Copied to
clipboard

G = D407S3order 480 = 25·3·5

The semidirect product of D40 and S3 acting through Inn(D40)

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D407S3, D6.2D20, C40.45D6, Dic605C2, D20.21D6, C24.18D10, C60.98C23, C120.7C22, Dic3.13D20, Dic30.30C22, (S3×C8)⋊2D5, (S3×C40)⋊2C2, (C3×D40)⋊3C2, C155(C4○D8), C3⋊C8.29D10, C6.8(C2×D20), C10.8(S3×D4), C8.12(S3×D5), C51(D83S3), C30.23(C2×D4), C2.13(S3×D20), C32(D407C2), (S3×C10).21D4, (C4×S3).40D10, D205S310C2, C6.D2011C2, (C5×Dic3).24D4, C12.76(C22×D5), (S3×C20).46C22, C20.148(C22×S3), (C3×D20).23C22, C4.97(C2×S3×D5), (C5×C3⋊C8).33C22, SmallGroup(480,349)

Series: Derived Chief Lower central Upper central

C1C60 — D407S3
C1C5C15C30C60C3×D20D205S3 — D407S3
C15C30C60 — D407S3
C1C2C4C8

Generators and relations for D407S3
 G = < a,b,c,d | a40=b2=c3=d2=1, bab=a-1, ac=ca, ad=da, bc=cb, dbd=a20b, dcd=c-1 >

Subgroups: 732 in 124 conjugacy classes, 40 normal (30 characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3, C6, C6 [×2], C8, C8, C2×C4 [×3], D4 [×4], Q8 [×2], D5 [×2], C10, C10, Dic3, Dic3 [×2], C12, D6, C2×C6 [×2], C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5 [×2], C20, C20, D10 [×2], C2×C10, C3⋊C8, C24, Dic6 [×2], C4×S3, C2×Dic3 [×2], C3⋊D4 [×2], C3×D4 [×2], C5×S3, C3×D5 [×2], C30, C4○D8, C40, C40, Dic10 [×2], C4×D5 [×2], D20 [×2], C5⋊D4 [×2], C2×C20, S3×C8, Dic12, D4.S3 [×2], C3×D8, D42S3 [×2], C5×Dic3, Dic15 [×2], C60, C6×D5 [×2], S3×C10, C40⋊C2 [×2], D40, Dic20, C2×C40, C4○D20 [×2], D83S3, C5×C3⋊C8, C120, D5×Dic3 [×2], C15⋊D4 [×2], C3×D20 [×2], S3×C20, Dic30 [×2], D407C2, C6.D20 [×2], C3×D40, S3×C40, Dic60, D205S3 [×2], D407S3
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C4○D8, D20 [×2], C22×D5, S3×D4, S3×D5, C2×D20, D83S3, C2×S3×D5, D407C2, S3×D20, D407S3

