metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D10.2Dic6, C3⋊C8.2F5, C12.8(C2×F5), C30.4(C4⋊C4), C4.18(S3×F5), (C6×D5).2Q8, C15⋊3C8.2C4, C20.18(C4×S3), C4.F5.2S3, C60.18(C2×C4), (C4×D5).63D6, C6.11(C4⋊F5), C3⋊2(D10.Q8), C15⋊2(C8.C4), C12.F5.2C2, C5⋊2(C12.53D4), C2.7(Dic3⋊F5), (C3×Dic5).29D4, C10.4(Dic3⋊C4), (D5×C12).49C22, Dic5.17(C3⋊D4), (C5×C3⋊C8).2C4, (D5×C3⋊C8).5C2, (C3×C4.F5).2C2, SmallGroup(480,238)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D10.2Dic6
G = < a,b,c,d | a10=b2=1, c12=a5, d2=a4bc6, bab=a-1, cac-1=a3, ad=da, cbc-1=a7b, bd=db, dcd-1=a-1bc11 >
Subgroups: 260 in 60 conjugacy classes, 26 normal (all characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, C6, C6, C8, C2×C4, D5, C10, C12, C12, C2×C6, C15, C2×C8, M4(2), Dic5, C20, D10, C3⋊C8, C3⋊C8, C24, C2×C12, C3×D5, C30, C8.C4, C5⋊2C8, C40, C5⋊C8, C4×D5, C2×C3⋊C8, C4.Dic3, C3×M4(2), C3×Dic5, C60, C6×D5, C8×D5, C4.F5, C4.F5, C12.53D4, C5×C3⋊C8, C15⋊3C8, C3×C5⋊C8, C15⋊C8, D5×C12, D10.Q8, D5×C3⋊C8, C3×C4.F5, C12.F5, D10.2Dic6
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, Q8, D6, C4⋊C4, F5, Dic6, C4×S3, C3⋊D4, C8.C4, C2×F5, Dic3⋊C4, C4⋊F5, C12.53D4, S3×F5, D10.Q8, Dic3⋊F5, D10.2Dic6
►On 240 points
Generators in S240
(1 56 43 164 223 13 68 31 152 235)(2 165 69 236 44 14 153 57 224 32)(3 237 154 33 70 15 225 166 45 58)(4 34 226 59 155 16 46 238 71 167)(5 60 47 168 227 17 72 35 156 239)(6 145 49 240 48 18 157 61 228 36)(7 217 158 37 50 19 229 146 25 62)(8 38 230 63 159 20 26 218 51 147)(9 64 27 148 231 21 52 39 160 219)(10 149 53 220 28 22 161 65 232 40)(11 221 162 41 54 23 233 150 29 66)(12 42 234 67 163 24 30 222 55 151)(73 126 111 188 212 85 138 99 176 200)(74 189 139 201 112 86 177 127 213 100)(75 202 178 101 140 87 214 190 113 128)(76 102 215 129 179 88 114 203 141 191)(77 130 115 192 216 89 142 103 180 204)(78 169 143 205 116 90 181 131 193 104)(79 206 182 105 144 91 194 170 117 132)(80 106 195 133 183 92 118 207 121 171)(81 134 119 172 196 93 122 107 184 208)(82 173 123 209 120 94 185 135 197 108)(83 210 186 109 124 95 198 174 97 136)(84 110 199 137 187 96 98 211 125 175)
(1 235)(2 44)(3 58)(4 155)(5 239)(6 48)(7 62)(8 159)(9 219)(10 28)(11 66)(12 163)(13 223)(14 32)(15 70)(16 167)(17 227)(18 36)(19 50)(20 147)(21 231)(22 40)(23 54)(24 151)(25 217)(26 51)(27 39)(29 221)(30 55)(31 43)(33 225)(34 59)(35 47)(37 229)(38 63)(41 233)(42 67)(45 237)(46 71)(52 148)(56 152)(60 156)(64 160)(68 164)(72 168)(73 111)(74 86)(75 214)(76 129)(77 115)(78 90)(79 194)(80 133)(81 119)(82 94)(83 198)(84 137)(85 99)(87 202)(88 141)(89 103)(91 206)(92 121)(93 107)(95 210)(96 125)(98 211)(100 177)(102 215)(104 181)(106 195)(108 185)(110 199)(112 189)(114 203)(116 169)(118 207)(120 173)(123 209)(124 186)(127 213)(128 190)(131 193)(132 170)(135 197)(136 174)(139 201)(140 178)(143 205)(144 182)(145 240)(146 158)(149 220)(150 162)(153 224)(154 166)(157 228)(161 232)(165 236)(171 183)(172 208)(175 187)(176 212)(179 191)(180 216)(184 196)(188 200)(192 204)
(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)
