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G = C42⋊6D15order 480 = 25·3·5

5th semidirect product of C42 and D15 acting via D15/C15=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C30 — C42⋊6D15
 Chief series C1 — C5 — C15 — C30 — C2×C30 — C22×D15 — C2×D60 — C42⋊6D15
 Lower central C15 — C2×C30 — C42⋊6D15
 Upper central C1 — C22 — C42

Generators and relations for C426D15
G = < a,b,c,d | a4=b4=c15=d2=1, ab=ba, ac=ca, dad=a-1, bc=cb, dbd=b-1, dcd=c-1 >

Subgroups: 1860 in 216 conjugacy classes, 71 normal (13 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×6], C22, C22 [×12], C5, S3 [×4], C6 [×3], C2×C4 [×3], D4 [×12], C23 [×4], D5 [×4], C10 [×3], C12 [×6], D6 [×12], C2×C6, C15, C42, C2×D4 [×6], C20 [×6], D10 [×12], C2×C10, D12 [×12], C2×C12 [×3], C22×S3 [×4], D15 [×4], C30 [×3], C41D4, D20 [×12], C2×C20 [×3], C22×D5 [×4], C4×C12, C2×D12 [×6], C60 [×6], D30 [×12], C2×C30, C4×C20, C2×D20 [×6], C4⋊D12, D60 [×12], C2×C60 [×3], C22×D15 [×4], C204D4, C4×C60, C2×D60 [×6], C426D15
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×6], C23, D5, D6 [×3], C2×D4 [×3], D10 [×3], D12 [×6], C22×S3, D15, C41D4, D20 [×6], C22×D5, C2×D12 [×3], D30 [×3], C2×D20 [×3], C4⋊D12, D60 [×6], C22×D15, C204D4, C2×D60 [×3], C426D15

Smallest permutation representation of C426D15
On 240 points
Generators in S240
```(1 140 17 129)(2 141 18 130)(3 142 19 131)(4 143 20 132)(5 144 21 133)(6 145 22 134)(7 146 23 135)(8 147 24 121)(9 148 25 122)(10 149 26 123)(11 150 27 124)(12 136 28 125)(13 137 29 126)(14 138 30 127)(15 139 16 128)(31 173 60 162)(32 174 46 163)(33 175 47 164)(34 176 48 165)(35 177 49 151)(36 178 50 152)(37 179 51 153)(38 180 52 154)(39 166 53 155)(40 167 54 156)(41 168 55 157)(42 169 56 158)(43 170 57 159)(44 171 58 160)(45 172 59 161)(61 204 80 185)(62 205 81 186)(63 206 82 187)(64 207 83 188)(65 208 84 189)(66 209 85 190)(67 210 86 191)(68 196 87 192)(69 197 88 193)(70 198 89 194)(71 199 90 195)(72 200 76 181)(73 201 77 182)(74 202 78 183)(75 203 79 184)(91 230 106 222)(92 231 107 223)(93 232 108 224)(94 233 109 225)(95 234 110 211)(96 235 111 212)(97 236 112 213)(98 237 113 214)(99 238 114 215)(100 239 115 216)(101 240 116 217)(102 226 117 218)(103 227 118 219)(104 228 119 220)(105 229 120 221)
(1 95 32 65)(2 96 33 66)(3 97 34 67)(4 98 35 68)(5 99 36 69)(6 100 37 70)(7 101 38 71)(8 102 39 72)(9 103 40 73)(10 104 41 74)(11 105 42 75)(12 91 43 61)(13 92 44 62)(14 93 45 63)(15 94 31 64)(16 109 60 83)(17 110 46 84)(18 111 47 85)(19 112 48 86)(20 113 49 87)(21 114 50 88)(22 115 51 89)(23 116 52 90)(24 117 53 76)(25 118 54 77)(26 119 55 78)(27 120 56 79)(28 106 57 80)(29 107 58 81)(30 108 59 82)(121 218 155 181)(122 219 156 182)(123 220 157 183)(124 221 158 184)(125 222 159 185)(126 223 160 186)(127 224 161 187)(128 225 162 188)(129 211 163 189)(130 212 164 190)(131 213 165 191)(132 214 151 192)(133 215 152 193)(134 216 153 194)(135 217 154 195)(136 230 170 204)(137 231 171 205)(138 232 172 206)(139 233 173 207)(140 234 174 208)(141 235 175 209)(142 236 176 210)(143 237 177 196)(144 238 178 197)(145 239 179 198)(146 240 180 199)(147 226 166 200)(148 227 167 201)(149 228 168 202)(150 229 169 203)
