Copied to
clipboard

## G = D5×Dic12order 480 = 25·3·5

### Direct product of D5 and Dic12

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — D5×Dic12
 Chief series C1 — C5 — C15 — C30 — C60 — D5×C12 — D5×Dic6 — D5×Dic12
 Lower central C15 — C30 — C60 — D5×Dic12
 Upper central C1 — C2 — C4 — C8

Generators and relations for D5×Dic12
G = < a,b,c,d | a5=b2=c24=1, d2=c12, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >

Subgroups: 636 in 120 conjugacy classes, 44 normal (30 characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×5], C22, C5, C6, C6 [×2], C8, C8, C2×C4 [×3], Q8 [×6], D5 [×2], C10, Dic3 [×4], C12, C12, C2×C6, C15, C2×C8, Q16 [×4], C2×Q8 [×2], Dic5, Dic5 [×2], C20, C20 [×2], D10, C24, C24, Dic6 [×2], Dic6 [×4], C2×Dic3 [×2], C2×C12, C3×D5 [×2], C30, C2×Q16, C52C8, C40, Dic10 [×4], C4×D5, C4×D5 [×2], C5×Q8 [×2], Dic12, Dic12 [×3], C2×C24, C2×Dic6 [×2], C5×Dic3 [×2], C3×Dic5, Dic15 [×2], C60, C6×D5, C8×D5, Dic20, C5⋊Q16 [×2], C5×Q16, Q8×D5 [×2], C2×Dic12, C3×C52C8, C120, D5×Dic3 [×2], C15⋊Q8 [×2], D5×C12, C5×Dic6 [×2], Dic30 [×2], D5×Q16, C5⋊Dic12 [×2], D5×C24, C5×Dic12, Dic60, D5×Dic6 [×2], D5×Dic12
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], Q16 [×2], C2×D4, D10 [×3], D12 [×2], C22×S3, C2×Q16, C22×D5, Dic12 [×2], C2×D12, S3×D5, D4×D5, C2×Dic12, C2×S3×D5, D5×Q16, D5×D12, D5×Dic12

Smallest permutation representation of D5×Dic12
On 240 points
Generators in S240
(1 38 104 206 63)(2 39 105 207 64)(3 40 106 208 65)(4 41 107 209 66)(5 42 108 210 67)(6 43 109 211 68)(7 44 110 212 69)(8 45 111 213 70)(9 46 112 214 71)(10 47 113 215 72)(11 48 114 216 49)(12 25 115 193 50)(13 26 116 194 51)(14 27 117 195 52)(15 28 118 196 53)(16 29 119 197 54)(17 30 120 198 55)(18 31 97 199 56)(19 32 98 200 57)(20 33 99 201 58)(21 34 100 202 59)(22 35 101 203 60)(23 36 102 204 61)(24 37 103 205 62)(73 183 130 162 220)(74 184 131 163 221)(75 185 132 164 222)(76 186 133 165 223)(77 187 134 166 224)(78 188 135 167 225)(79 189 136 168 226)(80 190 137 145 227)(81 191 138 146 228)(82 192 139 147 229)(83 169 140 148 230)(84 170 141 149 231)(85 171 142 150 232)(86 172 143 151 233)(87 173 144 152 234)(88 174 121 153 235)(89 175 122 154 236)(90 176 123 155 237)(91 177 124 156 238)(92 178 125 157 239)(93 179 126 158 240)(94 180 127 159 217)(95 181 128 160 218)(96 182 129 161 219)
(1 63)(2 64)(3 65)(4 66)(5 67)(6 68)(7 69)(8 70)(9 71)(10 72)(11 49)(12 50)(13 51)(14 52)(15 53)(16 54)(17 55)(18 56)(19 57)(20 58)(21 59)(22 60)(23 61)(24 62)(25 193)(26 194)(27 195)(28 196)(29 197)(30 198)(31 199)(32 200)(33 201)(34 202)(35 203)(36 204)(37 205)(38 206)(39 207)(40 208)(41 209)(42 210)(43 211)(44 212)(45 213)(46 214)(47 215)(48 216)(73 130)(74 131)(75 132)(76 133)(77 134)(78 135)(79 136)(80 137)(81 138)(82 139)(83 140)(84 141)(85 142)(86 143)(87 144)(88 121)(89 122)(90 123)(91 124)(92 125)(93 126)(94 127)(95 128)(96 129)(145 227)(146 228)(147 229)(148 230)(149 231)(150 232)(151 233)(152 234)(153 235)(154 236)(155 237)(156 238)(157 239)(158 240)(159 217)(160 218)(161 219)(162 220)(163 221)(164 222)(165 223)(166 224)(167 225)(168 226)
(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)
(1 231 13 219)(2 230 14 218)(3 229 15 217)(4 228 16 240)(5 227 17 239)(6 226 18 238)(7 225 19 237)(8 224 20 236)(9 223 21 235)(10 222 22 234)(11 221 23 233)(12 220 24 232)(25 73 37 85)(26 96 38 84)(27 95 39 83)(28 94 40 82)(29 93 41 81)(30 92 42 80)(31 91 43 79)(32 90 44 78)(33 89 45 77)(34 88 46 76)(35 87 47 75)(36 86 48 74)(49 163 61 151)(50 162 62 150)(51 161 63 149)(52 160 64 148)(53 159 65 147)(54 158 66 146)(55 157 67 145)(56 156 68 168)(57 155 69 167)(58 154 70 166)(59 153 71 165)(60 152 72 164)(97 177 109 189)(98 176 110 188)(99 175 111 187)(100 174 112 186)(101 173 113 185)(102 172 114 184)(103 171 115 183)(104 170 116 182)(105 169 117 181)(106 192 118 180)(107 191 119 179)(108 190 120 178)(121 214 133 202)(122 213 134 201)(123 212 135 200)(124 211 136 199)(125 210 137 198)(126 209 138 197)(127 208 139 196)(128 207 140 195)(129 206 141 194)(130 205 142 193)(131 204 143 216)(132 203 144 215)

