Copied to
clipboard

G = (C2×C6)⋊Dic10order 480 = 25·3·5

1st semidirect product of C2×C6 and Dic10 acting via Dic10/C10=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C2×C30)⋊3Q8, (C2×C6)⋊1Dic10, (C2×C10)⋊8Dic6, 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), C30.Q840C2, Dic155C440C2, C6.Dic1040C2, (C5×Dic3).42D4, (C2×Dic5).67D6, C10.30(C2×Dic6), C6.30(C2×Dic10), (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, (C10×Dic3).205C22, (C2×Dic15).146C22, (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×C6)⋊Dic10
C1C5C15C30C2×C30C6×Dic5C2×C15⋊Q8 — (C2×C6)⋊Dic10
C15C2×C30 — (C2×C6)⋊Dic10
C1C22C23

Generators and relations for (C2×C6)⋊Dic10
 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×C6)⋊Dic10
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×C6)⋊Dic10

Smallest permutation representation of (C2×C6)⋊Dic10
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)(21 169)(22 170)(23 171)(24 172)(25 173)(26 174)(27 175)(28 176)(29 177)(30 178)(31 179)(32 180)(33 161)(34 162)(35 163)(36 164)(37 165)(38 166)(39 167)(40 168)(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)(81 208)(82 209)(83 210)(84 211)(85 212)(86 213)(87 214)(88 215)(89 216)(90 217)(91 218)(92 219)(93 220)(94 201)(95 202)(96 203)(97 204)(98 205)(99 206)(100 207)(101 155)(102 156)(103 157)(104 158)(105 159)(106 160)(107 141)(108 142)(109 143)(110 144)(111 145)(112 146)(113 147)(114 148)(115 149)(116 150)(117 151)(118 152)(119 153)(120 154)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(127 137)(128 138)(129 139)(130 140)(181 191)(182 192)(183 193)(184 194)(185 195)(186 196)(187 197)(188 198)(189 199)(190 200)(221 231)(222 232)(223 233)(224 234)(225 235)(226 236)(227 237)(228 238)(229 239)(230 240)
(1 228 189 49 140 77)(2 78 121 50 190 229)(3 230 191 51 122 79)(4 80 123 52 192 231)(5 232 193 53 124 61)(6 62 125 54 194 233)(7 234 195 55 126 63)(8 64 127 56 196 235)(9 236 197 57 128 65)(10 66 129 58 198 237)(11 238 199 59 130 67)(12 68 131 60 200 239)(13 240 181 41 132 69)(14 70 133 42 182 221)(15 222 183 43 134 71)(16 72 135 44 184 223)(17 224 185 45 136 73)(18 74 137 46 186 225)(19 226 187 47 138 75)(20 76 139 48 188 227)(21 202 157 179 85 113)(22 114 86 180 158 203)(23 204 159 161 87 115)(24 116 88 162 160 205)(25 206 141 163 89 117)(26 118 90 164 142 207)(27 208 143 165 91 119)(28 120 92 166 144 209)(29 210 145 167 93 101)(30 102 94 168 146 211)(31 212 147 169 95 103)(32 104 96 170 148 213)(33 214 149 171 97 105)(34 106 98 172 150 215)(35 216 151 173 99 107)(36 108 100 174 152 217)(37 218 153 175 81 109)(38 110 82 176 154 219)(39 220 155 177 83 111)(40 112 84 178 156 201)
(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)
(1 156 11 146)(2 155 12 145)(3 154 13 144)(4 153 14 143)(5 152 15 142)(6 151 16 141)(7 150 17 160)(8 149 18 159)(9 148 19 158)(10 147 20 157)(21 198 31 188)(22 197 32 187)(23 196 33 186)(24 195 34 185)(25 194 35 184)(26 193 36 183)(27 192 37 182)(28 191 38 181)(29 190 39 200)(30 189 40 199)(41 120 51 110)(42 119 52 109)(43 118 53 108)(44 117 54 107)(45 116 55 106)(46 115 56 105)(47 114 57 104)(48 113 58 103)(49 112 59 102)(50 111 60 101)(61 174 71 164)(62 173 72 163)(63 172 73 162)(64 171 74 161)(65 170 75 180)(66 169 76 179)(67 168 77 178)(68 167 78 177)(69 166 79 176)(70 165 80 175)(81 133 91 123)(82 132 92 122)(83 131 93 121)(84 130 94 140)(85 129 95 139)(86 128 96 138)(87 127 97 137)(88 126 98 136)(89 125 99 135)(90 124 100 134)(201 238 211 228)(202 237 212 227)(203 236 213 226)(204 235 214 225)(205 234 215 224)(206 233 216 223)(207 232 217 222)(208 231 218 221)(209 230 219 240)(210 229 220 239)

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

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

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

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×C6)⋊Dic10C30.Q8Dic155C4C6.Dic10C3×C23.D5C30.38D4C2×C15⋊Q8Dic3×C2×C10C23.D5C5×Dic3C2×C30C22×Dic3C2×Dic5C22×C10C30C2×Dic3C22×C6C2×C10Dic3C2×C6C6C10C10C23C22C22C2C2
# reps1111111112222124248881124244

Matrix representation of (C2×C6)⋊Dic10 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×C6)⋊Dic10 in GAP, Magma, Sage, TeX

(C_2\times C_6)\rtimes {\rm Dic}_{10}
% in TeX

G:=Group("(C2xC6):Dic10");
// 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