(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)
(1 188)(2 187)(3 186)(4 185)(5 184)(6 183)(7 182)(8 181)(9 195)(10 194)(11 193)(12 192)(13 191)(14 190)(15 189)(16 208)(17 207)(18 206)(19 205)(20 204)(21 203)(22 202)(23 201)(24 200)(25 199)(26 198)(27 197)(28 196)(29 210)(30 209)(31 211)(32 225)(33 224)(34 223)(35 222)(36 221)(37 220)(38 219)(39 218)(40 217)(41 216)(42 215)(43 214)(44 213)(45 212)(46 233)(47 232)(48 231)(49 230)(50 229)(51 228)(52 227)(53 226)(54 240)(55 239)(56 238)(57 237)(58 236)(59 235)(60 234)(61 132)(62 131)(63 130)(64 129)(65 128)(66 127)(67 126)(68 125)(69 124)(70 123)(71 122)(72 121)(73 135)(74 134)(75 133)(76 147)(77 146)(78 145)(79 144)(80 143)(81 142)(82 141)(83 140)(84 139)(85 138)(86 137)(87 136)(88 150)(89 149)(90 148)(91 151)(92 165)(93 164)(94 163)(95 162)(96 161)(97 160)(98 159)(99 158)(100 157)(101 156)(102 155)(103 154)(104 153)(105 152)(106 177)(107 176)(108 175)(109 174)(110 173)(111 172)(112 171)(113 170)(114 169)(115 168)(116 167)(117 166)(118 180)(119 179)(120 178)```

`G:=sub<Sym(240)| (1,140,17,129)(2,141,18,130)(3,142,19,131)(4,143,20,132)(5,144,21,133)(6,145,22,134)(7,146,23,135)(8,147,24,121)(9,148,25,122)(10,149,26,123)(11,150,27,124)(12,136,28,125)(13,137,29,126)(14,138,30,127)(15,139,16,128)(31,173,60,162)(32,174,46,163)(33,175,47,164)(34,176,48,165)(35,177,49,151)(36,178,50,152)(37,179,51,153)(38,180,52,154)(39,166,53,155)(40,167,54,156)(41,168,55,157)(42,169,56,158)(43,170,57,159)(44,171,58,160)(45,172,59,161)(61,204,80,185)(62,205,81,186)(63,206,82,187)(64,207,83,188)(65,208,84,189)(66,209,85,190)(67,210,86,191)(68,196,87,192)(69,197,88,193)(70,198,89,194)(71,199,90,195)(72,200,76,181)(73,201,77,182)(74,202,78,183)(75,203,79,184)(91,230,106,222)(92,231,107,223)(93,232,108,224)(94,233,109,225)(95,234,110,211)(96,235,111,212)(97,236,112,213)(98,237,113,214)(99,238,114,215)(100,239,115,216)(101,240,116,217)(102,226,117,218)(103,227,118,219)(104,228,119,220)(105,229,120,221), (1,95,32,65)(2,96,33,66)(3,97,34,67)(4,98,35,68)(5,99,36,69)(6,100,37,70)(7,101,38,71)(8,102,39,72)(9,103,40,73)(10,104,41,74)(11,105,42,75)(12,91,43,61)(13,92,44,62)(14,93,45,63)(15,94,31,64)(16,109,60,83)(17,110,46,84)(18,111,47,85)(19,112,48,86)(20,113,49,87)(21,114,50,88)(22,115,51,89)(23,116,52,90)(24,117,53,76)(25,118,54,77)(26,119,55,78)(27,120,56,79)(28,106,57,80)(29,107,58,81)(30,108,59,82)(121,218,155,181)(122,219,156,182)(123,220,157,183)(124,221,158,184)(125,222,159,185)(126,223,160,186)(127,224,161,187)(128,225,162,188)(129,211,163,189)(130,212,164,190)(131,213,165,191)(132,214,151,192)(133,215,152,193)(134,216,153,194)(135,217,154,195)(136,230,170,204)(137,231,171,205)(138,232,172,206)(139,233,173,207)(140,234,174,208)(141,235,175,209)(142,236,176,210)(143,237,177,196)(144,238,178,197)(145,239,179,198)(146,240,180