metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C13⋊C16, C26.C8, C52.2C4, C2.(C13⋊C8), C4.2(C13⋊C4), C13⋊2C8.2C2, SmallGroup(208,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C13⋊C16 |
Generators and relations for C13⋊C16
G = < a,b | a13=b16=1, bab-1=a5 >
Character table of C13⋊C16
| class | 1 | 2 | 4A | 4B | 8A | 8B | 8C | 8D | 13A | 13B | 13C | 16A | 16B | 16C | 16D | 16E | 16F | 16G | 16H | 26A | 26B | 26C | 52A | 52B | 52C | 52D | 52E | 52F | |
| size | 1 | 1 | 1 | 1 | 13 | 13 | 13 | 13 | 4 | 4 | 4 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 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 | i | -i | -i | -i | i | i | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ4 | 1 | 1 | 1 | 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 | linear of order 4 |
| ρ5 | 1 | 1 | -1 | -1 | i | -i | -i | i | 1 | 1 | 1 | ζ8 | ζ87 | ζ83 | ζ83 | ζ85 | ζ85 | ζ8 | ζ87 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ6 | 1 | 1 | -1 | -1 | -i | i | i | -i | 1 | 1 | 1 | ζ87 | ζ8 | ζ85 | ζ85 | ζ83 | ζ83 | ζ87 | ζ8 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ7 | 1 | 1 | -1 | -1 | i | -i | -i | i | 1 | 1 | 1 | ζ85 | ζ83 | ζ87 | ζ87 | ζ8 | ζ8 | ζ85 | ζ83 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ8 | 1 | 1 | -1 | -1 | -i | i | i | -i | 1 | 1 | 1 | ζ83 | ζ85 | ζ8 | ζ8 | ζ87 | ζ87 | ζ83 | ζ85 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ9 | 1 | -1 | -i | i | ζ1610 | ζ166 | ζ1614 | ζ162 | 1 | 1 | 1 | ζ165 | ζ163 | ζ167 | ζ1615 | ζ16 | ζ169 | ζ1613 | ζ1611 | -1 | -1 | -1 | -i | i | i | -i | i | -i | linear of order 16 |
| ρ10 | 1 | -1 | -i | i | ζ162 | ζ1614 | ζ166 | ζ1610 | 1 | 1 | 1 | ζ169 | ζ1615 | ζ163 | ζ1611 | ζ165 | ζ1613 | ζ16 | ζ167 | -1 | -1 | -1 | -i | i | i | -i | i | -i | linear of order 16 |
| ρ11 | 1 | -1 | i | -i | ζ1614 | ζ162 | ζ1610 | ζ166 | 1 | 1 | 1 | ζ167 | ζ16 | ζ1613 | ζ165 | ζ1611 | ζ163 | ζ1615 | ζ169 | -1 | -1 | -1 | i | -i | -i | i | -i | i | linear of order 16 |
| ρ12 | 1 | -1 | i | -i | ζ166 | ζ1610 | ζ162 | ζ1614 | 1 | 1 | 1 | ζ1611 | ζ1613 | ζ169 | ζ16 | ζ1615 | ζ167 | ζ163 | ζ165 | -1 | -1 | -1 | i | -i | -i | i | -i | i | linear of order 16 |
| ρ13 | 1 | -1 | -i | i | ζ162 | ζ1614 | ζ166 | ζ1610 | 1 | 1 | 1 | ζ16 | ζ167 | ζ1611 | ζ163 | ζ1613 | ζ165 | ζ169 | ζ1615 | -1 | -1 | -1 | -i | i | i | -i | i | -i | linear of order 16 |
| ρ14 | 1 | -1 | -i | i | ζ1610 | ζ166 | ζ1614 | ζ162 | 1 | 1 | 1 | ζ1613 | ζ1611 | ζ1615 | ζ167 | ζ169 | ζ16 | ζ165 | ζ163 | -1 | -1 | -1 | -i | i | i | -i | i | -i | linear of order 16 |
| ρ15 | 1 | -1 | i | -i | ζ1614 | ζ162 | ζ1610 | ζ166 | 1 | 1 | 1 | ζ1615 | ζ169 | ζ165 | ζ1613 | ζ163 | ζ1611 | ζ167 | ζ16 | -1 | -1 | -1 | i | -i | -i | i | -i | i | linear of order 16 |
| ρ16 | 1 | -1 | i | -i | ζ166 | ζ1610 | ζ162 | ζ1614 | 1 | 1 | 1 | ζ163 | ζ165 | ζ16 | ζ169 | ζ167 | ζ1615 | ζ1611 | ζ1613 | -1 | -1 | -1 | i | -i | -i | i | -i | i | linear of order 16 |
