metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D10⋊2Dic6, Dic3.10D20, (C6×D5)⋊2Q8, C60⋊5C4⋊6C2, C6.34(Q8×D5), Dic3⋊C4⋊5D5, C6.14(C2×D20), (C2×C20).20D6, C10.14(S3×D4), C2.18(S3×D20), C30.45(C2×D4), C30.43(C2×Q8), C3⋊2(D10⋊2Q8), (C2×C12).19D10, (C2×C60).9C22, C15⋊15(C22⋊Q8), (C5×Dic3).7D4, C2.16(D5×Dic6), D10⋊C4.3S3, C6.Dic10⋊18C2, (C2×Dic5).35D6, C10.16(C2×Dic6), (C22×D5).50D6, C30.120(C4○D4), C6.72(D4⋊2D5), (C2×C30).112C23, C5⋊1(Dic3.D4), C10.71(D4⋊2S3), (C2×Dic3).105D10, D10⋊Dic3.12C2, (C6×Dic5).66C22, C2.17(C30.C23), (C10×Dic3).70C22, (C2×Dic15).90C22, (C2×C15⋊Q8)⋊8C2, (C2×C4).48(S3×D5), (C2×D5×Dic3).6C2, (C5×Dic3⋊C4)⋊5C2, (D5×C2×C6).20C22, C22.178(C2×S3×D5), (C3×D10⋊C4).3C2, (C2×C6).124(C22×D5), (C2×C10).124(C22×S3), SmallGroup(480,498)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D10⋊2Dic6
G = < a,b,c,d | a10=b2=c12=1, d2=c6, bab=cac-1=a-1, ad=da, cbc-1=a3b, bd=db, dcd-1=c-1 >
Subgroups: 748 in 148 conjugacy classes, 52 normal (44 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, C6, C6, C2×C4, C2×C4, Q8, C23, D5, C10, Dic3, Dic3, C12, C2×C6, C2×C6, C15, C22⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic5, C20, D10, D10, C2×C10, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C22×C6, C3×D5, C30, C22⋊Q8, Dic10, C4×D5, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×D5, Dic3⋊C4, Dic3⋊C4, C4⋊Dic3, C6.D4, C3×C22⋊C4, C2×Dic6, C22×Dic3, C5×Dic3, C5×Dic3, C3×Dic5, Dic15, C60, C6×D5, C6×D5, C2×C30, C4⋊Dic5, D10⋊C4, D10⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, Dic3.D4, D5×Dic3, C15⋊Q8, C6×Dic5, C10×Dic3, C2×Dic15, C2×C60, D5×C2×C6, D10⋊2Q8, D10⋊Dic3, C6.Dic10, C3×D10⋊C4, C5×Dic3⋊C4, C60⋊5C4, C2×D5×Dic3, C2×C15⋊Q8, D10⋊2Dic6
Quotients: C1, C2, C22, S3, D4, Q8, C23, D5, D6, C2×D4, C2×Q8, C4○D4, D10, Dic6, C22×S3, C22⋊Q8, D20, C22×D5, C2×Dic6, S3×D4, D4⋊2S3, S3×D5, C2×D20, D4⋊2D5, Q8×D5, Dic3.D4, C2×S3×D5, D10⋊2Q8, D5×Dic6, S3×D20, C30.C23, D10⋊2Dic6
►On 240 points
Generators in S240
(1 135 234 92 206 223 43 154 104 179)(2 180 105 155 44 224 207 93 235 136)(3 137 236 94 208 225 45 156 106 169)(4 170 107 145 46 226 209 95 237 138)(5 139 238 96 210 227 47 146 108 171)(6 172 97 147 48 228 211 85 239 140)(7 141 240 86 212 217 37 148 98 173)(8 174 99 149 38 218 213 87 229 142)(9 143 230 88 214 219 39 150 100 175)(10 176 101 151 40 220 215 89 231 144)(11 133 232 90 216 221 41 152 102 177)(12 178 103 153 42 222 205 91 233 134)(13 116 56 61 166 76 123 194 26 192)(14 181 27 195 124 77 167 62 57 117)(15 118 58 63 168 78 125 196 28 182)(16 183 29 197 126 79 157 64 59 119)(17 120 60 65 158 80 127 198 30 184)(18 185 31 199 128 81 159 66 49 109)(19 110 50 67 160 82 129 200 32 186)(20 187 33 201 130 83 161 68 51 111)(21 112 52 69 162 84 131 202 34 188)(22 189 35 203 132 73 163 70 53 113)(23 114 54 71 164 74 121 204 36 190)(24 191 25 193 122 75 165 72 55 115)
