direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: S3×Dic20, C40.44D6, Dic60⋊4C2, D6.12D20, C24.16D10, C120.6C22, C60.95C23, Dic3.3D20, Dic10.18D6, Dic30.27C22, C5⋊1(S3×Q16), C15⋊2(C2×Q16), C3⋊C8.27D10, (C5×S3)⋊1Q16, (S3×C8).1D5, C6.5(C2×D20), C10.5(S3×D4), C8.11(S3×D5), C3⋊1(C2×Dic20), (S3×C40).1C2, C3⋊Dic20⋊9C2, C2.10(S3×D20), C30.16(C2×D4), (C3×Dic20)⋊2C2, (S3×C10).19D4, (C4×S3).38D10, (S3×Dic10).2C2, (C5×Dic3).22D4, C12.72(C22×D5), (S3×C20).44C22, C20.145(C22×S3), (C3×Dic10).22C22, C4.94(C2×S3×D5), (C5×C3⋊C8).31C22, SmallGroup(480,338)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for S3×Dic20
G = < a,b,c,d | a3=b2=c40=1, d2=c20, 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, C3, C4, C4, C22, C5, S3, C6, C8, C8, C2×C4, Q8, C10, C10, Dic3, Dic3, C12, C12, D6, C15, C2×C8, Q16, C2×Q8, Dic5, C20, C20, C2×C10, C3⋊C8, C24, Dic6, C4×S3, C4×S3, C3×Q8, C5×S3, C30, C2×Q16, C40, C40, Dic10, Dic10, C2×Dic5, C2×C20, S3×C8, Dic12, C3⋊Q16, C3×Q16, S3×Q8, C5×Dic3, C3×Dic5, Dic15, C60, S3×C10, Dic20, Dic20, C2×C40, C2×Dic10, S3×Q16, C5×C3⋊C8, C120, S3×Dic5, C15⋊Q8, C3×Dic10, S3×C20, Dic30, C2×Dic20, C3⋊Dic20, C3×Dic20, S3×C40, Dic60, S3×Dic10, S3×Dic20
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, Q16, C2×D4, D10, C22×S3, C2×Q16, D20, C22×D5, S3×D4, S3×D5, Dic20, C2×D20, S3×Q16, C2×S3×D5, C2×Dic20, S3×D20, S3×Dic20
►On 240 points
Generators in S240
(1 167 102)(2 168 103)(3 169 104)(4 170 105)(5 171 106)(6 172 107)(7 173 108)(8 174 109)(9 175 110)(10 176 111)(11 177 112)(12 178 113)(13 179 114)(14 180 115)(15 181 116)(16 182 117)(17 183 118)(18 184 119)(19 185 120)(20 186 81)(21 187 82)(22 188 83)(23 189 84)(24 190 85)(25 191 86)(26 192 87)(27 193 88)(28 194 89)(29 195 90)(30 196 91)(31 197 92)(32 198 93)(33 199 94)(34 200 95)(35 161 96)(36 162 97)(37 163 98)(38 164 99)(39 165 100)(40 166 101)(41 145 208)(42 146 209)(43 147 210)(44 148 211)(45 149 212)(46 150 213)(47 151 214)(48 152 215)(49 153 216)(50 154 217)(51 155 218)(52 156 219)(53 157 220)(54 158 221)(55 159 222)(56 160 223)(57 121 224)(58 122 225)(59 123 226)(60 124 227)(61 125 228)(62 126 229)(63 127 230)(64 128 231)(65 129 232)(66 130 233)(67 131 234)(68 132 235)(69 133 236)(70 134 237)(71 135 238)(72 136 239)(73 137 240)(74 138 201)(75 139 202)(76 140 203)(77 141 204)(78 142 205)(79 143 206)(80 144 207)
(41 208)(42 209)(43 210)(44 211)(45 212)(46 213)(47 214)(48 215)(49 216)(50 217)(51 218)(52 219)(53 220)(54 221)(55 222)(56 223)(57 224)(58 225)(59 226)(60 227)(61 228)(62 229)(63 230)(64 231)(65 232)(66 233)(67 234)(68 235)(69 236)(70 237)(71 238)(72 239)(73 240)(74 201)(75 202)(76 203)(77 204)(78 205)(79 206)(80 207)(81 186)(82 187)(83 188)(84 189)(85 190)(86 191)(87 192)(88 193)(89 194)(90 195)(91 196)(92 197)(93 198)(94 199)(95 200)(96 161)(97 162)(98 163)(99 164)(100 165)(101 166)(102 167)(103 168)(104 169)(105 170)(106 171)(107 172)(108 173)(109 174)(110 175)(111 176)(112 177)(113 178)(114 179)(115 180)(116 181)(117 182)(118 183)(119 184)(120 185)
