metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: D13⋊C8, C52.3C4, D26.2C4, Dic13.4C22, C13⋊C8⋊3C2, C13⋊1(C2×C8), C4.3(C13⋊C4), C26.1(C2×C4), (C4×D13).5C2, C2.1(C2×C13⋊C4), SmallGroup(208,28)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — D13⋊C8 |
Generators and relations for D13⋊C8
G = < a,b,c | a13=b2=c8=1, bab=a-1, cac-1=a5, cbc-1=a4b >
Character table of D13⋊C8
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 13A | 13B | 13C | 26A | 26B | 26C | 52A | 52B | 52C | 52D | 52E | 52F | |
| size | 1 | 1 | 13 | 13 | 1 | 1 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ3 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ4 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ5 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | i | -i | -i | i | i | -i | -i | i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ6 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -i | i | i | -i | -i | i | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ7 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | i | i | i | -i | -i | -i | -i | i | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 4 |
| ρ8 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -i | -i | -i | i | i | i | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 4 |
| ρ9 | 1 | -1 | 1 | -1 | -i | i | -i | i | ζ85 | ζ85 | ζ8 | ζ87 | ζ83 | ζ87 | ζ83 | ζ8 | 1 | 1 | 1 | -1 | -1 | -1 | -i | -i | i | i | i | -i | linear of order 8 |
| ρ10 | 1 | -1 | 1 | -1 | i | -i | i | -i | ζ83 | ζ83 | ζ87 | ζ8 | ζ85 | ζ8 | ζ85 | ζ87 | 1 | 1 | 1 | -1 | -1 | -1 | i | i | -i | -i | -i | i | linear of order 8 |
| ρ11 | 1 | -1 | -1 | 1 | -i | i | i | -i | ζ83 | ζ87 | ζ83 | ζ85 | ζ8 | ζ8 | ζ85 | ζ87 | 1 | 1 | 1 | -1 | -1 | -1 | -i | -i | i | i | i | -i | linear of order 8 |
| ρ12 | 1 | -1 | 1 | -1 | -i | i | -i | i | ζ8 | ζ8 | ζ85 | ζ83 | ζ87 | ζ83 | ζ87 | ζ85 | 1 | 1 | 1 | -1 | -1 | -1 | -i | -i | i | i | i | -i | linear of order 8 |
| ρ13 | 1 | -1 | -1 | 1 | i | -i | -i | i | ζ85 | ζ8 | ζ85 | ζ83 | ζ87 | ζ87 | ζ83 | ζ8 | 1 | 1 | 1 | -1 | -1 | -1 | i | i | -i | -i | -i | i | linear of order 8 |
| ρ14 | 1 | -1 | 1 | -1 | i | -i | i | -i | ζ87 | ζ87 | ζ83 | ζ85 | ζ8 | ζ85 | ζ8 | ζ83 | 1 | 1 | 1 | -1 | -1 | -1 | i | i | -i | -i | -i | i | linear of order 8 |
| ρ15 | 1 | -1 | -1 | 1 | -i | i | i | -i | ζ87 | ζ83 | ζ87 | ζ8 | ζ85 | ζ85 | ζ8 | ζ83 | 1 | 1 | 1 | -1 | -1 | -1 | -i | -i | i | i | i | -i | linear of order 8 |
| ρ16 | 1 | -1 | -1 | 1 | i | -i | -i | i | ζ8 | ζ85 | ζ8 | ζ87 | ζ83 | ζ83 | ζ87 | ζ85 | 1 | 1 | 1 | -1 | -1 | -1 | i | i | -i | -i | -i | i | linear of order 8 |
| ρ17 | 4 | 4 | 0 | 0 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ139-ζ137-ζ136-ζ134 | orthogonal lifted from C2×C13⋊C4 |