(1 173)(2 38)(3 175)(4 40)(5 177)(6 42)(7 179)(8 44)(9 169)(10 46)(11 171)(12 48)(13 129)(14 68)(15 131)(16 70)(17 121)(18 72)(19 123)(20 62)(21 125)(22 64)(23 127)(24 66)(25 81)(26 32)(27 83)(28 34)(29 73)(30 36)(31 75)(33 77)(35 79)(37 92)(39 94)(41 96)(43 86)(45 88)(47 90)(49 115)(50 166)(51 117)(52 168)(53 119)(54 158)(55 109)(56 160)(57 111)(58 162)(59 113)(60 164)(61 67)(63 69)(65 71)(74 120)(76 110)(78 112)(80 114)(82 116)(84 118)(85 91)(87 93)(89 95)(97 103)(98 135)(99 105)(100 137)(101 107)(102 139)(104 141)(106 143)(108 133)(122 199)(124 201)(126 203)(128 193)(130 195)(132 197)(134 228)(136 218)(138 220)(140 222)(142 224)(144 226)(145 176)(146 232)(147 178)(148 234)(149 180)(150 236)(151 170)(152 238)(153 172)(154 240)(155 174)(156 230)(157 189)(159 191)(161 181)(163 183)(165 185)(167 187)(182 202)(184 204)(186 194)(188 196)(190 198)(192 200)(205 239)(206 217)(207 229)(208 219)(209 231)(210 221)(211 233)(212 223)(213 235)(214 225)(215 237)(216 227)
(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)
(1 130 7 124)(2 129 8 123)(3 128 9 122)(4 127 10 121)(5 126 11 132)(6 125 12 131)(13 44 19 38)(14 43 20 37)(15 42 21 48)(16 41 22 47)(17 40 23 46)(18 39 24 45)(25 106 31 100)(26 105 32 99)(27 104 33 98)(28 103 34 97)(29 102 35 108)(30 101 36 107)(49 214 55 208)(50 213 56 207)(51 212 57 206)(52 211 58 205)(53 210 59 216)(54 209 60 215)(61 93 67 87)(62 92 68 86)(63 91 69 85)(64 90 70 96)(65 89 71 95)(66 88 72 94)(73 139 79 133)(74 138 80 144)(75 137 81 143)(76 136 82 142)(77 135 83 141)(78 134 84 140)(109 219 115 225)(110 218 116 224)(111 217 117 223)(112 228 118 222)(113 227 119 221)(114 226 120 220)(145 184 151 190)(146 183 152 189)(147 182 153 188)(148 181 154 187)(149 192 155 186)(150 191 156 185)(157 232 163 238)(158 231 164 237)(159 230 165 236)(160 229 166 235)(161 240 167 234)(162 239 168 233)(169 199 175 193)(170 198 176 204)(171 197 177 203)(172 196 178 202)(173 195 179 201)(174 194 180 200)
G:=sub<Sym(240)| (1,135,234,92,206,223,43,154,104,179)(2,180,105,155,44,224,207,93,235,136)(3,137,236,94,208,225,45,156,106,169)(4,170,107,145,46,226,209,95,237,138)(5,139,238,96,210,227,47,146,108,171)(6,172,97,147,48,228,211,85,239,140)(7,141,240,86,212,217,37,148,98,173)(8,174,99,149,38,218,213,87,229,142)(9,143,230,88,214,219,39,150,100,175)(10,176,101,151,40,220,215,89,231,144)(11,133,232,90,216,221,41,152,102,177)(12,178,103,153,42,222,205,91,233,134)(13,116,56,61,166,76,123,194,26,192)(14,181,27,195,124,77,167,62,57,117)(15,118,58,63,168,78,125,196,28,182)(16,183,29,197,126,79,157,64,59,119)(17,120,60,65,158,80,127,198,30,184)(18,185,31,199,128,81,159,66,49,109)(19,110,50,67,160,82,129,200,32,186)(20,187,33,201,130,83,161,68,51,111)(21,112,52,69,162,84,131,202,34,188)(22,189,35,203,132,73,163,70,53,113)(23,114,54,71,164,74,121,204,36,190)(24,191,25,193,122,75,165,72,55,115), (1,173)(2,38)(3,175)(4,40)(5,177)(6,42)(7,179)(8,44)(9,169)(10,46)(11,171)(12,48)(13,129)(14,68)(15,131)(16,70)(17,121)(18,72)(19,123)(20,62)(21,125)(22,64)(23,127)(24,66)(25,81)(26,32)(27,83)(28,34)(29,73)(30,36)(31,75)(33,77)(35,79)(37,92)(39,94)(41,96)(43,86)(45,88)(47,90)(49,115)(50,166)(51,117)(52,168)(53,119)(54,158)(55,109)(56,160)(57,111)(58,162)(59,113)(60,164)(61,67)(63,69)(65,71)(74,120)(76,110)(78,112)(80,114)(82,116)(84,118)(85,91)(87,93)(89,95)(97,103)(98,135)(99,105)(100,137)(101,107)(102,139)(104,141)(106,143)(108,133)(122,199)(124,201)(126,203)(128,193)(130,195)(132,197)(134,228)(136,218)(138,220)(140