,199)(147,226,166,200)(148,227,167,201)(149,228,168,202)(150,229,169,203), (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), (1,188)(2,187)(3,186)(4,185)(5,184)(6,183)(7,182)(8,181)(9,195)(10,194)(11,193)(12,192)(13,191)(14,190)(15,189)(16,208)(17,207)(18,206)(19,205)(20,204)(21,203)(22,202)(23,201)(24,200)(25,199)(26,198)(27,197)(28,196)(29,210)(30,209)(31,211)(32,225)(33,224)(34,223)(35,222)(36,221)(37,220)(38,219)(39,218)(40,217)(41,216)(42,215)(43,214)(44,213)(45,212)(46,233)(47,232)(48,231)(49,230)(50,229)(51,228)(52,227)(53,226)(54,240)(55,239)(56,238)(57,237)(58,236)(59,235)(60,234)(61,132)(62,131)(63,130)(64,129)(65,128)(66,127)(67,126)(68,125)(69,124)(70,123)(71,122)(72,121)(73,135)(74,134)(75,133)(76,147)(77,146)(78,145)(79,144)(80,143)(81,142)(82,141)(83,140)(84,139)(85,138)(86,137)(87,136)(88,150)(89,149)(90,148)(91,151)(92,165)(93,164)(94,163)(95,162)(96,161)(97,160)(98,159)(99,158)(100,157)(101,156)(102,155)(103,154)(104,153)(105,152)(106,177)(107,176)(108,175)(109,174)(110,173)(111,172)(112,171)(113,170)(114,169)(115,168)(116,167)(117,166)(118,180)(119,179)(120,178)>;`

`G:=Group( (1,140,17,129)(2,141,18,130)(3,142,19,131)(4,143,20,132)(5,144,21,133)(6,145,22,134)(7,146,23,135)(8,147,24,121)(9,148,25,122)(10,149,26,123)(11,150,27,124)(12,136,28,125)(13,137,29,126)(14,138,30,127)(15,139,16,128)(31,173,60,162)(32,174,46,163)(33,175,47,164)(34,176,48,165)(35,177,49,151)(36,178,50,152)(37,179,51,153)(38,180,52,154)(39,166,53,155)(40,167,54,156)(41,168,55,157)(42,169,56,158)(43,170,57,159)(44,171,58,160)(45,172,59,161)(61,204,80,185)(62,205,81,186)(63,206,82,187)(64,207,83,188)(65,208,84,189)(66,209,85,190)(67,210,86,191)(68,196,87,192)(69,197,88,193)(70,198,89,194)(71,199,90,195)(72,200,76,181)(73,201,77,182)(74,202,78,183)(75,203,79,184)(91,230,106,222)(92,231,107,223)(93,232,108,224)(94,233,109,225)(95,234,110,211)(96,235,111,212)(97,236,112,213)(98,237,113,214)(99,238,114,215)(100,239,115,216)(101,240,116,217)(102,226,117,218)(103,227,118,219)(104,228,119,220)(105,229,120,221), (1,95,32,65)(2,96,33,66)(3,97,34,67)(4,98,35,68)(5,99,36,69)(6,100,37,70)(7,101,38,71)(8,102,39,72)(9,103,40,73)(10,104,41,74)(11,105,42,75)(12,91,43,61)(13,92,44,62)(14,93,45,63)(15,94,31,64)(16,109,60,83)(17,110,46,84)(18,111,47,85)(19,112,48,86)(20,113,49,87)(21,114,50,88)(22,115,51,89)(23,116,52,90)(24,117,53,76)(25,118,54,77)(26,119,55,78)(27,120,56,79)(28,106,57,80)(29,107,58,81)(30,108,59,82)(121,218,155,181)(122,219,156,182)(123,220,157,183)(124,221,158,184)(125,222,159,185)(126,223,160,186)(127,224,161,187)(128,225,162,188)(129,211,163,189)(130,212,164,190)(131,213,165,191)(132,214,151,192)(133,215,152,193)(134,216,153,194)(135,217,154,195)(136,230,170,204)(137,231,171,205)(138,232,172,206)(139,233,173,207)(140,234,174,208)(141,235,175,209)(142,236,176,210)(143,237,177,196)(144,238,178,197)(145,239,179,198)(146,240,180,199)(147,226,166,200)(148,227,167,201)(149,228,168,202)(150,229,169,203), (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