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G = D20.37D6order 480 = 25·3·5

8th non-split extension by D20 of D6 acting via D6/C6=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C60.62D4, D20.37D6, C60.154C23, Dic6.37D10, Dic10.37D6, C4○D20.4S3, (C2×Dic6)⋊8D5, (C2×C30).50D4, C30.82(C2×D4), (C2×C20).93D6, C60.7C44C2, (C10×Dic6)⋊1C2, C15⋊Q1613C2, (C2×C12).93D10, C54(Q8.14D6), C157(C8.C22), C30.D414C2, C4.17(C15⋊D4), C34(C20.C23), C12.83(C5⋊D4), C20.27(C3⋊D4), C20.93(C22×S3), (C2×C60).26C22, C12.91(C22×D5), C153C8.25C22, (C3×D20).43C22, C22.10(C15⋊D4), (C5×Dic6).44C22, (C3×Dic10).44C22, C4.127(C2×S3×D5), (C2×C4).12(S3×D5), C6.76(C2×C5⋊D4), (C3×C4○D20).1C2, C10.77(C2×C3⋊D4), C2.10(C2×C15⋊D4), (C2×C6).13(C5⋊D4), (C2×C10).54(C3⋊D4), SmallGroup(480,383)

Series: Derived Chief Lower central Upper central

C1C60 — D20.37D6
C1C5C15C30C60C3×D20C30.D4 — D20.37D6
C15C30C60 — D20.37D6
C1C2C2×C4

Generators and relations for D20.37D6
 G = < a,b,c,d | a20=b2=1, c6=d2=a10, bab=a-1, ac=ca, dad-1=a11, bc=cb, dbd-1=a15b, dcd-1=a10c5 >

Subgroups: 492 in 120 conjugacy classes, 44 normal (34 characteristic)
C1, C2, C2 [×2], C3, C4 [×2], C4 [×3], C22, C22, C5, C6, C6 [×2], C8 [×2], C2×C4, C2×C4 [×2], D4 [×2], Q8 [×4], D5, C10, C10, Dic3 [×2], C12 [×2], C12, C2×C6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5, C20 [×2], C20 [×2], D10, C2×C10, C3⋊C8 [×2], Dic6 [×2], Dic6, C2×Dic3, C2×C12, C2×C12, C3×D4 [×2], C3×Q8, C3×D5, C30, C30, C8.C22, C52C8 [×2], Dic10, C4×D5, D20, C5⋊D4, C2×C20, C2×C20, C5×Q8 [×3], C4.Dic3, D4.S3 [×2], C3⋊Q16 [×2], C2×Dic6, C3×C4○D4, C5×Dic3 [×2], C3×Dic5, C60 [×2], C6×D5, C2×C30, C4.Dic5, Q8⋊D5 [×2], C5⋊Q16 [×2], C4○D20, Q8×C10, Q8.14D6, C153C8 [×2], C3×Dic10, D5×C12, C3×D20, C3×C5⋊D4, C5×Dic6 [×2], C5×Dic6, C10×Dic3, C2×C60, C20.C23, C30.D4 [×2], C15⋊Q16 [×2], C60.7C4, C3×C4○D20, C10×Dic6, D20.37D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C8.C22, C5⋊D4 [×2], C22×D5, C2×C3⋊D4, S3×D5, C2×C5⋊D4, Q8.14D6, C15⋊D4 [×2], C2×S3×D5, C20.C23, C2×C15⋊D4, D20.37D6

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

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

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

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

57 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B6A6B6C6D8A8B10A···10F12A12B12C12D12E15A15B20A20B20C20D20E···20L30A···30F60A···60H
order12223444445566668810···10121212121215152020202020···2030···3060···60
size112202221212202224202060602···2224202044444412···124···44···4

57 irreducible representations

dim111111222222222222244444444
type+++++++++++++++-+--+-
imageC1C2C2C2C2C2S3D4D4D5D6D6D6D10D10C3⋊D4C3⋊D4C5⋊D4C5⋊D4C8.C22S3×D5Q8.14D6C15⋊D4C2×S3×D5C15⋊D4C20.C23D20.37D6
kernelD20.37D6C30.D4C15⋊Q16C60.7C4C3×C4○D20C10×Dic6C4○D20C60C2×C30C2×Dic6Dic10D20C2×C20Dic6C2×C12C20C2×C10C12C2×C6C15C2×C4C5C4C4C22C3C1
# reps122111111211142224412222248

Matrix representation of D20.37D6 in GL4(𝔽241) generated by

552200
13818600
4712492184
9112457149
,
350714
440206206
19411714957
916214957
,
03700
135600
09999142
139999198
,
21718100
1022400
15910091125
18610034150
G:=sub<GL(4,GF(241))| [55,138,47,91,22,186,124,124,0,0,92,57,0,0,184,149],[35,44,194,91,0,0,117,62,7,206,149,149,14,206,57,57],[0,13,0,13,37,56,99,99,0,0,99,99,0,0,142,198],[217,102,159,186,181,24,100,100,0,0,91,34,0,0,125,150] >;

D20.37D6 in GAP, Magma, Sage, TeX

D_{20}._{37}D_6
% in TeX

G:=Group("D20.37D6");
// GroupNames label

G:=SmallGroup(480,383);
// by ID

G=gap.SmallGroup(480,383);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,141,120,219,100,675,346,80,1356,18822]);
// Polycyclic

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

׿
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