,222)(142,224)(144,226)(145,176)(146,232)(147,178)(148,234)(149,180)(150,236)(151,170)(152,238)(153,172)(154,240)(155,174)(156,230)(157,189)(159,191)(161,181)(163,183)(165,185)(167,187)(182,202)(184,204)(186,194)(188,196)(190,198)(192,200)(205,239)(206,217)(207,229)(208,219)(209,231)(210,221)(211,233)(212,223)(213,235)(214,225)(215,237)(216,227), (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), (1,130,7,124)(2,129,8,123)(3,128,9,122)(4,127,10,121)(5,126,11,132)(6,125,12,131)(13,44,19,38)(14,43,20,37)(15,42,21,48)(16,41,22,47)(17,40,23,46)(18,39,24,45)(25,106,31,100)(26,105,32,99)(27,104,33,98)(28,103,34,97)(29,102,35,108)(30,101,36,107)(49,214,55,208)(50,213,56,207)(51,212,57,206)(52,211,58,205)(53,210,59,216)(54,209,60,215)(61,93,67,87)(62,92,68,86)(63,91,69,85)(64,90,70,96)(65,89,71,95)(66,88,72,94)(73,139,79,133)(74,138,80,144)(75,137,81,143)(76,136,82,142)(77,135,83,141)(78,134,84,140)(109,219,115,225)(110,218,116,224)(111,217,117,223)(112,228,118,222)(113,227,119,221)(114,226,120,220)(145,184,151,190)(146,183,152,189)(147,182,153,188)(148,181,154,187)(149,192,155,186)(150,191,156,185)(157,232,163,238)(158,231,164,237)(159,230,165,236)(160,229,166,235)(161,240,167,234)(162,239,168,233)(169,199,175,193)(170,198,176,204)(171,197,177,203)(172,196,178,202)(173,195,179,201)(174,194,180,200)>;
G:=Group( (1,135,234,92,206,223,43,154,104,179)(2,180,105,155,44,224,207,93,235,136)(3,137,236,94,208,225,45,156,106,169)(4,170,107,145,46,226,209,95,237,138)(5,139,238,96,210,227,47,146,108,171)(6,172,97,147,48,228,211,85,239,140)(7,141,240,86,212,217,37,148,98,173)(8,174,99,149,38,218,213,87,229,142)(9,143,230,88,214,219,39,150,100,175)(10,176,101,151,40,220,215,89,231,144)(11,133,232,90,216,221,41,152,102,177)(12,178,103,153,42,222,205,91,233,134)(13,116,56,61,166,76,123,194,26,192)(14,181,27,195,124,77,167,62,57,117)(15,118,58,63,168,78,125,196,28,182)(16,183,29,197,126,79,157,64,59,119)(17,120,60,65,158,80,127,198,30,184)(18,185,31,199,128,81,159,66,49,109)(19,110,50,67,160,82,129,200,32,186)(20,187,33,201,130,83,161,68,51,111)(21,112,52,69,162,84,131,202,34,188)(22,189,35,203,132,73,163,70,53,113)(23,114,54,71,164,74,121,204,36,190)(24,191,25,193,122,75,165,72,55,115), (1,173)(2,38)(3,175)(4,40)(5,177)(6,42)(7,179)(8,44)(9,169)(10,46)(11,171)(12,48)(13,129)(14,68)(15,131)(16,70)(17,121)(18,72)(19,123)(20,62)(21,125)(22,64)(23,127)(24,66)(25,81)(26,32)(27,83)(28,34)(29,73)(30,36)(31,75)(33,77)(35,79)(37,92)(39,94)(41,96)(43,86)(45,88)(47,90)(49,115)(50,166)(51,117)(52,168)(53,119)(54,158)(55,109)(56,160)(57,111)(58,162)(59,113)(60,164)(61,67)(63,69)(65,71)(74,120)(76,110)(78,112)(80,114)(82,116)(84,118)(85,91)(87,93)(89,95)(97,103)(98,135)(99,105)(100,137)(101,107)(102,139)(104,141)(106,143)(108,133)(122,199)(124,201)(126,203)(128,193)(130,195)(132,197)(134,228)(136,218)(138,220)(140,222)(142,224)(144,226)(145,176)(146,232)(147,178)(148,234)(149,180)(150,236)(151,170)(152,238)(153,172)(154,240)(155,174)(156,230)(157,189)(159,191)(161,181)(163,183)(165,185)(167,187)(182,202)(184,204)(186,194)(188,196)(190,198)(192,200)(205,239)(206,217)(207,229)(208,219)(209,231)(210,221)(211,233)(212,223)(213