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G = D20.28D6order 480 = 25·3·5

11st non-split extension by D20 of D6 acting via D6/S3=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D20.28D6, C60.42C23, Dic6.14D10, Dic30.16C22, Q8⋊D54S3, (S3×Q8)⋊2D5, C52C8.9D6, C5⋊Dic127C2, C157Q168C2, C57(D4.D6), Q8.11(S3×D5), (C3×Q8).6D10, (C5×Q8).38D6, (S3×C10).37D4, (C4×S3).11D10, C30.204(C2×D4), C30.D48C2, C10.152(S3×D4), D6.Dic57C2, D205S3.1C2, D6.15(C5⋊D4), C32(C20.C23), C1521(C8.C22), C20.42(C22×S3), (C5×Dic3).17D4, C12.42(C22×D5), (S3×C20).14C22, C153C8.16C22, (C3×D20).16C22, (Q8×C15).12C22, Dic3.12(C5⋊D4), (C5×Dic6).15C22, (C5×S3×Q8)⋊2C2, C4.42(C2×S3×D5), (C3×Q8⋊D5)⋊6C2, C6.55(C2×C5⋊D4), C2.33(S3×C5⋊D4), (C3×C52C8).12C22, SmallGroup(480,594)

Series: Derived Chief Lower central Upper central

C1C60 — D20.28D6
C1C5C15C30C60C3×D20D205S3 — D20.28D6
C15C30C60 — D20.28D6
C1C2C4Q8

Generators and relations for D20.28D6
 G = < a,b,c,d | a20=b2=1, c6=d2=a10, bab=a-1, cac-1=dad-1=a11, cbc-1=dbd-1=a15b, dcd-1=a10c5 >

Subgroups: 572 in 120 conjugacy classes, 40 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3, C6, C6, C8 [×2], C2×C4 [×3], D4 [×2], Q8, Q8 [×3], D5, C10, C10, Dic3, Dic3 [×2], C12, C12, D6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5, C20, C20 [×3], D10, C2×C10, C3⋊C8, C24, Dic6, Dic6 [×2], C4×S3, C4×S3, C2×Dic3, C3⋊D4, C3×D4, C3×Q8, C5×S3, C3×D5, C30, C8.C22, C52C8, C52C8, Dic10, C4×D5, D20, C5⋊D4, C2×C20 [×2], C5×Q8, C5×Q8 [×2], C8⋊S3, Dic12, D4.S3, C3⋊Q16, C3×SD16, D42S3, S3×Q8, C5×Dic3, C5×Dic3, Dic15, C60, C60, C6×D5, S3×C10, C4.Dic5, Q8⋊D5, Q8⋊D5, C5⋊Q16 [×2], C4○D20, Q8×C10, D4.D6, C3×C52C8, C153C8, D5×Dic3, C15⋊D4, C3×D20, C5×Dic6, C5×Dic6, S3×C20, S3×C20, Dic30, Q8×C15, C20.C23, D6.Dic5, C30.D4, C5⋊Dic12, C3×Q8⋊D5, C157Q16, D205S3, C5×S3×Q8, D20.28D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C8.C22, C5⋊D4 [×2], C22×D5, S3×D4, S3×D5, C2×C5⋊D4, D4.D6, C2×S3×D5, C20.C23, S3×C5⋊D4, D20.28D6

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

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

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

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

48 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B6A6B8A8B10A10B10C10D10E10F12A12B15A15B20A···20F20G···20L24A24B30A30B60A···60F
order12223444445566881010101010101212151520···2020···202424303060···60
size116202246126022240206022666648444···412···122020448···8

48 irreducible representations

dim1111111122222222222244444448
type++++++++++++++++++-++-+-
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C5⋊D4C5⋊D4C8.C22S3×D4S3×D5D4.D6C2×S3×D5C20.C23S3×C5⋊D4D20.28D6
kernelD20.28D6D6.Dic5C30.D4C5⋊Dic12C3×Q8⋊D5C157Q16D205S3C5×S3×Q8Q8⋊D5C5×Dic3S3×C10S3×Q8C52C8D20C5×Q8Dic6C4×S3C3×Q8Dic3D6C15C10Q8C5C4C3C2C1
# reps1111111111121112224411222442

Matrix representation of D20.28D6 in GL8(𝔽241)

51240000000
1911000000
00512400000
0019110000
000024012300
0000192100
000064215149
0000215106118240
,
5938000000
86182000000
0059380000
00861820000
00001841351232
000099191249
0000794824177
000090538783
,
1651381651380000
15276152760000
76103000000
89165000000
00004319500
000014519800
000014883199145
000029744642
,
76103761030000
89165891650000
001651380000
00152760000
00001995900
00002074200
000015048198207
00005918818243

G:=sub<GL(8,GF(241))| [51,191,0,0,0,0,0,0,240,1,0,0,0,0,0,0,0,0,51,191,0,0,0,0,0,0,240,1,0,0,0,0,0,0,0,0,240,192,64,215,0,0,0,0,123,1,215,106,0,0,0,0,0,0,1,118,0,0,0,0,0,0,49,240],[59,86,0,0,0,0,0,0,38,182,0,0,0,0,0,0,0,0,59,86,0,0,0,0,0,0,38,182,0,0,0,0,0,0,0,0,184,99,79,90,0,0,0,0,135,191,48,53,0,0,0,0,123,2,24,87,0,0,0,0,2,49,177,83],[165,152,76,89,0,0,0,0,138,76,103,165,0,0,0,0,165,152,0,0,0,0,0,0,138,76,0,0,0,0,0,0,0,0,0,0,43,145,148,29,0,0,0,0,195,198,83,74,0,0,0,0,0,0,199,46,0,0,0,0,0,0,145,42],[76,89,0,0,0,0,0,0,103,165,0,0,0,0,0,0,76,89,165,152,0,0,0,0,103,165,138,76,0,0,0,0,0,0,0,0,199,207,150,59,0,0,0,0,59,42,48,188,0,0,0,0,0,0,198,182,0,0,0,0,0,0,207,43] >;

D20.28D6 in GAP, Magma, Sage, TeX

D_{20}._{28}D_6
% in TeX

G:=Group("D20.28D6");
// GroupNames label

G:=SmallGroup(480,594);
// by ID

G=gap.SmallGroup(480,594);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,254,219,100,675,185,80,1356,18822]);
// Polycyclic

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

׿
×
𝔽