# Group 1760.1272 downloaded from the LMFDB on 19 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(68087895572095937607106960000309,1760); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.4; e := GPC.6;
GPerm := Group( (2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,17)(18,19), (12,14)(13,15), (12,13)(14,15)(16,18)(17,19), (12,15)(13,14)(16,17)(18,19), (16,17)(18,19), (2,4,6,8,9)(3,5,7,10,11), (1,2,5,8,6,9,11,7,10,4,3) );
GLZN := Group([[[ZmodnZObj(1,44), ZmodnZObj(22,44)], [ZmodnZObj(0,44), ZmodnZObj(1,44)]],[[ZmodnZObj(23,44), ZmodnZObj(38,44)], [ZmodnZObj(22,44), ZmodnZObj(21,44)]],[[ZmodnZObj(23,44), ZmodnZObj(22,44)], [ZmodnZObj(22,44), ZmodnZObj(23,44)]],[[ZmodnZObj(1,44), ZmodnZObj(4,44)], [ZmodnZObj(0,44), ZmodnZObj(1,44)]],[[ZmodnZObj(1,44), ZmodnZObj(0,44)], [ZmodnZObj(0,44), ZmodnZObj(9,44)]],[[ZmodnZObj(43,44), ZmodnZObj(0,44)], [ZmodnZObj(0,44), ZmodnZObj(43,44)]],[[ZmodnZObj(23,44), ZmodnZObj(0,44)], [ZmodnZObj(0,44), ZmodnZObj(1,44)]]]);

 
# Booleans 
booleans_1760_1272 := rec( 
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_1760_1272:=rec(); 
chartbl_1760_1272.IsFinite:= true; 
chartbl_1760_1272.UnderlyingCharacteristic:= 0; 
chartbl_1760_1272.UnderlyingGroup:= GLZN;
chartbl_1760_1272.Size:= 1760;
chartbl_1760_1272.InfoText:= "Character table for group 1760.1272 downloaded from the LMFDB."; 
chartbl_1760_1272.Identifier:= " C2^4*F11 "; 
chartbl_1760_1272.NrConjugacyClasses:= 176; 
chartbl_1760_1272.ConjugacyClasses:= [[1, 0, 0, 1], [23, 0, 0, 1], [21, 22, 22, 21], [23, 22, 22, 23], [1, 22, 0, 1], [43, 22, 22, 21], [1, 22, 22, 23], [43, 0, 0, 43], [23, 22, 0, 1], [21, 0, 22, 21], [23, 0, 22, 23], [21, 0, 0, 43], [43, 0, 22, 21], [1, 0, 22, 23], [43, 22, 0, 43], [21, 22, 0, 43], [43, 28, 0, 1], [21, 20, 0, 1], [23, 38, 22, 21], [21, 6, 22, 23], [43, 6, 0, 1], [1, 2, 22, 21], [43, 42, 22, 23], [1, 16, 0, 43], [21, 42, 0, 1], [23, 16, 22, 21], [21, 28, 22, 23], [23, 24, 0, 43], [1, 24, 22, 21], [43, 20, 22, 23], [1, 38, 0, 43], [23, 2, 0, 43], [1, 20, 0, 37], [1, 28, 0, 25], [1, 12, 0, 5], [1, 24, 0, 9], [43, 8, 0, 9], [43, 40, 0, 5], [43, 12, 0, 25], [43, 4, 0, 37], [23, 16, 0, 37], [23, 24, 0, 25], [23, 20, 0, 9], [23, 8, 0, 5], [21, 12, 0, 9], [21, 0, 0, 5], [21, 16, 0, 25], [21, 8, 0, 37], [21, 2, 22, 29], [21, 38, 22, 41], [21, 42, 22, 13], [21, 10, 22, 17], [23, 14, 22, 13], [23, 26, 22, 17], [23, 10, 22, 41], [23, 18, 22, 29], [23, 42, 22, 15], [23, 6, 22, 3], [23, 2, 22, 31], [23, 34, 22, 27], [21, 30, 22, 31], [21, 18, 22, 27], [21, 34, 22, 3], [21, 26, 22, 15], [1, 42, 0, 37], [1, 6, 0, 25], [1, 2, 0, 9], [1, 34, 0, 5], [43, 30, 0, 9], [43, 18, 0, 5], [43, 34, 0, 25], [43, 26, 0, 37], [43, 6, 22, 29], [43, 42, 22, 41], [43, 2, 22, 13], [43, 14, 22, 17], [1, 10, 22, 13], [1, 22, 22, 17], [1, 6, 22, 41], [1, 14, 22, 29], [1, 38, 22, 15], [1, 2, 22, 3], [1, 42, 22, 31], [1, 30, 22, 27], [43, 34, 22, 31], [43, 22, 22, 27], [43, 38, 22, 3], [43, 30, 22, 15], [43, 24, 0, 7], [43, 16, 0, 19], [43, 20, 0, 35], [43, 32, 0, 39], [1, 36, 0, 35], [1, 4, 0, 39], [1, 32, 0, 19], [1, 40, 0, 7], [23, 38, 0, 37], [23, 2, 0, 25], [23, 42, 0, 9], [23, 30, 0, 5], [21, 34, 0, 9], [21, 22, 0, 5], [21, 38, 0, 25], [21, 30, 0, 37], [21, 24, 22, 29], [21, 16, 22, 41], [21, 20, 22, 13], [21, 32, 22, 17], [23, 36, 22, 13], [23, 4, 22, 17], [23, 32, 22, 41], [23, 40, 22, 29], [23, 20, 22, 15], [23, 28, 22, 3], [23, 24, 22, 31], [23, 12, 22, 27], [21, 8, 22, 31], [21, 40, 22, 27], [21, 12, 22, 3], [21, 4, 22, 15], [21, 28, 0, 7], [21, 20, 0, 19], [21, 24, 0, 35], [21, 36, 0, 39], [23, 32, 0, 35], [23, 0, 0, 39], [23, 28, 0, 19], [23, 36, 0, 7], [43, 28, 22, 29], [43, 20, 22, 41], [43, 24, 22, 13], [43, 36, 22, 17], [1, 32, 22, 13], [1, 0, 22, 17], [1, 28, 22, 41], [1, 36, 22, 29], [1, 16, 22, 15], [1, 24, 22, 3], [1, 20, 22, 31], [1, 8, 22, 27], [43, 12, 22, 31], [43, 0, 22, 27], [43, 16, 22, 3], [43, 8, 22, 15], [43, 2, 0, 7], [43, 38, 0, 19], [43, 42, 0, 35], [43, 10, 0, 39], [1, 14, 0, 35], [1, 26, 0, 39], [1, 10, 0, 19], [1, 18, 0, 7], [21, 6, 0, 7], [21, 42, 0, 19], [21, 2, 0, 35], [21, 14, 0, 39], [23, 10, 0, 35], [23, 22, 0, 39], [23, 6, 0, 19], [23, 14, 0, 7], [1, 36, 0, 1], [23, 40, 0, 1], [21, 30, 22, 21], [43, 26, 22, 21], [23, 14, 22, 23], [1, 18, 22, 23], [1, 14, 0, 1], [23, 18, 0, 1], [43, 8, 0, 43], [21, 4, 0, 43], [21, 8, 22, 21], [43, 4, 22, 21], [23, 36, 22, 23], [1, 40, 22, 23], [43, 30, 0, 43], [21, 26, 0, 43]];
chartbl_1760_1272.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];
chartbl_1760_1272.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 35, 36, 34, 33, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 35, 36, 33, 34, 33, 34, 36, 35, 161, 161, 161, 161, 161, 161, 161, 161, 161, 161, 161, 161, 161, 161, 161, 161], [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, 1, 1, 1, 1, 17, 17, 17, 17, 2, 2, 2, 2, 18, 18, 18, 18, 3, 3, 3, 3, 19, 19, 19, 19, 4, 4, 4, 4, 20, 20, 20, 20, 5, 5, 5, 5, 21, 21, 21, 21, 6, 6, 6, 6, 22, 22, 22, 22, 7, 7, 7, 7, 23, 23, 23, 23, 8, 8, 8, 8, 24, 24, 24, 24, 9, 9, 9, 9, 25, 25, 25, 25, 10, 10, 10, 10, 26, 26, 26, 26, 11, 11, 11, 11, 27, 27, 27, 27, 12, 12, 12, 12, 28, 28, 28, 28, 13, 13, 13, 13, 29, 29, 29, 29, 14, 14, 14, 14, 30, 30, 30, 30, 15, 15, 15, 15, 31, 31, 31, 31, 16, 16, 16, 16, 32, 32, 32, 32, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176], [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, 1, 2, 3, 6, 4, 7, 5, 9, 8, 12, 10, 13, 11, 14, 15, 16]];
chartbl_1760_1272.SizesCentralizers:= [1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 1760, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176, 176];
chartbl_1760_1272.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "2T", "2U", "2V", "2W", "2X", "2Y", "2Z", "2AA", "2AB", "2AC", "2AD", "2AE", "5A1", "5A-1", "5A2", "5A-2", "10A1", "10A-1", "10A3", "10A-3", "10B1", "10B-1", "10B3", "10B-3", "10C1", "10C-1", "10C3", "10C-3", "10D1", "10D-1", "10D3", "10D-3", "10E1", "10E-1", "10E3", "10E-3", "10F1", "10F-1", "10F3", "10F-3", "10G1", "10G-1", "10G3", "10G-3", "10H1", "10H-1", "10H3", "10H-3", "10I1", "10I-1", "10I3", "10I-3", "10J1", "10J-1", "10J3", "10J-3", "10K1", "10K-1", "10K3", "10K-3", "10L1", "10L-1", "10L3", "10L-3", "10M1", "10M-1", "10M3", "10M-3", "10N1", "10N-1", "10N3", "10N-3", "10O1", "10O-1", "10O3", "10O-3", "10P1", "10P-1", "10P3", "10P-3", "10Q1", "10Q-1", "10Q3", "10Q-3", "10R1", "10R-1", "10R3", "10R-3", "10S1", "10S-1", "10S3", "10S-3", "10T1", "10T-1", "10T3", "10T-3", "10U1", "10U-1", "10U3", "10U-3", "10V1", "10V-1", "10V3", "10V-3", "10W1", "10W-1", "10W3", "10W-3", "10X1", "10X-1", "10X3", "10X-3", "10Y1", "10Y-1", "10Y3", "10Y-3", "10Z1", "10Z-1", "10Z3", "10Z-3", "10AA1", "10AA-1", "10AA3", "10AA-3", "10AB1", "10AB-1", "10AB3", "10AB-3", "10AC1", "10AC-1", "10AC3", "10AC-3", "10AD1", "10AD-1", "10AD3", "10AD-3", "10AE1", "10AE-1", "10AE3", "10AE-3", "11A", "22A", "22B", "22C", "22D", "22E", "22F", "22G", "22H", "22I", "22J", "22K", "22L", "22M", "22N", "22O"];
chartbl_1760_1272.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22];
chartbl_1760_1272.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, 1, 1, 1, 1, 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ConvertToLibraryCharacterTableNC(chartbl_1760_1272);