,235)(214,225)(215,237)(216,227), (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), (1,130,7,124)(2,129,8,123)(3,128,9,122)(4,127,10,121)(5,126,11,132)(6,125,12,131)(13,44,19,38)(14,43,20,37)(15,42,21,48)(16,41,22,47)(17,40,23,46)(18,39,24,45)(25,106,31,100)(26,105,32,99)(27,104,33,98)(28,103,34,97)(29,102,35,108)(30,101,36,107)(49,214,55,208)(50,213,56,207)(51,212,57,206)(52,211,58,205)(53,210,59,216)(54,209,60,215)(61,93,67,87)(62,92,68,86)(63,91,69,85)(64,90,70,96)(65,89,71,95)(66,88,72,94)(73,139,79,133)(74,138,80,144)(75,137,81,143)(76,136,82,142)(77,135,83,141)(78,134,84,140)(109,219,115,225)(110,218,116,224)(111,217,117,223)(112,228,118,222)(113,227,119,221)(114,226,120,220)(145,184,151,190)(146,183,152,189)(147,182,153,188)(148,181,154,187)(149,192,155,186)(150,191,156,185)(157,232,163,238)(158,231,164,237)(159,230,165,236)(160,229,166,235)(161,240,167,234)(162,239,168,233)(169,199,175,193)(170,198,176,204)(171,197,177,203)(172,196,178,202)(173,195,179,201)(174,194,180,200) );
G=PermutationGroup([[(1,135,234,92,206,223,43,154,104,179),(2,180,105,155,44,224,207,93,235,136),(3,137,236,94,208,225,45,156,106,169),(4,170,107,145,46,226,209,95,237,138),(5,139,238,96,210,227,47,146,108,171),(6,172,97,147,48,228,211,85,239,140),(7,141,240,86,212,217,37,148,98,173),(8,174,99,149,38,218,213,87,229,142),(9,143,230,88,214,219,39,150,100,175),(10,176,101,151,40,220,215,89,231,144),(11,133,232,90,216,221,41,152,102,177),(12,178,103,153,42,222,205,91,233,134),(13,116,56,61,166,76,123,194,26,192),(14,181,27,195,124,77,167,62,57,117),(15,118,58,63,168,78,125,196,28,182),(16,183,29,197,126,79,157,64,59,119),(17,120,60,65,158,80,127,198,30,184),(18,185,31,199,128,81,159,66,49,109),(19,110,50,67,160,82,129,200,32,186),(20,187,33,201,130,83,161,68,51,111),(21,112,52,69,162,84,131,202,34,188),(22,189,35,203,132,73,163,70,53,113),(23,114,54,71,164,74,121,204,36,190),(24,191,25,193,122,75,165,72,55,115)], [(1,173),(2,38),(3,175),(4,40),(5,177),(6,42),(7,179),(8,44),(9,169),(10,46),(11,171),(12,48),(13,129),(14,68),(15,131),(16,70),(17,121),(18,72),(19,123),(20,62),(21,125),(22,64),(23,127),(24,66),(25,81),(26,32),(27,83),(28,34),(29,73),(30,36),(31,75),(33,77),(35,79),(37,92),(39,94),(41,96),(43,86),(45,88),(47,90),(49,115),(50,166),(51,117),(52,168),(53,119),(54,158),(55,109),(56,160),(57,111),(58,162),(59,113),(60,164),(61,67),(63,69),(65,71),(74,120),(76,110),(78,112),(80,114),(82,116),(84,118),(85,91),(87,93),(89,95),(97,103),(98,135),(99,105),(100,137),(101,107),(102,139),(104,141),(106,143),(108,133),(122,199),(124,201),(126,203),(128,193),(130,195),(132,197),(134,228),(136,218),(138,220),(140,222),(142,224),(144,226),(145,176),(146,232),(147,178),(148,234),(149,180),(150,236),(151,170),(152,238),(153,172),(154,240),(155,174),(156,230),(157,189),(159,191),(161,181),(163,183),(165,185),(167,187),(182,202),(184,204),(186,194),(188,196),(190,198),(192,200),(205,239),(206,217),(207,229),(208,219),(209,231),(210,221),(211,233),(212,223),(213,235),(214,225),(215,237),(216,227)], [(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)], [(1,130,7,124),(2,129,8,123),(3,128,9,122),(4,127,10,121),(5,126,11