| ρ17 | 4 | 4 | 4 | 4 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ139+ζ137+ζ136+ζ134 | orthogonal lifted from C13⋊C4 |
| ρ18 | 4 | 4 | 4 | 4 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1311+ζ1310+ζ133+ζ132 | orthogonal lifted from C13⋊C4 |
| ρ19 | 4 | 4 | 4 | 4 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1312+ζ138+ζ135+ζ13 | orthogonal lifted from C13⋊C4 |
| ρ20 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | -ζ139-ζ137-ζ136-ζ134 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1311-ζ1310-ζ133-ζ132 | symplectic lifted from C13⋊C8, Schur index 2 |
| ρ21 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ139-ζ137-ζ136-ζ134 | symplectic lifted from C13⋊C8, Schur index 2 |
| ρ22 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1312-ζ138-ζ135-ζ13 | symplectic lifted from C13⋊C8, Schur index 2 |
| ρ23 | 4 | -4 | -4i | 4i | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | complex faithful, Schur index 4 |
| ρ24 | 4 | -4 | 4i | -4i | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | complex faithful, Schur index 4 |
| ρ25 | 4 | -4 | 4i | -4i | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | complex faithful, Schur index 4 |
| ρ26 | 4 | -4 | -4i | 4i | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | complex faithful, Schur index 4 |
| ρ27 | 4 | -4 | 4i | -4i | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | complex faithful, Schur index 4 |
| ρ28 | 4 | -4 | -4i | 4i | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | ζ43ζ1311+ζ43ζ1310+ζ43ζ133+ζ43ζ132 | ζ4ζ1311+ζ4ζ1310+ζ4ζ133+ζ4ζ132 | ζ4ζ139+ζ4ζ137+ζ4ζ136+ζ4ζ134 | ζ43ζ139+ζ43ζ137+ζ43ζ136+ζ43ζ134 | ζ4ζ1312+ζ4ζ138+ζ4ζ135+ζ4ζ13 | ζ43ζ1312+ζ43ζ138+ζ43ζ135+ζ43ζ13 | complex faithful, Schur index 4 |
►Regular action on 208 points
Generators in S208
(1 57 168 39 207 104 30 178 130 81 74 118 153)(2 105 75 169 179 154 208 82 58 31 119 40 131)(3 155 120 76 83 132 180 32 106 193 41 170 59)(4 133 42 121 17 60 84 194 156 181 171 77 107)(5 61 172 43 195 108 18 182 134 85 78 122 157)(6 109 79 173 183 158 196 86 62 19 123 44 135)(7 159 124 80 87 136 184 20 110 197 45 174 63)(8 137 46 125 21 64 88 198 160 185 175 65 111)(9 49 176 47 199 112 22 186 138 89 66 126 145)(10 97 67 161 187 146 200 90 50 23 127 48 139)(11 147 128 68 91 140 188 24 98 201 33 162 51)(12 141 34 113 25 52 92 202 148 189 163 69 99)(13 53 164 35 203 100 26 190 142 93 70 114 149)(14 101 71 165 191 150 204 94 54 27 115 36 143)(15 151 116 72 95 144 192 28 102 205 37 166 55)(16 129 38 117 29 56 96 206 152 177 167 73 103)
(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)