(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)
(1 157 21 137)(2 156 22 136)(3 155 23 135)(4 154 24 134)(5 153 25 133)(6 152 26 132)(7 151 27 131)(8 150 28 130)(9 149 29 129)(10 148 30 128)(11 147 31 127)(12 146 32 126)(13 145 33 125)(14 144 34 124)(15 143 35 123)(16 142 36 122)(17 141 37 121)(18 140 38 160)(19 139 39 159)(20 138 40 158)(41 94 61 114)(42 93 62 113)(43 92 63 112)(44 91 64 111)(45 90 65 110)(46 89 66 109)(47 88 67 108)(48 87 68 107)(49 86 69 106)(50 85 70 105)(51 84 71 104)(52 83 72 103)(53 82 73 102)(54 81 74 101)(55 120 75 100)(56 119 76 99)(57 118 77 98)(58 117 78 97)(59 116 79 96)(60 115 80 95)(161 226 181 206)(162 225 182 205)(163 224 183 204)(164 223 184 203)(165 222 185 202)(166 221 186 201)(167 220 187 240)(168 219 188 239)(169 218 189 238)(170 217 190 237)(171 216 191 236)(172 215 192 235)(173 214 193 234)(174 213 194 233)(175 212 195 232)(176 211 196 231)(177 210 197 230)(178 209 198 229)(179 208 199 228)(180 207 200 227)
G:=sub<Sym(240)| (1,167,102)(2,168,103)(3,169,104)(4,170,105)(5,171,106)(6,172,107)(7,173,108)(8,174,109)(9,175,110)(10,176,111)(11,177,112)(12,178,113)(13,179,114)(14,180,115)(15,181,116)(16,182,117)(17,183,118)(18,184,119)(19,185,120)(20,186,81)(21,187,82)(22,188,83)(23,189,84)(24,190,85)(25,191,86)(26,192,87)(27,193,88)(28,194,89)(29,195,90)(30,196,91)(31,197,92)(32,198,93)(33,199,94)(34,200,95)(35,161,96)(36,162,97)(37,163,98)(38,164,99)(39,165,100)(40,166,101)(41,145,208)(42,146,209)(43,147,210)(44,148,211)(45,149,212)(46,150,213)(47,151,214)(48,152,215)(49,153,216)(50,154,217)(51,155,218)(52,156,219)(53,157,220)(54,158,221)(55,159,222)(56,160,223)(57,121,224)(58,122,225)(59,123,226)(60,124,227)(61,125,228)(62,126,229)(63,127,230)(64,128,231)(65,129,232)(66,130,233)(67,131,234)(68,132,235)(69,133,236)(70,134,237)(71,135,238)(72,136,239)(73,137,240)(74,138,201)(75,139,202)(76,140,203)(77,141,204)(78,142,205)(79,143,206)(80,144,207), (41,208)(42,209)(43,210)(44,211)(45,212)(46,213)(47,214)(48,215)(49,216)(50,217)(51,218)(52,219)(53,220)(54,221)(55,222)(56,223)(57,224)(58,225)(59,226)(60,227)(61,228)(62,229)(63,230)(64,231)(65,232)(66,233)(67,234)(68,235)(69,236)(70,237)(71,238)(72,239)(73,240)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,186)(82,187)(83,188)(84,189)(85,190)(86,191)(87,192)(88,193)(89,194)(90,195)(91,196)(92,197)(93,198)(94,199)(95,200)(96,161)(97,162)(98,163)(99,164)(100,165)(101,166)(102,167)(103,168)(104,169)(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)(115,180)(116,181)(117,182)(118,183)(119,184)(120,185), (