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G = D20.34D6order 480 = 25·3·5

5th non-split extension by D20 of D6 acting via D6/C6=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D20.34D6, C60.108D4, D12.34D10, C60.150C23, Dic6.36D10, Dic10.36D6, C4○D122D5, C4○D202S3, C1510(C4○D8), C15⋊D815C2, C30.72(C2×D4), (C2×C20).84D6, (C2×C30).40D4, C15⋊Q1615C2, (C2×C12).85D10, C56(Q8.13D6), C30.D415C2, C20.D615C2, C36(D4.8D10), C4.32(C15⋊D4), C20.90(C3⋊D4), C12.90(C5⋊D4), C20.85(C22×S3), C12.85(C22×D5), (C2×C60).216C22, C153C8.44C22, (C5×D12).40C22, (C3×D20).40C22, C22.1(C15⋊D4), (C5×Dic6).43C22, (C3×Dic10).43C22, C4.123(C2×S3×D5), (C5×C4○D12)⋊9C2, (C3×C4○D20)⋊9C2, (C2×C153C8)⋊20C2, C2.6(C2×C15⋊D4), C6.72(C2×C5⋊D4), (C2×C4).197(S3×D5), (C2×C6).9(C5⋊D4), C10.73(C2×C3⋊D4), (C2×C10).8(C3⋊D4), SmallGroup(480,373)

Series: Derived Chief Lower central Upper central

C1C60 — D20.34D6
C1C5C15C30C60C3×D20C15⋊D8 — D20.34D6
C15C30C60 — D20.34D6
C1C4C2×C4

Generators and relations for D20.34D6
 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=c5 >

Subgroups: 524 in 124 conjugacy classes, 44 normal (all characteristic)
C1, C2, C2 [×3], C3, C4 [×2], C4 [×2], C22, C22 [×2], C5, S3, C6, C6 [×2], C8 [×2], C2×C4, C2×C4 [×2], D4 [×4], Q8 [×2], D5, C10, C10 [×2], Dic3, C12 [×2], C12, D6, C2×C6, C2×C6, C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5, C20 [×2], C20, D10, C2×C10, C2×C10, C3⋊C8 [×2], Dic6, C4×S3, D12, C3⋊D4, C2×C12, C2×C12, C3×D4 [×2], C3×Q8, C5×S3, C3×D5, C30, C30, C4○D8, C52C8 [×2], Dic10, C4×D5, D20, C5⋊D4, C2×C20, C2×C20, C5×D4 [×2], C5×Q8, C2×C3⋊C8, D4⋊S3, D4.S3, Q82S3, C3⋊Q16, C4○D12, C3×C4○D4, C5×Dic3, C3×Dic5, C60 [×2], C6×D5, S3×C10, C2×C30, C2×C52C8, D4⋊D5, D4.D5, Q8⋊D5, C5⋊Q16, C4○D20, C5×C4○D4, Q8.13D6, C153C8 [×2], C3×Dic10, D5×C12, C3×D20, C3×C5⋊D4, C5×Dic6, S3×C20, C5×D12, C5×C3⋊D4, C2×C60, D4.8D10, C15⋊D8, C30.D4, C20.D6, C15⋊Q16, C2×C153C8, C3×C4○D20, C5×C4○D12, D20.34D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C4○D8, C5⋊D4 [×2], C22×D5, C2×C3⋊D4, S3×D5, C2×C5⋊D4, Q8.13D6, C15⋊D4 [×2], C2×S3×D5, D4.8D10, C2×C15⋊D4, D20.34D6

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

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

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

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

60 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B6C6D8A8B8C8D10A10B10C10D10E10F10G10H12A12B12C12D12E15A15B20A20B20C20D20E20F20G20H20I20J30A···30F60A···60H
order1222234444455666688881010101010101010121212121215152020202020202020202030···3060···60
size1121220211212202224202030303030224412121212224202044222244121212124···44···4

60 irreducible representations

dim111111112222222222222224444444
type+++++++++++++++++++-+-
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C3⋊D4C3⋊D4C4○D8C5⋊D4C5⋊D4S3×D5Q8.13D6C15⋊D4C2×S3×D5C15⋊D4D4.8D10D20.34D6
kernelD20.34D6C15⋊D8C30.D4C20.D6C15⋊Q16C2×C153C8C3×C4○D20C5×C4○D12C4○D20C60C2×C30C4○D12Dic10D20C2×C20Dic6D12C2×C12C20C2×C10C15C12C2×C6C2×C4C5C4C4C22C3C1
# reps111111111112111222224442222248

Matrix representation of D20.34D6 in GL6(𝔽241)

010000
240510000
0064000
0015917700
00002400
00000240
,
1251440000
121160000
003013500
0017921100
0000171140
000010170
,
100000
010000
00177000
00017700
000001
00002401
,
24000000
02400000
00644700
00017700
00008971
0000160152

G:=sub<GL(6,GF(241))| [0,240,0,0,0,0,1,51,0,0,0,0,0,0,64,159,0,0,0,0,0,177,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[125,12,0,0,0,0,144,116,0,0,0,0,0,0,30,179,0,0,0,0,135,211,0,0,0,0,0,0,171,101,0,0,0,0,140,70],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,177,0,0,0,0,0,0,177,0,0,0,0,0,0,0,240,0,0,0,0,1,1],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,64,0,0,0,0,0,47,177,0,0,0,0,0,0,89,160,0,0,0,0,71,152] >;

D20.34D6 in GAP, Magma, Sage, TeX

D_{20}._{34}D_6
% in TeX

G:=Group("D20.34D6");
// GroupNames label

G:=SmallGroup(480,373);
// by ID

G=gap.SmallGroup(480,373);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,141,100,675,346,80,1356,18822]);
// 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=c^5>;
// generators/relations

׿
×
𝔽