| ρ18 | 4 | 4 | 0 | 0 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1311-ζ1310-ζ133-ζ132 | orthogonal lifted from C2×C13⋊C4 |
| ρ19 | 4 | 4 | 0 | 0 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1312+ζ138+ζ135+ζ13 | orthogonal lifted from C13⋊C4 |
| ρ20 | 4 | 4 | 0 | 0 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1311+ζ1310+ζ133+ζ132 | orthogonal lifted from C13⋊C4 |
| ρ21 | 4 | 4 | 0 | 0 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1312-ζ138-ζ135-ζ13 | orthogonal lifted from C2×C13⋊C4 |
| ρ22 | 4 | 4 | 0 | 0 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ139+ζ137+ζ136+ζ134 | orthogonal lifted from C13⋊C4 |
| ρ23 | 4 | -4 | 0 | 0 | 4i | -4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | complex faithful, Schur index 2 |
| ρ24 | 4 | -4 | 0 | 0 | 4i | -4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | complex faithful, Schur index 2 |
| ρ25 | 4 | -4 | 0 | 0 | 4i | -4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | complex faithful, Schur index 2 |
| ρ26 | 4 | -4 | 0 | 0 | -4i | 4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | complex faithful, Schur index 2 |
| ρ27 | 4 | -4 | 0 | 0 | -4i | 4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | complex faithful, Schur index 2 |
| ρ28 | 4 | -4 | 0 | 0 | -4i | 4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | complex faithful, Schur index 2 |
►On 104 points
Generators in S104
(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)
(1 13)(2 12)(3 11)(4 10)(5 9)(6 8)(14 18)(15 17)(19 26)(20 25)(21 24)(22 23)(27 39)(28 38)(29 37)(30 36)(31 35)(32 34)(40 52)(41 51)(42 50)(43 49)(44 48)(45 47)(53 61)(54 60)(55 59)(56 58)(62 65)(63 64)(66 68)(69 78)(70 77)(71 76)(72 75)(73 74)(79 90)(80 89)(81 88)(82 87)(83 86)(84 85)(92 99)(93 98)(94 97)(95 96)(100 104)(101 103)
(1 96 40 74 23 85 27 64)(2 104 52 66 24 80 39 56)(3 99 51 71 25 88 38 61)(4 94 50 76 26 83 37 53)(5 102 49 68 14 91 36 58)(6 97 48 73 15 86 35 63)(7 92 47 78 16 81 34 55)(8 100 46 70 17 89 33 60)(9 95 45 75 18 84 32 65)(10 103 44 67 19 79 31 57)(11 98 43 72 20 87 30 62)(12 93 42 77 21 82 29 54)(13 101 41 69 22 90 28 59)
G:=sub<Sym(104)| (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), (1,13)(2,12)(3,11)(4,10)(5,9)(6,8)(14,18)(15,17)(19,26)(20,25)(21,24)(22,23)(27,39)(28,38)(29,37)(30,36)(31,35)(32,34)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(53,61)(54,60)(55,59)(56,58)(62,65)(63,64)(66,68)(69,78)(70,77)(71,76)(72,75)(73,74)(79,90)(80,89)(81,88)(82,87)(83,86)(84,85)(92,99)(93,98)(94,97)(95,96)(100,104)(101,103), (1,96,40,74,23,85,27,64)(2,104,52,66,24,80,39,56)(3,99,51,71,25,88,38,61)(4,94,50,76,26,83,37,53)(5,102,49,68,14,91,36,58)(6,97,48,73,15,86,35,63)(7,92,47,78,16,81,34,55)(8,100,46,70,17,89,33,60)(9,95,45,75,18,84,32,65)(10,103,44,67,19,79,31,57)(11,98,43,72,20,87,30,62)(12,93,42,77,21,82,29,54)(13,101,41,69,22,90,28,59)>;