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), (1,157,21,137)(2,156,22,136)(3,155,23,135)(4,154,24,134)(5,153,25,133)(6,152,26,132)(7,151,27,131)(8,150,28,130)(9,149,29,129)(10,148,30,128)(11,147,31,127)(12,146,32,126)(13,145,33,125)(14,144,34,124)(15,143,35,123)(16,142,36,122)(17,141,37,121)(18,140,38,160)(19,139,39,159)(20,138,40,158)(41,94,61,114)(42,93,62,113)(43,92,63,112)(44,91,64,111)(45,90,65,110)(46,89,66,109)(47,88,67,108)(48,87,68,107)(49,86,69,106)(50,85,70,105)(51,84,71,104)(52,83,72,103)(53,82,73,102)(54,81,74,101)(55,120,75,100)(56,119,76,99)(57,118,77,98)(58,117,78,97)(59,116,79,96)(60,115,80,95)(161,226,181,206)(162,225,182,205)(163,224,183,204)(164,223,184,203)(165,222,185,202)(166,221,186,201)(167,220,187,240)(168,219,188,239)(169,218,189,238)(170,217,190,237)(171,216,191,236)(172,215,192,235)(173,214,193,234)(174,213,194,233)(175,212,195,232)(176,211,196,231)(177,210,197,230)(178,209,198,229)(179,208,199,228)(180,207,200,227)>;
G:=Group( (1,167,102)(2,168,103)(3,169,104)(4,170,105)(5,171,106)(6,172,107)(7,173,108)(8,174,109)(9,175,110)(10,176,111)(11,177,112)(12,178,113)(13,179,114)(14,180,115)(15,181,116)(16,182,117)(17,183,118)(18,184,119)(19,185,120)(20,186,81)(21,187,82)(22,188,83)(23,189,84)(24,190,85)(25,191,86)(26,192,87)(27,193,88)(28,194,89)(29,195,90)(30,196,91)(31,197,92)(32,198,93)(33,199,94)(34,200,95)(35,161,96)(36,162,97)(37,163,98)(38,164,99)(39,165,100)(40,166,101)(41,145,208)(42,146,209)(43,147,210)(44,148,211)(45,149,212)(46,150,213)(47,151,214)(48,152,215)(49,153,216)(50,154,217)(51,155,218)(52,156,219)(53,157,220)(54,158,221)(55,159,222)(56,160,223)(57,121,224)(58,122,225)(59,123,226)(60,124,227)(61,125,228)(62,126,229)(63,127,230)(64,128,231)(65,129,232)(66,130,233)(67,131,234)(68,132,235)(69,133,236)(70,134,237)(71,135,238)(72,136,239)(73,137,240)(74,138,201)(75,139,202)(76,140,203)(77,141,204)(78,142,205)(79,143,206)(80,144,207), (41,208)(42,209)(43,210)(44,211)(45,212)(46,213)(47,214)(48,215)(49,216)(50,217)(51,218)(52,219)(53,220)(54,221)(55,222)(56,223)(57,224)(58,225)(59,226)(60,227)(61,228)(62,229)(63,230)(64,231)(65,232)(66,233)(67,234)(68,235)(69,236)(70,237)(71,238)(72,239)(73,240)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,186)(82,187)(83,188)(84,189)(85,190)(86,191)(87,192)(88,193)(89,194)(90,195)(91,196)(92,197)(93,198)(94,199)(95,200)(96,161)(97,162)(98,163)(99,164)(100,165)(101,166)(102,167)(103,168)(104,169)(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)(115,180)(116,181)(117,182)(118,183)(119,184)(120,185), (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), (1,157,21,137)(2,156,22,136)(3,155,23,135)(4,154,24,134)(5,153,25,133)(6,152,26,132)(7,151,27,131)(8,150,28,130)(9,149,29,129)(10,148,30,128)(11,147,31,127)(12,146,32,126)(13,145,33,125)(14,144,34,124)(15