), (1,188)(2,187)(3,186)(4,185)(5,184)(6,183)(7,182)(8,181)(9,195)(10,194)(11,193)(12,192)(13,191)(14,190)(15,189)(16,208)(17,207)(18,206)(19,205)(20,204)(21,203)(22,202)(23,201)(24,200)(25,199)(26,198)(27,197)(28,196)(29,210)(30,209)(31,211)(32,225)(33,224)(34,223)(35,222)(36,221)(37,220)(38,219)(39,218)(40,217)(41,216)(42,215)(43,214)(44,213)(45,212)(46,233)(47,232)(48,231)(49,230)(50,229)(51,228)(52,227)(53,226)(54,240)(55,239)(56,238)(57,237)(58,236)(59,235)(60,234)(61,132)(62,131)(63,130)(64,129)(65,128)(66,127)(67,126)(68,125)(69,124)(70,123)(71,122)(72,121)(73,135)(74,134)(75,133)(76,147)(77,146)(78,145)(79,144)(80,143)(81,142)(82,141)(83,140)(84,139)(85,138)(86,137)(87,136)(88,150)(89,149)(90,148)(91,151)(92,165)(93,164)(94,163)(95,162)(96,161)(97,160)(98,159)(99,158)(100,157)(101,156)(102,155)(103,154)(104,153)(105,152)(106,177)(107,176)(108,175)(109,174)(110,173)(111,172)(112,171)(113,170)(114,169)(115,168)(116,167)(117,166)(118,180)(119,179)(120,178) );`

`G=PermutationGroup([(1,140,17,129),(2,141,18,130),(3,142,19,131),(4,143,20,132),(5,144,21,133),(6,145,22,134),(7,146,23,135),(8,147,24,121),(9,148,25,122),(10,149,26,123),(11,150,27,124),(12,136,28,125),(13,137,29,126),(14,138,30,127),(15,139,16,128),(31,173,60,162),(32,174,46,163),(33,175,47,164),(34,176,48,165),(35,177,49,151),(36,178,50,152),(37,179,51,153),(38,180,52,154),(39,166,53,155),(40,167,54,156),(41,168,55,157),(42,169,56,158),(43,170,57,159),(44,171,58,160),(45,172,59,161),(61,204,80,185),(62,205,81,186),(63,206,82,187),(64,207,83,188),(65,208,84,189),(66,209,85,190),(67,210,86,191),(68,196,87,192),(69,197,88,193),(70,198,89,194),(71,199,90,195),(72,200,76,181),(73,201,77,182),(74,202,78,183),(75,203,79,184),(91,230,106,222),(92,231,107,223),(93,232,108,224),(94,233,109,225),(95,234,110,211),(96,235,111,212),(97,236,112,213),(98,237,113,214),(99,238,114,215),(100,239,115,216),(101,240,116,217),(102,226,117,218),(103,227,118,219),(104,228,119,220),(105,229,120,221)], [(1,95,32,65),(2,96,33,66),(3,97,34,67),(4,98,35,68),(5,99,36,69),(6,100,37,70),(7,101,38,71),(8,102,39,72),(9,103,40,73),(10,104,41,74),(11,105,42,75),(12,91,43,61),(13,92,44,62),(14,93,45,63),(15,94,31,64),(16,109,60,83),(17,110,46,84),(18,111,47,85),(19,112,48,86),(20,113,49,87),(21,114,50,88),(22,115,51,89),(23,116,52,90),(24,117,53,76),(25,118,54,77),(26,119,55,78),(27,120,56,79),(28,106,57,80),(29,107,58,81),(30,108,59,82),(121,218,155,181),(122,219,156,182),(123,220,157,183),(124,221,158,184),(125,222,159,185),(126,223,160,186),(127,224,161,187),(128,225,162,188),(129,211,163,189),(130,212,164,190),(131,213,165,191),(132,214,151,192),(133,215,152,193),(134,216,153,194),(135,217,154,195),(136,230,170,204),(137,231,171,205),(138,232,172,206),(139,233,173,207),(140,234,174,208),(141,235,175,209),(142,236,176,210),(143,237,177,196),(144,238,178,197),(145,239,179,198),(146,240,180,199),(147,226,166,200),(148,227,167,201),(149,228,168,202),(150,229,169,203)], [(