G:=sub<Sym(208)| (1,57,168,39,207,104,30,178,130,81,74,118,153)(2,105,75,169,179,154,208,82,58,31,119,40,131)(3,155,120,76,83,132,180,32,106,193,41,170,59)(4,133,42,121,17,60,84,194,156,181,171,77,107)(5,61,172,43,195,108,18,182,134,85,78,122,157)(6,109,79,173,183,158,196,86,62,19,123,44,135)(7,159,124,80,87,136,184,20,110,197,45,174,63)(8,137,46,125,21,64,88,198,160,185,175,65,111)(9,49,176,47,199,112,22,186,138,89,66,126,145)(10,97,67,161,187,146,200,90,50,23,127,48,139)(11,147,128,68,91,140,188,24,98,201,33,162,51)(12,141,34,113,25,52,92,202,148,189,163,69,99)(13,53,164,35,203,100,26,190,142,93,70,114,149)(14,101,71,165,191,150,204,94,54,27,115,36,143)(15,151,116,72,95,144,192,28,102,205,37,166,55)(16,129,38,117,29,56,96,206,152,177,167,73,103), (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)>;
G:=Group( (1,57,168,39,207,104,30,178,130,81,74,118,153)(2,105,75,169,179,154,208,82,58,31,119,40,131)(3,155,120,76,83,132,180,32,106,193,41,170,59)(4,133,42,121,17,60,84,194,156,181,171,77,107)(5,61,172,43,195,108,18,182,134,85,78,122,157)(6,109,79,173,183,158,196,86,62,19,123,44,135)(7,159,124,80,87,136,184,20,110,197,45,174,63)(8,137,46,125,21,64,88,198,160,185,175,65,111)(9,49,176,47,199,112,22,186,138,89,66,126,145)(10,97,67,161,187,146,200,90,50,23,127,48,139)(11,147,128,68,91,140,188,24,98,201,33,162,51)(12,141,34,113,25,52,92,202,148,189,163,69,99)(13,53,164,35,203,100,26,190,142,93,70,114,149)(14,101,71,165,191,150,204,94,54,27,115,36,143)(15,151,116,72,95,144,192,28,102,205,37,166,55)(16,129,38,117,29,56,96,206,152,177,167,73,103), (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) );
G=PermutationGroup([[(1,57,168,39,207,104,30,178,130,81,74,118,153),(2,105,75,169,179,154,208,82,58,31,119,40,131),(3,155,120,76,83,132,180,32,106,193,41,170,59),(4,133,42,121,17,60,84,194,156,181,171,77,107),(5,61,172,43,195,108,18,182,134,85,78,122,157),(6,109,79,173,183,158,196,86,62,19,123,44,135),(7,159,124,80,87,136,184,20,110,197,45,174,63),(8,137,46,125,21,64,88,198,160,185,175,65,111),(9,49,176,47,199,112,22,186,138,89,66,126,145),(10,97,67,161,187,146,200,90,50,23,127,48,139),(11,147,128,68,91,140,188,24,98,201,33,162,51),(12,141,34,113,25,52,92,202,148,189,163,69,99),(13,53,164,35,203,100,26,190,142,93,70,114,149),(14,101,71,165,191,150,204,94,54,27,115,36,143),(15,151,116,72,95,144,192,28,102,205,37,166,55),(16,129,38,117,29,56,96,206,152,177,167,73,103)], [(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)]])
C13⋊C16 is a maximal subgroup of
D13⋊C16 D26.C8 C52.C8
C13⋊C16 is a maximal quotient of C13⋊C32
Matrix representation of C13⋊C16 ►in GL4(𝔽5) generated by
| 2 | 0 | 3 | 2 |
| 3 | 1 | 2 | 3 |
| 1 | 0 | 2 | 3 |
| 4 | 4 | 2 | 4 |
| 0 | 2 | 1 | 0 |
| 3 | 0 | 2 | 2 |
| 4 | 0 | 0 | 0 |
| 1 | 0 | 2 | 0 |
G:=sub<GL(4,GF(5))| [2,3,1,4,0,1,0,4,3,2,2,2,2,3,3,4],[0,3,4,1,2,0,0,0,1,2,0,2,0,2,0,0] >;
C13⋊C16 in GAP, Magma, Sage, TeX
C_{13}\rtimes C_{16} % in TeX
G:=Group("C13:C16"); // GroupNames label
G:=SmallGroup(208,3);
// by ID
G=gap.SmallGroup(208,3);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-13,10,26,42,3204,2409]);
// Polycyclic
G:=Group<a,b|a^13=b^16=1,b*a*b^-1=a^5>;
// generators/relations
Export
Subgroup lattice of C13⋊C16 in TeX
Character table of C13⋊C16 in TeX