(1 201 19 195 13 213 7 207)(2 200 8 206 14 212 20 194)(3 211 21 205 15 199 9 193)(4 210 10 216 16 198 22 204)(5 197 23 215 17 209 11 203)(6 196 12 202 18 208 24 214)(25 92 152 189 37 80 164 177)(26 170 165 73 38 182 153 85)(27 78 154 175 39 90 166 187)(28 180 167 83 40 192 155 95)(29 88 156 185 41 76 168 173)(30 190 145 93 42 178 157 81)(31 74 158 171 43 86 146 183)(32 176 147 79 44 188 159 91)(33 84 160 181 45 96 148 169)(34 186 149 89 46 174 161 77)(35 94 162 191 47 82 150 179)(36 172 151 75 48 184 163 87)(49 122 234 101 61 134 222 113)(50 106 223 127 62 118 235 139)(51 132 236 111 63 144 224 99)(52 116 225 137 64 104 237 125)(53 142 238 97 65 130 226 109)(54 102 227 123 66 114 239 135)(55 128 240 107 67 140 228 119)(56 112 229 133 68 100 217 121)(57 138 218 117 69 126 230 105)(58 98 231 143 70 110 219 131)(59 124 220 103 71 136 232 115)(60 108 233 129 72 120 221 141)
G:=sub<Sym(240)| (1,56,43,164,223,13,68,31,152,235)(2,165,69,236,44,14,153,57,224,32)(3,237,154,33,70,15,225,166,45,58)(4,34,226,59,155,16,46,238,71,167)(5,60,47,168,227,17,72,35,156,239)(6,145,49,240,48,18,157,61,228,36)(7,217,158,37,50,19,229,146,25,62)(8,38,230,63,159,20,26,218,51,147)(9,64,27,148,231,21,52,39,160,219)(10,149,53,220,28,22,161,65,232,40)(11,221,162,41,54,23,233,150,29,66)(12,42,234,67,163,24,30,222,55,151)(73,126,111,188,212,85,138,99,176,200)(74,189,139,201,112,86,177,127,213,100)(75,202,178,101,140,87,214,190,113,128)(76,102,215,129,179,88,114,203,141,191)(77,130,115,192,216,89,142,103,180,204)(78,169,143,205,116,90,181,131,193,104)(79,206,182,105,144,91,194,170,117,132)(80,106,195,133,183,92,118,207,121,171)(81,134,119,172,196,93,122,107,184,208)(82,173,123,209,120,94,185,135,197,108)(83,210,186,109,124,95,198,174,97,136)(84,110,199,137,187,96,98,211,125,175), (1,235)(2,44)(3,58)(4,155)(5,239)(6,48)(7,62)(8,159)(9,219)(10,28)(11,66)(12,163)(13,223)(14,32)(15,70)(16,167)(17,227)(18,36)(19,50)(20,147)(21,231)(22,40)(23,54)(24,151)(25,217)(26,51)(27,39)(29,221)(30,55)(31,43)(33,225)(34,59)(35,47)(37,229)(38,63)(41,233)(42,67)(45,237)(46,71)(52,148)(56,152)(60,156)(64,160)(68,164)(72,168)(73,111)(74,86)(75,214)(76,129)(77,115)(78,90)(79,194)(80,133)(81,119)(82,94)(83,198)(84,137)(85,99)(87,202)(88,141)(89,103)(91,206)(92,121)(93,107)(95,210)(96,125)(98,211)(100,177)(102,215)(104,181)(106,195)(108,185)(110,199)(112,189)(114,203)(116,169)(118,207)(120,173)(123,209)(124,186)(127,213)(128,190)(131,193)(132,170)(135,197)(136,174)(139,201)(140,178)(143,205)(144,182)(145,240)(146,158)(149,220)(150,162)(153,224)(154,166)(157,228)(161,232)(165,236)(171,183)(172,208)(175,187)(176,212)(179,191)(180,216)(184,196)(188,200)(192,204), (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), (1,201,19,195,13,213,7,207)(2,200,8,206,14,212,20,194)(3,211,21,205,15,199,9,193)(4,210,10,216,16,198,22,204)(5,197,23,215,17,209,11,203)(6,196,12,202,18,208,24,214)(25,92,152,189,37,80,164,177)(26,170,165,73,38,182,153,85)(27,78,154,175,39,90,166,187)(28,180,167,83,40,192,155,95)(29,88,156,185,41,76,168,173)(30,190,145,93,42,178,157,81)(31,74,158,171,43,86,146,183)(32,176,147,79,44,188,159,91)(33,84