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G = D20.5D6order 480 = 25·3·5

5th non-split extension by D20 of D6 acting via D6/C3=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D20.5D6, D30.3D4, C40.29D6, Dic126D5, C24.26D10, Dic10.3D6, Dic15.3D4, Dic6.4D10, C60.146C23, C120.49C22, C8.5(S3×D5), C40⋊C24S3, D15⋊Q89C2, C6.35(D4×D5), C40⋊S38C2, C30.28(C2×D4), C10.35(S3×D4), C52(D4.D6), (C5×Dic12)⋊8C2, C15⋊Q1611C2, C32(Q16⋊D5), C155(C8.C22), D20⋊S3.2C2, C20.D612C2, C20.81(C22×S3), C12.81(C22×D5), C2.13(C20⋊D6), C153C8.23C22, (C4×D15).32C22, (C3×D20).29C22, (C5×Dic6).30C22, (C3×Dic10).29C22, C4.119(C2×S3×D5), (C3×C40⋊C2)⋊8C2, SmallGroup(480,354)

Series: Derived Chief Lower central Upper central

C1C60 — D20.5D6
C1C5C15C30C60C3×D20D20⋊S3 — D20.5D6
C15C30C60 — D20.5D6
C1C2C4C8

Generators and relations for D20.5D6
 G = < a,b,c,d | a20=b2=1, c6=a15, d2=a10, bab=a-1, ac=ca, dad-1=a11, cbc-1=dbd-1=a15b, dcd-1=a5c5 >

Subgroups: 684 in 120 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3, C6, C6, C8, C8, C2×C4 [×3], D4 [×2], Q8 [×4], D5 [×2], C10, Dic3 [×3], C12, C12, D6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5 [×2], C20, C20 [×2], D10 [×2], C3⋊C8, C24, Dic6 [×2], Dic6, C4×S3 [×2], C2×Dic3, C3⋊D4, C3×D4, C3×Q8, C3×D5, D15, C30, C8.C22, C52C8, C40, Dic10, Dic10, C4×D5 [×3], D20, D20, C5×Q8 [×2], C8⋊S3, Dic12, D4.S3, C3⋊Q16, C3×SD16, D42S3, S3×Q8, C5×Dic3 [×2], C3×Dic5, Dic15, C60, C6×D5, D30, C8⋊D5, C40⋊C2, Q8⋊D5, C5⋊Q16, C5×Q16, Q8×D5, Q82D5, D4.D6, C153C8, C120, D5×Dic3, D30.C2, C3⋊D20, C15⋊Q8, C3×Dic10, C3×D20, C5×Dic6 [×2], C4×D15, Q16⋊D5, C20.D6, C15⋊Q16, C3×C40⋊C2, C5×Dic12, C40⋊S3, D20⋊S3, D15⋊Q8, D20.5D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C8.C22, C22×D5, S3×D4, S3×D5, D4×D5, D4.D6, C2×S3×D5, Q16⋊D5, C20⋊D6, D20.5D6

Smallest permutation representation of D20.5D6
On 240 points
Generators in S240
(1 87 107 129 34 19 81 101 123 28 13 75 119 141 46 7 93 113 135 40)(2 88 108 130 35 20 82 102 124 29 14 76 120 142 47 8 94 114 136 41)(3 89 109 131 36 21 83 103 125 30 15 77 97 143 48 9 95 115 137 42)(4 90 110 132 37 22 84 104 126 31 16 78 98 144 25 10 96 116 138 43)(5 91 111 133 38 23 85 105 127 32 17 79 99 121 26 11 73 117 139 44)(6 92 112 134 39 24 86 106 128 33 18 80 100 122 27 12 74 118 140 45)(49 234 183 194 156 67 228 177 212 150 61 222 171 206 168 55 240 189 200 162)(50 235 184 195 157 68 229 178 213 151 62 223 172 207 145 56 217 190 201 163)(51 236 185 196 158 69 230 179 214 152 63 224 173 208 146 57 218 191 202 164)(52 237 186 197 159 70 231 180 215 153 64 225 174 209 147 58 219 192 203 165)(53 238 187 198 160 71 232 181 216 154 65 226 175 210 148 59 220 169 204 166)(54 239 188 199 161 72 233 182 193 155 66 227 176 211 149 60 221 170 205 167)
(1 201)(2 196)(3 215)(4 210)(5 205)(6 200)(7 195)(8 214)(9 209)(10 204)(11 199)(12 194)(13 213)(14 208)(15 203)(16 198)(17 193)(18 212)(19 207)(20 202)(21 197)(22 216)(23 211)(24 206)(25 166)(26 161)(27 156)(28 151)(29 146)(30 165)(31 160)(32 155)(33 150)(34 145)(35 164)(36 159)(37 154)(38 149)(39 168)(40 163)(41 158)(42 153)(43 148)(44 167)(45 162)(46 157)(47 152)(48 147)(49 140)(50 135)(51 130)(52 125)(53 144)(54 139)(55 134)(56 129)(57 124)(58 143)(59 138)(60 133)(61 128)(62 123)(63 142)(64 137)(65 132)(66 127)(67 122)(68 141)(69 136)(70 131)(71 126)(72 121)(73 188)(74 183)(75 178)(76 173)(77 192)(78 187)(79 182)(80 177)(81 172)(82 191)(83 186)(84 181)(85 176)(86 171)(87 190)(88 185)(89 180)(90 175)(91 170)(92 189)(93 184)(94 179)(95 174)(96 169)(97 219)(98 238)(99 233)(100 228)(101 223)(102 218)(103 237)(104 232)(105 227)(106 222)(107 217)(108 236)(109 231)(110 226)(111 221)(112 240)(113 235)(114 230)(115 225)(116 220)(117 239)(118 234)(119 229)(120 224)
(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)
(1 150 13 162)(2 149 14 161)(3 148 15 160)(4 147 16 159)(5 146 17 158)(6 145 18 157)(7 168 19 156)(8 167 20 155)(9 166 21 154)(10 165 22 153)(11 164 23 152)(12 163 24 151)(25 215 37 203)(26 214 38 202)(27 213 39 201)(28 212 40 200)(29 211 41 199)(30 210 42 198)(31 209 43 197)(32 208 44 196)(33 207 45 195)(34 206 46 194)(35 205 47 193)(36 204 48 216)(49 75 61 87)(50 74 62 86)(51 73 63 85)(52 96 64 84)(53 95 65 83)(54 94 66 82)(55 93 67 81)(56 92 68 80)(57 91 69 79)(58 90 70 78)(59 89 71 77)(60 88 72 76)(97 232 109 220)(98 231 110 219)(99 230 111 218)(100 229 112 217)(101 228 113 240)(102 227 114 239)(103 226 115 238)(104 225 116 237)(105 224 117 236)(106 223 118 235)(107 222 119 234)(108 221 120 233)(121 191 133 179)(122 190 134 178)(123 189 135 177)(124 188 136 176)(125 187 137 175)(126 186 138 174)(127 185 139 173)(128 184 140 172)(129 183 141 171)(130 182 142 170)(131 181 143 169)(132 180 144 192)

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

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

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

48 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B6A6B8A8B10A10B12A12B15A15B20A20B20C20D20E20F24A24B30A30B40A40B40C40D60A60B60C60D120A···120H
order1222344444556688101012121515202020202020242430304040404060606060120···120
size112030221212203022240460224404444242424244444444444444···4

48 irreducible representations

dim11111111222222222444444444
type+++++++++++++++++-+++-+
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10C8.C22S3×D4S3×D5D4×D5D4.D6C2×S3×D5Q16⋊D5C20⋊D6D20.5D6
kernelD20.5D6C20.D6C15⋊Q16C3×C40⋊C2C5×Dic12C40⋊S3D20⋊S3D15⋊Q8C40⋊C2Dic15D30Dic12C40Dic10D20C24Dic6C15C10C8C6C5C4C3C2C1
# reps11111111111211124112222448

Matrix representation of D20.5D6 in GL6(𝔽241)

010000
240510000
00144471330
00194970133
00118097194
00011847144
,
010000
100000
00240130104208
0011111033137
0096271111
0021469130131
,
24000000
02400000
001321412374
00100232237233
0049192100109
004998132232
,
24000000
02400000
00156179142142
002385099
001731736285
0006823179

G:=sub<GL(6,GF(241))| [0,240,0,0,0,0,1,51,0,0,0,0,0,0,144,194,118,0,0,0,47,97,0,118,0,0,133,0,97,47,0,0,0,133,194,144],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,240,111,96,214,0,0,130,110,27,69,0,0,104,33,1,130,0,0,208,137,111,131],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,132,100,49,49,0,0,141,232,192,98,0,0,237,237,100,132,0,0,4,233,109,232],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,156,23,173,0,0,0,179,85,173,68,0,0,142,0,62,23,0,0,142,99,85,179] >;

D20.5D6 in GAP, Magma, Sage, TeX

D_{20}._5D_6
% in TeX

G:=Group("D20.5D6");
// GroupNames label

G:=SmallGroup(480,354);
// by ID

G=gap.SmallGroup(480,354);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,254,303,58,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^20=b^2=1,c^6=a^15,d^2=a^10,b*a*b=a^-1,a*c=c*a,d*a*d^-1=a^11,c*b*c^-1=d*b*d^-1=a^15*b,d*c*d^-1=a^5*c^5>;
// generators/relations

׿
×
𝔽