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)], [(1,188),(2,187),(3,186),(4,185),(5,184),(6,183),(7,182),(8,181),(9,195),(10,194),(11,193),(12,192),(13,191),(14,190),(15,189),(16,208),(17,207),(18,206),(19,205),(20,204),(21,203),(22,202),(23,201),(24,200),(25,199),(26,198),(27,197),(28,196),(29,210),(30,209),(31,211),(32,225),(33,224),(34,223),(35,222),(36,221),(37,220),(38,219),(39,218),(40,217),(41,216),(42,215),(43,214),(44,213),(45,212),(46,233),(47,232),(48,231),(49,230),(50,229),(51,228),(52,227),(53,226),(54,240),(55,239),(56,238),(57,237),(58,236),(59,235),(60,234),(61,132),(62,131),(63,130),(64,129),(65,128),(66,127),(67,126),(68,125),(69,124),(70,123),(71,122),(72,121),(73,135),(74,134),(75,133),(76,147),(77,146),(78,145),(79,144),(80,143),(81,142),(82,141),(83,140),(84,139),(85,138),(86,137),(87,136),(88,150),(89,149),(90,148),(91,151),(92,165),(93,164),(94,163),(95,162),(96,161),(97,160),(98,159),(99,158),(100,157),(101,156),(102,155),(103,154),(104,153),(105,152),(106,177),(107,176),(108,175),(109,174),(110,173),(111,172),(112,171),(113,170),(114,169),(115,168),(116,167),(117,166),(118,180),(119,179),(120,178)])`

126 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 3 4A ··· 4F 5A 5B 6A 6B 6C 10A ··· 10F 12A ··· 12L 15A 15B 15C 15D 20A ··· 20X 30A ··· 30L 60A ··· 60AV order 1 2 2 2 2 2 2 2 3 4 ··· 4 5 5 6 6 6 10 ··· 10 12 ··· 12 15 15 15 15 20 ··· 20 30 ··· 30 60 ··· 60 size 1 1 1 1 60 60 60 60 2 2 ··· 2 2 2 2 2 2 2 ··· 2 2 ··· 2 2 2 2 2 2 ··· 2 2 ··· 2 2 ··· 2

126 irreducible representations

 dim 1 1 1 2 2 2 2 2 2 2 2 2 2 type + + + + + + + + + + + + + image C1 C2 C2 S3 D4 D5 D6 D10 D12 D15 D20 D30 D60 kernel C42⋊6D15 C4×C60 C2×D60 C4×C20 C60 C4×C12 C2×C20 C2×C12 C20 C42 C12 C2×C4 C4 # reps 1 1 6 1 6 2 3 6 12 4 24 12 48

Matrix representation of C426D15 in GL6(𝔽61)

 60 0 0 0 0 0 0 60 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 32 7 0 0 0 0 54 29
,
 60 0 0 0 0 0 0 60 0 0 0 0 0 0 25 57 0 0 0 0 4 36 0 0 0 0 0 0 29 54 0 0 0 0 7 32
,
 14 56 0 0 0 0 42 33 0 0 0 0 0 0 60 43 0 0 0 0 18 18 0 0 0 0 0 0 60 17 0 0 0 0 44 44
,
 60 1 0 0 0 0 0 1 0 0 0 0 0 0 25 27 0 0 0 0 4 36 0 0 0 0 0 0 60 17 0 0 0 0 0 1

`G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,32,54,0,0,0,0,7,29],[60,0,0,0,0,0,0,60,0,0,0,0,0,0,25,4,0,0,0,0,57,36,0,0,0,0,0,0,29,7,0,0,0,0,54,32],[14,42,0,0,0,0,56,33,0,0,0,0,0,0,60,18,0,0,0,0,43,18,0,0,0,0,0,0,60,44,0,0,0,0,17,44],[60,0,0,0,0,0,1,1,0,0,0,0,0,0,25,4,0,0,0,0,27,36,0,0,0,0,0,0,60,0,0,0,0,0,17,1] >;`

C426D15 in GAP, Magma, Sage, TeX

`C_4^2\rtimes_6D_{15}`
`% in TeX`

`G:=Group("C4^2:6D15");`
`// GroupNames label`

`G:=SmallGroup(480,839);`
`// by ID`

`G=gap.SmallGroup(480,839);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,120,254,58,2693,18822]);`
`// Polycyclic`

`G:=Group<a,b,c,d|a^4=b^4=c^15=d^2=1,a*b=b*a,a*c=c*a,d*a*d=a^-1,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;`
`// generators/relations`

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