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G = D6.9D20order 480 = 25·3·5

6th non-split extension by D6 of D20 acting via D20/D10=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D6.9D20, D6⋊C46D5, C605C47C2, (S3×C10).7D4, C6.22(C2×D20), C2.23(S3×D20), (C2×C20).28D6, C30.63(C2×D4), C10.21(S3×D4), D10⋊C45S3, (C2×C12).28D10, C53(C23.9D6), (C2×C60).13C22, C6.Dic1026C2, (C22×D5).18D6, C10.62(C4○D12), C30.126(C4○D4), C6.31(D42D5), D10⋊Dic318C2, (C2×C30).147C23, (C2×Dic5).120D6, (C2×Dic3).45D10, (C22×S3).47D10, C32(C22.D20), C10.73(D42S3), C2.18(D125D5), C1515(C22.D4), (C6×Dic5).88C22, C2.18(C30.C23), (C10×Dic3).89C22, (C2×Dic15).114C22, (C5×D6⋊C4)⋊6C2, (C2×S3×Dic5)⋊11C2, (C2×C4).61(S3×D5), (C2×C15⋊D4).7C2, (C3×D10⋊C4)⋊5C2, (D5×C2×C6).32C22, C22.199(C2×S3×D5), (S3×C2×C10).34C22, (C2×C6).159(C22×D5), (C2×C10).159(C22×S3), SmallGroup(480,533)

Series: Derived Chief Lower central Upper central

C1C2×C30 — D6.9D20
C1C5C15C30C2×C30D5×C2×C6C2×C15⋊D4 — D6.9D20
C15C2×C30 — D6.9D20
C1C22C2×C4

Generators and relations for D6.9D20
 G = < a,b,c,d | a6=b2=c20=1, d2=a3, bab=a-1, ac=ca, ad=da, cbc-1=a3b, bd=db, dcd-1=a3c-1 >

Subgroups: 812 in 156 conjugacy classes, 48 normal (44 characteristic)
C1, C2 [×3], C2 [×3], C3, C4 [×5], C22, C22 [×7], C5, S3 [×2], C6 [×3], C6, C2×C4, C2×C4 [×6], D4 [×2], C23 [×2], D5, C10 [×3], C10 [×2], Dic3 [×3], C12 [×2], D6 [×2], D6 [×2], C2×C6, C2×C6 [×3], C15, C22⋊C4 [×3], C4⋊C4 [×2], C22×C4, C2×D4, Dic5 [×3], C20 [×2], D10 [×3], C2×C10, C2×C10 [×4], C4×S3 [×2], C2×Dic3, C2×Dic3 [×2], C3⋊D4 [×2], C2×C12, C2×C12, C22×S3, C22×C6, C5×S3 [×2], C3×D5, C30 [×3], C22.D4, C2×Dic5, C2×Dic5 [×4], C5⋊D4 [×2], C2×C20, C2×C20, C22×D5, C22×C10, Dic3⋊C4, C4⋊Dic3, D6⋊C4, C6.D4, C3×C22⋊C4, S3×C2×C4, C2×C3⋊D4, C5×Dic3, C3×Dic5, Dic15 [×2], C60, C6×D5 [×3], S3×C10 [×2], S3×C10 [×2], C2×C30, C4⋊Dic5 [×2], D10⋊C4, D10⋊C4, C5×C22⋊C4, C22×Dic5, C2×C5⋊D4, C23.9D6, S3×Dic5 [×2], C15⋊D4 [×2], C6×Dic5, C10×Dic3, C2×Dic15 [×2], C2×C60, D5×C2×C6, S3×C2×C10, C22.D20, D10⋊Dic3, C6.Dic10, C3×D10⋊C4, C5×D6⋊C4, C605C4, C2×S3×Dic5, C2×C15⋊D4, D6.9D20
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, C4○D4 [×2], D10 [×3], C22×S3, C22.D4, D20 [×2], C22×D5, C4○D12, S3×D4, D42S3, S3×D5, C2×D20, D42D5 [×2], C23.9D6, C2×S3×D5, C22.D20, D125D5, S3×D20, C30.C23, D6.9D20

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

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

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

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

60 conjugacy classes

class 1 2A2B2C2D2E2F 3 4A4B4C4D4E4F4G5A5B6A6B6C6D6E10A···10F10G10H10I10J12A12B12C12D15A15B20A20B20C20D20E20F20G20H30A···30F60A···60H
order122222234444444556666610···1010101010121212121515202020202020202030···3060···60
size11116620241010123030602222220202···212121212442020444444121212124···44···4

60 irreducible representations

dim1111111122222222222244444444
type+++++++++++++++++++-+-+-+-
imageC1C2C2C2C2C2C2C2S3D4D5D6D6D6C4○D4D10D10D10D20C4○D12S3×D4D42S3S3×D5D42D5C2×S3×D5D125D5S3×D20C30.C23
kernelD6.9D20D10⋊Dic3C6.Dic10C3×D10⋊C4C5×D6⋊C4C605C4C2×S3×Dic5C2×C15⋊D4D10⋊C4S3×C10D6⋊C4C2×Dic5C2×C20C22×D5C30C2×Dic3C2×C12C22×S3D6C10C10C10C2×C4C6C22C2C2C2
# reps1111111112211142228411242444

Matrix representation of D6.9D20 in GL4(𝔽61) generated by

601900
48200
0010
0001
,
591900
48200
0010
0001
,
532000
12800
00240
00328
,
11000
01100
004114
00220
G:=sub<GL(4,GF(61))| [60,48,0,0,19,2,0,0,0,0,1,0,0,0,0,1],[59,48,0,0,19,2,0,0,0,0,1,0,0,0,0,1],[53,12,0,0,20,8,0,0,0,0,24,3,0,0,0,28],[11,0,0,0,0,11,0,0,0,0,41,2,0,0,14,20] >;

D6.9D20 in GAP, Magma, Sage, TeX

D_6._9D_{20}
% in TeX

G:=Group("D6.9D20");
// GroupNames label

G:=SmallGroup(480,533);
// by ID

G=gap.SmallGroup(480,533);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,254,219,142,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^6=b^2=c^20=1,d^2=a^3,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^3*b,b*d=d*b,d*c*d^-1=a^3*c^-1>;
// generators/relations

׿
×
𝔽