G:=Group( (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), (1,13)(2,12)(3,11)(4,10)(5,9)(6,8)(14,18)(15,17)(19,26)(20,25)(21,24)(22,23)(27,39)(28,38)(29,37)(30,36)(31,35)(32,34)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(53,61)(54,60)(55,59)(56,58)(62,65)(63,64)(66,68)(69,78)(70,77)(71,76)(72,75)(73,74)(79,90)(80,89)(81,88)(82,87)(83,86)(84,85)(92,99)(93,98)(94,97)(95,96)(100,104)(101,103), (1,96,40,74,23,85,27,64)(2,104,52,66,24,80,39,56)(3,99,51,71,25,88,38,61)(4,94,50,76,26,83,37,53)(5,102,49,68,14,91,36,58)(6,97,48,73,15,86,35,63)(7,92,47,78,16,81,34,55)(8,100,46,70,17,89,33,60)(9,95,45,75,18,84,32,65)(10,103,44,67,19,79,31,57)(11,98,43,72,20,87,30,62)(12,93,42,77,21,82,29,54)(13,101,41,69,22,90,28,59) );
G=PermutationGroup([[(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)], [(1,13),(2,12),(3,11),(4,10),(5,9),(6,8),(14,18),(15,17),(19,26),(20,25),(21,24),(22,23),(27,39),(28,38),(29,37),(30,36),(31,35),(32,34),(40,52),(41,51),(42,50),(43,49),(44,48),(45,47),(53,61),(54,60),(55,59),(56,58),(62,65),(63,64),(66,68),(69,78),(70,77),(71,76),(72,75),(73,74),(79,90),(80,89),(81,88),(82,87),(83,86),(84,85),(92,99),(93,98),(94,97),(95,96),(100,104),(101,103)], [(1,96,40,74,23,85,27,64),(2,104,52,66,24,80,39,56),(3,99,51,71,25,88,38,61),(4,94,50,76,26,83,37,53),(5,102,49,68,14,91,36,58),(6,97,48,73,15,86,35,63),(7,92,47,78,16,81,34,55),(8,100,46,70,17,89,33,60),(9,95,45,75,18,84,32,65),(10,103,44,67,19,79,31,57),(11,98,43,72,20,87,30,62),(12,93,42,77,21,82,29,54),(13,101,41,69,22,90,28,59)]])
D13⋊C8 is a maximal subgroup of
C8×C13⋊C4 C104⋊C4 D52⋊1C4 D13.Q16 D13⋊M4(2) Dic26.C4 D52.C4
D13⋊C8 is a maximal quotient of D13⋊C16 D26.C8 C4×C13⋊C8 D26⋊C8 Dic13⋊C8
Matrix representation of D13⋊C8 ►in GL4(𝔽5) generated by
| 4 | 4 | 0 | 3 |
| 0 | 1 | 3 | 1 |
| 1 | 3 | 3 | 4 |
| 4 | 4 | 2 | 0 |
| 1 | 3 | 1 | 3 |
| 1 | 3 | 3 | 4 |
| 0 | 1 | 3 | 1 |
| 4 | 4 | 4 | 3 |
| 2 | 4 | 3 | 0 |
| 0 | 0 | 1 | 4 |
| 2 | 0 | 3 | 0 |
| 2 | 0 | 0 | 0 |
G:=sub<GL(4,GF(5))| [4,0,1,4,4,1,3,4,0,3,3,2,3,1,4,0],[1,1,0,4,3,3,1,4,1,3,3,4,3,4,1,3],[2,0,2,2,4,0,0,0,3,1,3,0,0,4,0,0] >;
D13⋊C8 in GAP, Magma, Sage, TeX
D_{13}\rtimes C_8 % in TeX
G:=Group("D13:C8"); // GroupNames label
G:=SmallGroup(208,28);
// by ID
G=gap.SmallGroup(208,28);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-13,20,46,42,3204,1214]);
// Polycyclic
G:=Group<a,b,c|a^13=b^2=c^8=1,b*a*b=a^-1,c*a*c^-1=a^5,c*b*c^-1=a^4*b>;
// generators/relations
Export
Subgroup lattice of D13⋊C8 in TeX
Character table of D13⋊C8 in TeX