Smallest permutation representation of D407S3
On 240 points
Generators in S240
(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)
(1 175)(2 174)(3 173)(4 172)(5 171)(6 170)(7 169)(8 168)(9 167)(10 166)(11 165)(12 164)(13 163)(14 162)(15 161)(16 200)(17 199)(18 198)(19 197)(20 196)(21 195)(22 194)(23 193)(24 192)(25 191)(26 190)(27 189)(28 188)(29 187)(30 186)(31 185)(32 184)(33 183)(34 182)(35 181)(36 180)(37 179)(38 178)(39 177)(40 176)(41 238)(42 237)(43 236)(44 235)(45 234)(46 233)(47 232)(48 231)(49 230)(50 229)(51 228)(52 227)(53 226)(54 225)(55 224)(56 223)(57 222)(58 221)(59 220)(60 219)(61 218)(62 217)(63 216)(64 215)(65 214)(66 213)(67 212)(68 211)(69 210)(70 209)(71 208)(72 207)(73 206)(74 205)(75 204)(76 203)(77 202)(78 201)(79 240)(80 239)(81 132)(82 131)(83 130)(84 129)(85 128)(86 127)(87 126)(88 125)(89 124)(90 123)(91 122)(92 121)(93 160)(94 159)(95 158)(96 157)(97 156)(98 155)(99 154)(100 153)(101 152)(102 151)(103 150)(104 149)(105 148)(106 147)(107 146)(108 145)(109 144)(110 143)(111 142)(112 141)(113 140)(114 139)(115 138)(116 137)(117 136)(118 135)(119 134)(120 133)
(1 119 233)(2 120 234)(3 81 235)(4 82 236)(5 83 237)(6 84 238)(7 85 239)(8 86 240)(9 87 201)(10 88 202)(11 89 203)(12 90 204)(13 91 205)(14 92 206)(15 93 207)(16 94 208)(17 95 209)(18 96 210)(19 97 211)(20 98 212)(21 99 213)(22 100 214)(23 101 215)(24 102 216)(25 103 217)(26 104 218)(27 105 219)(28 106 220)(29 107 221)(30 108 222)(31 109 223)(32 110 224)(33 111 225)(34 112 226)(35 113 227)(36 114 228)(37 115 229)(38 116 230)(39 117 231)(40 118 232)(41 170 129)(42 171 130)(43 172 131)(44 173 132)(45 174 133)(46 175 134)(47 176 135)(48 177 136)(49 178 137)(50 179 138)(51 180 139)(52 181 140)(53 182 141)(54 183 142)(55 184 143)(56 185 144)(57 186 145)(58 187 146)(59 188 147)(60 189 148)(61 190 149)(62 191 150)(63 192 151)(64 193 152)(65 194 153)(66 195 154)(67 196 155)(68 197 156)(69 198 157)(70 199 158)(71 200 159)(72 161 160)(73 162 121)(74 163 122)(75 164 123)(76 165 124)(77 166 125)(78 167 126)(79 168 127)(80 169 128)
(41 149)(42 150)(43 151)(44 152)(45 153)(46 154)(47 155)(48 156)(49 157)(50 158)(51 159)(52 160)(53 121)(54 122)(55 123)(56 124)(57 125)(58 126)(59 127)(60 128)(61 129)(62 130)(63 131)(64 132)(65 133)(66 134)(67 135)(68 136)(69 137)(70 138)(71 139)(72 140)(73 141)(74 142)(75 143)(76 144)(77 145)(78 146)(79 147)(80 148)(81 235)(82 236)(83 237)(84 238)(85 239)(86 240)(87 201)(88 202)(89 203)(90 204)(91 205)(92 206)(93 207)(94 208)(95 209)(96 210)(97 211)(98 212)(99 213)(100 214)(101 215)(102 216)(103 217)(104 218)(105 219)(106 220)(107 221)(108 222)(109 223)(110 224)(111 225)(112 226)(113 227)(114 228)(115 229)(116 230)(117 231)(118 232)(119 233)(120 234)(161 181)(162 182)(163 183)(164 184)(165 185)(166 186)(167 187)(168 188)(169 189)(170 190)(171 191)(172 192)(173 193)(174 194)(175 195)(176 196)(177 197)(178 198)(179 199)(180 200)

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

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

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

69 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B6C8A8B8C8D10A10B10C10D10E10F 12 15A15B20A20B20C20D20E20F20G20H24A24B30A30B40A···40H40I···40P60A60B60C60D120A···120H
order1222234444455666888810101010101012151520202020202020202424303040···4040···4060606060120···120
size116202022336060222404022662266664442222666644442···26···644444···4

69 irreducible representations

dim1111112222222222222444444
type+++++++++++++++++++-++-
imageC1C2C2C2C2C2S3D4D4D5D6D6D10D10D10C4○D8D20D20D407C2S3×D4S3×D5D83S3C2×S3×D5S3×D20D407S3
kernelD407S3C6.D20C3×D40S3×C40Dic60D205S3D40C5×Dic3S3×C10S3×C8C40D20C3⋊C8C24C4×S3C15Dic3D6C3C10C8C5C4C2C1
# reps12111211121222244416122248

Matrix representation of D407S3 in GL4(𝔽241) generated by

11621800
021400
0010
0001
,
6713200
20717400
002400
000240
,
1000
0100
00240240
0010
,
18900
024000
0010
00240240
G:=sub<GL(4,GF(241))| [116,0,0,0,218,214,0,0,0,0,1,0,0,0,0,1],[67,207,0,0,132,174,0,0,0,0,240,0,0,0,0,240],[1,0,0,0,0,1,0,0,0,0,240,1,0,0,240,0],[1,0,0,0,89,240,0,0,0,0,1,240,0,0,0,240] >;

D407S3 in GAP, Magma, Sage, TeX

D_{40}\rtimes_7S_3
% in TeX

G:=Group("D40:7S3");
// GroupNames label

G:=SmallGroup(480,349);
// by ID

G=gap.SmallGroup(480,349);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,254,142,675,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^40=b^2=c^3=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^20*b,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