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G = (C2×C10)⋊8Dic6order 480 = 25·3·5

2nd semidirect product of C2×C10 and Dic6 acting via Dic6/Dic3=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C2×C30)⋊3Q8, (C2×C10)⋊8Dic6, (C2×C6)⋊1Dic10, C222(C15⋊Q8), C30.63(C2×Q8), C10.166(S3×D4), C30.255(C2×D4), C1523(C22⋊Q8), C23.35(S3×D5), C23.D5.4S3, C6.88(C4○D20), C33(C20.48D4), Dic155C440C2, C30.Q840C2, C6.Dic1040C2, (C2×Dic5).67D6, (C5×Dic3).42D4, C6.30(C2×Dic10), C10.30(C2×Dic6), (C22×C6).50D10, C30.161(C4○D4), (C2×C30).217C23, C57(Dic3.D4), (C22×C10).113D6, C10.60(D42S3), (C22×Dic3).6D5, (C2×Dic3).167D10, C30.38D4.10C2, Dic3.19(C5⋊D4), (C22×C30).79C22, C2.31(Dic5.D6), (C6×Dic5).124C22, (C2×Dic15).146C22, (C10×Dic3).205C22, (C2×C15⋊Q8)⋊17C2, C2.12(C2×C15⋊Q8), C6.69(C2×C5⋊D4), C2.46(S3×C5⋊D4), (Dic3×C2×C10).7C2, C22.246(C2×S3×D5), (C3×C23.D5).5C2, (C2×C6).229(C22×D5), (C2×C10).229(C22×S3), SmallGroup(480,651)

Series: Derived Chief Lower central Upper central

C1C2×C30 — (C2×C10)⋊8Dic6
C1C5C15C30C2×C30C6×Dic5C2×C15⋊Q8 — (C2×C10)⋊8Dic6
C15C2×C30 — (C2×C10)⋊8Dic6
C1C22C23

Generators and relations for (C2×C10)⋊8Dic6
 G = < a,b,c,d | a2=b6=c20=1, d2=c10, ab=ba, ac=ca, dad-1=ab3, cbc-1=b-1, bd=db, dcd-1=c-1 >

Subgroups: 620 in 148 conjugacy classes, 56 normal (44 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×7], C22, C22 [×2], C22 [×2], C5, C6 [×3], C6 [×2], C2×C4 [×8], Q8 [×2], C23, C10 [×3], C10 [×2], Dic3 [×2], Dic3 [×3], C12 [×2], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C22⋊C4 [×2], C4⋊C4 [×3], C22×C4, C2×Q8, Dic5 [×4], C20 [×3], C2×C10, C2×C10 [×2], C2×C10 [×2], Dic6 [×2], C2×Dic3 [×2], C2×Dic3 [×4], C2×C12 [×2], C22×C6, C30 [×3], C30 [×2], C22⋊Q8, Dic10 [×2], C2×Dic5 [×2], C2×Dic5 [×2], C2×C20 [×4], C22×C10, Dic3⋊C4 [×2], C4⋊Dic3, C6.D4, C3×C22⋊C4, C2×Dic6, C22×Dic3, C5×Dic3 [×2], C5×Dic3, C3×Dic5 [×2], Dic15 [×2], C2×C30, C2×C30 [×2], C2×C30 [×2], C10.D4 [×2], C4⋊Dic5, C23.D5, C23.D5, C2×Dic10, C22×C20, Dic3.D4, C15⋊Q8 [×2], C6×Dic5 [×2], C10×Dic3 [×2], C10×Dic3 [×2], C2×Dic15 [×2], C22×C30, C20.48D4, C30.Q8, Dic155C4, C6.Dic10, C3×C23.D5, C30.38D4, C2×C15⋊Q8, Dic3×C2×C10, (C2×C10)⋊8Dic6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], Q8 [×2], C23, D5, D6 [×3], C2×D4, C2×Q8, C4○D4, D10 [×3], Dic6 [×2], C22×S3, C22⋊Q8, Dic10 [×2], C5⋊D4 [×2], C22×D5, C2×Dic6, S3×D4, D42S3, S3×D5, C2×Dic10, C4○D20, C2×C5⋊D4, Dic3.D4, C15⋊Q8 [×2], C2×S3×D5, C20.48D4, Dic5.D6, C2×C15⋊Q8, S3×C5⋊D4, (C2×C10)⋊8Dic6

Smallest permutation representation of (C2×C10)⋊8Dic6
On 240 points
Generators in S240
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(21 149)(22 150)(23 151)(24 152)(25 153)(26 154)(27 155)(28 156)(29 157)(30 158)(31 159)(32 160)(33 141)(34 142)(35 143)(36 144)(37 145)(38 146)(39 147)(40 148)(41 51)(42 52)(43 53)(44 54)(45 55)(46 56)(47 57)(48 58)(49 59)(50 60)(61 71)(62 72)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(81 229)(82 230)(83 231)(84 232)(85 233)(86 234)(87 235)(88 236)(89 237)(90 238)(91 239)(92 240)(93 221)(94 222)(95 223)(96 224)(97 225)(98 226)(99 227)(100 228)(101 196)(102 197)(103 198)(104 199)(105 200)(106 181)(107 182)(108 183)(109 184)(110 185)(111 186)(112 187)(113 188)(114 189)(115 190)(116 191)(117 192)(118 193)(119 194)(120 195)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(127 137)(128 138)(129 139)(130 140)(161 171)(162 172)(163 173)(164 174)(165 175)(166 176)(167 177)(168 178)(169 179)(170 180)(201 211)(202 212)(203 213)(204 214)(205 215)(206 216)(207 217)(208 218)(209 219)(210 220)
(1 61 139 179 205 41)(2 42 206 180 140 62)(3 63 121 161 207 43)(4 44 208 162 122 64)(5 65 123 163 209 45)(6 46 210 164 124 66)(7 67 125 165 211 47)(8 48 212 166 126 68)(9 69 127 167 213 49)(10 50 214 168 128 70)(11 71 129 169 215 51)(12 52 216 170 130 72)(13 73 131 171 217 53)(14 54 218 172 132 74)(15 75 133 173 219 55)(16 56 220 174 134 76)(17 77 135 175 201 57)(18 58 202 176 136 78)(19 79 137 177 203 59)(20 60 204 178 138 80)(21 106 223 159 191 85)(22 86 192 160 224 107)(23 108 225 141 193 87)(24 88 194 142 226 109)(25 110 227 143 195 89)(26 90 196 144 228 111)(27 112 229 145 197 91)(28 92 198 146 230 113)(29 114 231 147 199 93)(30 94 200 148 232 115)(31 116 233 149 181 95)(32 96 182 150 234 117)(33 118 235 151 183 97)(34 98 184 152 236 119)(35 120 237 153 185 99)(36 100 186 154 238 101)(37 102 239 155 187 81)(38 82 188 156 240 103)(39 104 221 157 189 83)(40 84 190 158 222 105)
(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 33 11 23)(2 32 12 22)(3 31 13 21)(4 30 14 40)(5 29 15 39)(6 28 16 38)(7 27 17 37)(8 26 18 36)(9 25 19 35)(10 24 20 34)(41 97 51 87)(42 96 52 86)(43 95 53 85)(44 94 54 84)(45 93 55 83)(46 92 56 82)(47 91 57 81)(48 90 58 100)(49 89 59 99)(50 88 60 98)(61 118 71 108)(62 117 72 107)(63 116 73 106)(64 115 74 105)(65 114 75 104)(66 113 76 103)(67 112 77 102)(68 111 78 101)(69 110 79 120)(70 109 80 119)(121 233 131 223)(122 232 132 222)(123 231 133 221)(124 230 134 240)(125 229 135 239)(126 228 136 238)(127 227 137 237)(128 226 138 236)(129 225 139 235)(130 224 140 234)(141 179 151 169)(142 178 152 168)(143 177 153 167)(144 176 154 166)(145 175 155 165)(146 174 156 164)(147 173 157 163)(148 172 158 162)(149 171 159 161)(150 170 160 180)(181 217 191 207)(182 216 192 206)(183 215 193 205)(184 214 194 204)(185 213 195 203)(186 212 196 202)(187 211 197 201)(188 210 198 220)(189 209 199 219)(190 208 200 218)

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

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

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

72 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D4E4F4G4H5A5B6A6B6C6D6E10A···10N12A12B12C12D15A15B20A···20P30A···30N
order122222344444444556666610···1012121212151520···2030···30
size111122266662020606022222442···220202020446···64···4

72 irreducible representations

dim1111111122222222222224444444
type++++++++++-+++++--+-+-+
imageC1C2C2C2C2C2C2C2S3D4Q8D5D6D6C4○D4D10D10Dic6C5⋊D4Dic10C4○D20S3×D4D42S3S3×D5C15⋊Q8C2×S3×D5Dic5.D6S3×C5⋊D4
kernel(C2×C10)⋊8Dic6C30.Q8Dic155C4C6.Dic10C3×C23.D5C30.38D4C2×C15⋊Q8Dic3×C2×C10C23.D5C5×Dic3C2×C30C22×Dic3C2×Dic5C22×C10C30C2×Dic3C22×C6C2×C10Dic3C2×C6C6C10C10C23C22C22C2C2
# reps1111111112222124248881124244

Matrix representation of (C2×C10)⋊8Dic6 in GL4(𝔽61) generated by

1000
606000
00600
00060
,
60000
06000
00060
00160
,
34000
18900
003651
002625
,
544700
47700
003846
001523
G:=sub<GL(4,GF(61))| [1,60,0,0,0,60,0,0,0,0,60,0,0,0,0,60],[60,0,0,0,0,60,0,0,0,0,0,1,0,0,60,60],[34,18,0,0,0,9,0,0,0,0,36,26,0,0,51,25],[54,47,0,0,47,7,0,0,0,0,38,15,0,0,46,23] >;

(C2×C10)⋊8Dic6 in GAP, Magma, Sage, TeX

(C_2\times C_{10})\rtimes_8{\rm Dic}_6
% in TeX

G:=Group("(C2xC10):8Dic6");
// GroupNames label

G:=SmallGroup(480,651);
// by ID

G=gap.SmallGroup(480,651);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,64,422,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^6=c^20=1,d^2=c^10,a*b=b*a,a*c=c*a,d*a*d^-1=a*b^3,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