,143,35,123)(16,142,36,122)(17,141,37,121)(18,140,38,160)(19,139,39,159)(20,138,40,158)(41,94,61,114)(42,93,62,113)(43,92,63,112)(44,91,64,111)(45,90,65,110)(46,89,66,109)(47,88,67,108)(48,87,68,107)(49,86,69,106)(50,85,70,105)(51,84,71,104)(52,83,72,103)(53,82,73,102)(54,81,74,101)(55,120,75,100)(56,119,76,99)(57,118,77,98)(58,117,78,97)(59,116,79,96)(60,115,80,95)(161,226,181,206)(162,225,182,205)(163,224,183,204)(164,223,184,203)(165,222,185,202)(166,221,186,201)(167,220,187,240)(168,219,188,239)(169,218,189,238)(170,217,190,237)(171,216,191,236)(172,215,192,235)(173,214,193,234)(174,213,194,233)(175,212,195,232)(176,211,196,231)(177,210,197,230)(178,209,198,229)(179,208,199,228)(180,207,200,227) );
G=PermutationGroup([[(1,167,102),(2,168,103),(3,169,104),(4,170,105),(5,171,106),(6,172,107),(7,173,108),(8,174,109),(9,175,110),(10,176,111),(11,177,112),(12,178,113),(13,179,114),(14,180,115),(15,181,116),(16,182,117),(17,183,118),(18,184,119),(19,185,120),(20,186,81),(21,187,82),(22,188,83),(23,189,84),(24,190,85),(25,191,86),(26,192,87),(27,193,88),(28,194,89),(29,195,90),(30,196,91),(31,197,92),(32,198,93),(33,199,94),(34,200,95),(35,161,96),(36,162,97),(37,163,98),(38,164,99),(39,165,100),(40,166,101),(41,145,208),(42,146,209),(43,147,210),(44,148,211),(45,149,212),(46,150,213),(47,151,214),(48,152,215),(49,153,216),(50,154,217),(51,155,218),(52,156,219),(53,157,220),(54,158,221),(55,159,222),(56,160,223),(57,121,224),(58,122,225),(59,123,226),(60,124,227),(61,125,228),(62,126,229),(63,127,230),(64,128,231),(65,129,232),(66,130,233),(67,131,234),(68,132,235),(69,133,236),(70,134,237),(71,135,238),(72,136,239),(73,137,240),(74,138,201),(75,139,202),(76,140,203),(77,141,204),(78,142,205),(79,143,206),(80,144,207)], [(41,208),(42,209),(43,210),(44,211),(45,212),(46,213),(47,214),(48,215),(49,216),(50,217),(51,218),(52,219),(53,220),(54,221),(55,222),(56,223),(57,224),(58,225),(59,226),(60,227),(61,228),(62,229),(63,230),(64,231),(65,232),(66,233),(67,234),(68,235),(69,236),(70,237),(71,238),(72,239),(73,240),(74,201),(75,202),(76,203),(77,204),(78,205),(79,206),(80,207),(81,186),(82,187),(83,188),(84,189),(85,190),(86,191),(87,192),(88,193),(89,194),(90,195),(91,196),(92,197),(93,198),(94,199),(95,200),(96,161),(97,162),(98,163),(99,164),(100,165),(101,166),(102,167),(103,168),(104,169),(105,170),(106,171),(107,172),(108,173),(109,174),(110,175),(111,176),(112,177),(113,178),(114,179),(115,180),(116,181),(117,182),(118,183),(119,184),(120,185)], [(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)], [(1,157,21,137),(2,156,22,136),(3,155,23,135),(4,154,24,134),(5,153,25,133),(6,152,26,132),(7,151,27,131),(8,150,28,130),(9,149,29,129),(10,148,30,128),(11,147,31,127),(12,146,32,126),(13,145,33,125),(14,144,34,124),(15,143,35,123),(16,142,36,122),(17,141,37,121),(18,140,38,160),(19,139,39,159),(20,138,40,158),(41,94,61,114),(42,93,62,113),(43,92,63,112),(44,91,64,111),(45,90,65,110),(46,89,66,109),(47,88,67,108),(48,87,68,107),(49,86,69,106),(50,85,70,105),(51,84,71,104),(52,83,72,103),(53,82,73,102),(54,81,74,101),(55,120,75,100),(56,119,76,99),(57,118,77,98),(58,117,78,97),(59,116,79,96),(60,115,80,95),(161,226,181,206),(162,225,182,205),(163,224,183,204),(164,223,184,203),(165,222,185,202),(166,221,186,201),(167,220,187,240),(168,219,188,239),(169,218,189,238),(170,217,190,237),(171,216,191,236),(172,215,192,235),(173,214,193,234),(174,213,194,233),(175,212,195,232),(176,211,196,231),(177,210,197,230),(178,209,198,229),(179,208,199,228),(180,207,200,227)]])
69 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 6 | 8A | 8B | 8C | 8D | 10A | 10B | 10C | 10D | 10E | 10F | 12A | 12B | 12C | 15A | 15B | 20A | 20B | 20C | 20D | 20E | 20F | 20G | 20H | 24A | 24B | 30A | 30B | 40A | ··· | 40H | 40I | ··· | 40P | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 30 | 30 | 40 | ··· | 40 | 40 | ··· | 40 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 3 | 3 | 2 | 2 | 6 | 20 | 20 | 60 | 60 | 2 | 2 | 2 | 2 | 2 | 6 | 6 | 2 | 2 | 6 | 6 | 6 | 6 | 4 | 40 | 40 | 4 | 4 | 2 | 2 | 2 | 2 | 6 | 6 | 6 | 6 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 6 | ··· | 6 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
69 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 | Q16 | D10 | D10 | D10 | D20 | D20 | Dic20 | S3×D4 | S3×D5 | S3×Q16 | C2×S3×D5 | S3×D20 | S3×Dic20 |
| kernel | S3×Dic20 | C3⋊Dic20 | C3×Dic20 | S3×C40 | Dic60 | S3×Dic10 | Dic20 | C5×Dic3 | S3×C10 | S3×C8 | C40 | Dic10 | C5×S3 | C3⋊C8 | C24 | C4×S3 | Dic3 | D6 | S3 | C10 | C8 | C5 | C4 | C2 | C1 |
| # reps | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 2 | 4 | 2 | 2 | 2 | 4 | 4 | 16 | 1 | 2 | 2 | 2 | 4 | 8 |
Matrix representation of S3×Dic20 ►in GL4(𝔽241) generated by
| 240 | 240 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 240 | 240 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 29 | 20 |
| 0 | 0 | 221 | 194 |
| 240 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 |
| 0 | 0 | 78 | 22 |
| 0 | 0 | 63 | 163 |
G:=sub<GL(4,GF(241))| [240,1,0,0,240,0,0,0,0,0,1,0,0,0,0,1],[1,240,0,0,0,240,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,29,221,0,0,20,194],[240,0,0,0,0,240,0,0,0,0,78,63,0,0,22,163] >;
S3×Dic20 in GAP, Magma, Sage, TeX
S_3\times {\rm Dic}_{20} % in TeX
G:=Group("S3xDic20"); // GroupNames label
G:=SmallGroup(480,338);
// by ID
G=gap.SmallGroup(480,338);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,142,675,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^2=c^40=1,d^2=c^20,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