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

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

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

60 conjugacy classes

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E 4F 5A 5B 6A 6B 6C 8A 8B 8C 8D 10A 10B 12A 12B 12C 12D 15A 15B 20A 20B 20C 20D 20E 20F 24A 24B 24C 24D 24E 24F 24G 24H 30A 30B 40A 40B 40C 40D 60A 60B 60C 60D 120A ··· 120H order 1 2 2 2 3 4 4 4 4 4 4 5 5 6 6 6 8 8 8 8 10 10 12 12 12 12 15 15 20 20 20 20 20 20 24 24 24 24 24 24 24 24 30 30 40 40 40 40 60 60 60 60 120 ··· 120 size 1 1 5 5 2 2 10 12 12 60 60 2 2 2 10 10 2 2 10 10 2 2 2 2 10 10 4 4 4 4 24 24 24 24 2 2 2 2 10 10 10 10 4 4 4 4 4 4 4 4 4 4 4 ··· 4

60 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 type + + + + + + + + + + + + + - + + + + - + + + - + - image C1 C2 C2 C2 C2 C2 S3 D4 D4 D5 D6 D6 D6 Q16 D10 D10 D12 D12 Dic12 S3×D5 D4×D5 C2×S3×D5 D5×Q16 D5×D12 D5×Dic12 kernel D5×Dic12 C5⋊Dic12 D5×C24 C5×Dic12 Dic60 D5×Dic6 C8×D5 C3×Dic5 C6×D5 Dic12 C5⋊2C8 C40 C4×D5 C3×D5 C24 Dic6 Dic5 D10 D5 C8 C6 C4 C3 C2 C1 # reps 1 2 1 1 1 2 1 1 1 2 1 1 1 4 2 4 2 2 8 2 2 2 4 4 8

Matrix representation of D5×Dic12 in GL4(𝔽241) generated by

 0 1 0 0 240 189 0 0 0 0 1 0 0 0 0 1
,
 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1
,
 1 0 0 0 0 1 0 0 0 0 123 131 0 0 74 22
,
 1 0 0 0 0 1 0 0 0 0 211 135 0 0 129 30
G:=sub<GL(4,GF(241))| [0,240,0,0,1,189,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,123,74,0,0,131,22],[1,0,0,0,0,1,0,0,0,0,211,129,0,0,135,30] >;

D5×Dic12 in GAP, Magma, Sage, TeX

D_5\times {\rm Dic}_{12}
% in TeX

G:=Group("D5xDic12");
// GroupNames label

G:=SmallGroup(480,335);
// by ID

G=gap.SmallGroup(480,335);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,135,142,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^5=b^2=c^24=1,d^2=c^12,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