,132),(6,125,12,131),(13,44,19,38),(14,43,20,37),(15,42,21,48),(16,41,22,47),(17,40,23,46),(18,39,24,45),(25,106,31,100),(26,105,32,99),(27,104,33,98),(28,103,34,97),(29,102,35,108),(30,101,36,107),(49,214,55,208),(50,213,56,207),(51,212,57,206),(52,211,58,205),(53,210,59,216),(54,209,60,215),(61,93,67,87),(62,92,68,86),(63,91,69,85),(64,90,70,96),(65,89,71,95),(66,88,72,94),(73,139,79,133),(74,138,80,144),(75,137,81,143),(76,136,82,142),(77,135,83,141),(78,134,84,140),(109,219,115,225),(110,218,116,224),(111,217,117,223),(112,228,118,222),(113,227,119,221),(114,226,120,220),(145,184,151,190),(146,183,152,189),(147,182,153,188),(148,181,154,187),(149,192,155,186),(150,191,156,185),(157,232,163,238),(158,231,164,237),(159,230,165,236),(160,229,166,235),(161,240,167,234),(162,239,168,233),(169,199,175,193),(170,198,176,204),(171,197,177,203),(172,196,178,202),(173,195,179,201),(174,194,180,200)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 15A | 15B | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 10 | 10 | 2 | 4 | 6 | 6 | 12 | 20 | 30 | 30 | 60 | 2 | 2 | 2 | 2 | 2 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 20 | 20 | 4 | 4 | 4 | 4 | 4 | 4 | 12 | ··· | 12 | 4 | ··· | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | + | - | + | + | - | + | - | - | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | Q8 | D5 | D6 | D6 | D6 | C4○D4 | D10 | D10 | Dic6 | D20 | S3×D4 | D4⋊2S3 | S3×D5 | D4⋊2D5 | Q8×D5 | C2×S3×D5 | D5×Dic6 | S3×D20 | C30.C23 |
| kernel | D10⋊2Dic6 | D10⋊Dic3 | C6.Dic10 | C3×D10⋊C4 | C5×Dic3⋊C4 | C60⋊5C4 | C2×D5×Dic3 | C2×C15⋊Q8 | D10⋊C4 | C5×Dic3 | C6×D5 | Dic3⋊C4 | C2×Dic5 | C2×C20 | C22×D5 | C30 | C2×Dic3 | C2×C12 | D10 | Dic3 | C10 | C10 | C2×C4 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 4 | 2 | 4 | 8 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
Matrix representation of D10⋊2Dic6 ►in GL6(𝔽61)
| 17 | 17 | 0 | 0 | 0 | 0 |
| 44 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 17 | 17 | 0 | 0 | 0 | 0 |
| 1 | 44 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 29 | 54 | 0 | 0 | 0 | 0 |
| 59 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 41 | 0 | 0 |
| 0 | 0 | 55 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 1 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 37 | 0 | 0 |
| 0 | 0 | 0 | 50 | 0 | 0 |
| 0 | 0 | 0 | 0 | 38 | 46 |
| 0 | 0 | 0 | 0 | 23 | 23 |
G:=sub<GL(6,GF(61))| [17,44,0,0,0,0,17,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[17,1,0,0,0,0,17,44,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[29,59,0,0,0,0,54,32,0,0,0,0,0,0,60,55,0,0,0,0,41,1,0,0,0,0,0,0,60,60,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,11,0,0,0,0,0,37,50,0,0,0,0,0,0,38,23,0,0,0,0,46,23] >;
D10⋊2Dic6 in GAP, Magma, Sage, TeX
D_{10}\rtimes_2{\rm Dic}_6 % in TeX
G:=Group("D10:2Dic6"); // GroupNames label
G:=SmallGroup(480,498);
// by ID
G=gap.SmallGroup(480,498);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,254,219,142,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^10=b^2=c^12=1,d^2=c^6,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^3*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations