,9,7,8)(12,14,13), (2,5,3,4)(6,8,7,9,10), (2,4,3,5)(6,10,9,7,8), (1,11,12,13,14)(2,4,3,5), (1,11,12,13,14)(2,5,3,4), (1,11)(2,5,3,4)(6,8,7,9,10), (1,11)(2,4,3,5)(6,10,9,7,8), (2,4,3,5)(6,7,10,8,9)(11,12)(13,14), (2,5,3,4)(6,7,10,8,9)(11,12)(13,14), (1,11,12,13,14)(2,4,3,5)(6,7,10,8,9), (1,11,12,13,14)(2,5,3,4)(6,7,10,8,9), (1,14,13,12)(6,9,8,10,7), (1,11,13,12)(2,3)(4,5)(6,7,10,8,9), (1,11,14,13,12)(6,10,8,7), (1,12,13,14,11)(6,7,8,10), (1,11,14,12,13)(2,5,3,4)(7,10,9,8), (1,13,12,14,11)(2,4,3,5)(7,8,9,10), (1,14,11,13)(2,5,3,4)(6,8,7,9,10), (1,13,11,14)(2,4,3,5)(6,10,9,7,8), (1,12,13,14,11)(2,3)(4,5)(6,7,8,10), (1,11,14,13,12)(2,3)(4,5)(6,10,8,7), (1,14,11,12,13)(2,4,3,5)(6,10)(8,9), (1,13,12,11,14)(2,5,3,4)(6,10)(8,9), (1,11,13,12,14)(2,4,3,5)(7,10,9,8), (1,14,12,13,11)(2,5,3,4)(7,8,9,10), (1,11)(6,7,10,8,9)(12,13,14), (1,11)(2,3)(4,5)(6,7,10,8,9)(12,13,14), (2,3)(4,5)(6,10,9,7,8)(12,14,13), (2,4,3,5)(6,7,10,8,9)(12,13,14), (2,5,3,4)(6,7,10,8,9)(12,13,14), (1,11)(2,4,3,5)(6,7,10,8,9)(12,13,14), (1,11)(2,5,3,4)(6,7,10,8,9)(12,13,14)];
chartbl_9600_cc.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];
chartbl_9600_cc.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 2, 2, 4, 4, 3, 3, 3, 3, 2, 2, 4, 4, 2, 2, 2, 2, 8, 8, 7, 7, 2, 2, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 2, 2, 4, 4, 8, 8, 11, 11, 7, 7, 11, 11, 12, 12, 12, 12, 66, 67, 68, 13, 13, 13, 13, 13, 13, 13, 66, 67, 66, 66, 66, 66, 68, 67, 67, 71, 71, 71, 71, 71, 71, 73, 73, 74, 74, 74, 74, 73, 73, 74, 74, 73, 73, 73, 73, 74, 74, 71, 71, 109, 76, 76, 77, 77, 76, 76, 76, 76, 82, 82, 81, 81, 83, 83, 84, 84, 80, 80, 83, 83, 77, 77, 84, 84, 109, 109, 109, 136, 136, 136, 136], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 30, 31, 33, 32, 35, 34, 37, 36, 39, 38, 41, 40, 43, 42, 45, 44, 47, 46, 49, 48, 51, 50, 53, 52, 54, 55, 57, 56, 59, 58, 61, 60, 63, 62, 65, 64, 66, 67, 68, 5, 6, 2, 9, 3, 4, 10, 76, 77, 78, 79, 80, 81, 82, 83, 84, 15, 14, 26, 27, 34, 35, 36, 37, 16, 17, 38, 39, 40, 41, 42, 43, 20, 21, 18, 19, 25, 24, 23, 22, 66, 111, 110, 113, 112, 115, 114, 117, 116, 119, 118, 120, 121, 123, 122, 125, 124, 127, 126, 129, 128, 131, 130, 133, 132, 78, 79, 76, 110, 111, 114, 115], [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, 1, 1, 1, 69, 70, 71, 72, 73, 74, 75, 2, 2, 5, 6, 7, 8, 2, 3, 4, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 13, 15, 14, 14, 15, 26, 27, 28, 29, 14, 15, 30, 31, 18, 19, 16, 17, 32, 33, 20, 21, 22, 23, 24, 25, 69, 70, 71, 85, 86, 87, 88]];
chartbl_9600_cc.SizesCentralizers:= [9600, 9600, 1920, 1920, 960, 960, 640, 640, 192, 192, 128, 128, 480, 9600, 9600, 1920, 1920, 1920, 1920, 1920, 1920, 1920, 1920, 1920, 1920, 960, 960, 640, 640, 320, 320, 320, 320, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 2400, 400, 100, 480, 480, 480, 96, 96, 96, 96, 2400, 400, 240, 240, 160, 160, 100, 80, 80, 480, 480, 480, 480, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 120, 2400, 2400, 400, 400, 240, 240, 160, 160, 100, 100, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 120, 120, 120, 120, 120, 120, 120];
chartbl_9600_cc.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "3A", "4A1", "4A-1", "4B1", "4B-1", "4C1", "4C-1", "4D1", "4D-1", "4E1", "4E-1", "4F1", "4F-1", "4G1", "4G-1", "4H1", "4H-1", "4I", "4J", "4K1", "4K-1", "4L1", "4L-1", "4M1", "4M-1", "4N1", "4N-1", "4O1", "4O-1", "4P1", "4P-1", "4Q1", "4Q-1", "4R1", "4R-1", "4S1", "4S-1", "4T1", "4T-1", "4U1", "4U-1", "4V", "4W", "4X1", "4X-1", "4Y1", "4Y-1", "4Z1", "4Z-1", "4AA1", "4AA-1", "4AB1", "4AB-1", "5A", "5B", "5C", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "10A", "10B", "10C", "10D", "10E", "10F", "10G", "10H", "10I", "12A1", "12A-1", "12B1", "12B-1", "12C1", "12C-1", "12D1", "12D-1", "12E1", "12E-1", "12F1", "12F-1", "12G1", "12G-1", "12H1", "12H-1", "12I1", "12I-1", "12J1", "12J-1", "12K1", "12K-1", "12L1", "12L-1", "15A", "20A1", "20A-1", "20B1", "20B-1", "20C1", "20C-1", "20D1", "20D-1", "20E1", "20E-1", "20F", "20G", "20H1", "20H-1", "20I1", "20I-1", "20J1", "20J-1", "20K1", "20K-1", "20L1", "20L-1", "20M1", "20M-1", "30A", "30B", "30C", "60A1", "60A-1", "60B1", "60B-1"];
chartbl_9600_cc.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 60, 60, 60, 60];
chartbl_9600_cc.Irr:= [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1], [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, -6, 4, 0, 0, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -4, -4, 0, 0, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 24, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 24, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, -6, 4, 0, 0, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 4, 4, 0, 0, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, -24, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, -24*E(4), 24*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8*E(4), -8*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, -2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6*E(4), 6*E(4), -4*E(4), 4*E(4), 0, 0, -2*E(4), 2*E(4), E(4), -1*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, -24, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 24*E(4), -24*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8*E(4), 8*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, -2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6*E(4), -6*E(4), 4*E(4), -4*E(4), 0, 0, 2*E(4), -2*E(4), -1*E(4), E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_9600_cc);