,160,181,45,96,148,169)(34,186,149,89,46,174,161,77)(35,94,162,191,47,82,150,179)(36,172,151,75,48,184,163,87)(49,122,234,101,61,134,222,113)(50,106,223,127,62,118,235,139)(51,132,236,111,63,144,224,99)(52,116,225,137,64,104,237,125)(53,142,238,97,65,130,226,109)(54,102,227,123,66,114,239,135)(55,128,240,107,67,140,228,119)(56,112,229,133,68,100,217,121)(57,138,218,117,69,126,230,105)(58,98,231,143,70,110,219,131)(59,124,220,103,71,136,232,115)(60,108,233,129,72,120,221,141)>;
G:=Group( (1,56,43,164,223,13,68,31,152,235)(2,165,69,236,44,14,153,57,224,32)(3,237,154,33,70,15,225,166,45,58)(4,34,226,59,155,16,46,238,71,167)(5,60,47,168,227,17,72,35,156,239)(6,145,49,240,48,18,157,61,228,36)(7,217,158,37,50,19,229,146,25,62)(8,38,230,63,159,20,26,218,51,147)(9,64,27,148,231,21,52,39,160,219)(10,149,53,220,28,22,161,65,232,40)(11,221,162,41,54,23,233,150,29,66)(12,42,234,67,163,24,30,222,55,151)(73,126,111,188,212,85,138,99,176,200)(74,189,139,201,112,86,177,127,213,100)(75,202,178,101,140,87,214,190,113,128)(76,102,215,129,179,88,114,203,141,191)(77,130,115,192,216,89,142,103,180,204)(78,169,143,205,116,90,181,131,193,104)(79,206,182,105,144,91,194,170,117,132)(80,106,195,133,183,92,118,207,121,171)(81,134,119,172,196,93,122,107,184,208)(82,173,123,209,120,94,185,135,197,108)(83,210,186,109,124,95,198,174,97,136)(84,110,199,137,187,96,98,211,125,175), (1,235)(2,44)(3,58)(4,155)(5,239)(6,48)(7,62)(8,159)(9,219)(10,28)(11,66)(12,163)(13,223)(14,32)(15,70)(16,167)(17,227)(18,36)(19,50)(20,147)(21,231)(22,40)(23,54)(24,151)(25,217)(26,51)(27,39)(29,221)(30,55)(31,43)(33,225)(34,59)(35,47)(37,229)(38,63)(41,233)(42,67)(45,237)(46,71)(52,148)(56,152)(60,156)(64,160)(68,164)(72,168)(73,111)(74,86)(75,214)(76,129)(77,115)(78,90)(79,194)(80,133)(81,119)(82,94)(83,198)(84,137)(85,99)(87,202)(88,141)(89,103)(91,206)(92,121)(93,107)(95,210)(96,125)(98,211)(100,177)(102,215)(104,181)(106,195)(108,185)(110,199)(112,189)(114,203)(116,169)(118,207)(120,173)(123,209)(124,186)(127,213)(128,190)(131,193)(132,170)(135,197)(136,174)(139,201)(140,178)(143,205)(144,182)(145,240)(146,158)(149,220)(150,162)(153,224)(154,166)(157,228)(161,232)(165,236)(171,183)(172,208)(175,187)(176,212)(179,191)(180,216)(184,196)(188,200)(192,204), (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), (1,201,19,195,13,213,7,207)(2,200,8,206,14,212,20,194)(3,211,21,205,15,199,9,193)(4,210,10,216,16,198,22,204)(5,197,23,215,17,209,11,203)(6,196,12,202,18,208,24,214)(25,92,152,189,37,80,164,177)(26,170,165,73,38,182,153,85)(27,78,154,175,39,90,166,187)(28,180,167,83,40,192,155,95)(29,88,156,185,41,76,168,173)(30,190,145,93,42,178,157,81)(31,74,158,171,43,86,146,183)(32,176,147,79,44,188,159,91)(33,84,160,181,45,96,148,169)(34,186,149,89,46,174,161,77)(35,94,162,191,47,82,150,179)(36,172,151,75,48,184,163,87)(49,122,234,101,61,134,222,113)(50,106,223,127,62,118,235,139)(51,132,236,111,63,144,224,99)(52,116,225,137,64,104,237,125)(53,142,238,97,65,130,226,109)(54,102,227,123,66,114,239,135)(55,128,240,107,67,140,228,119)(56,112,229,133,68,100,217,121)(57,138,218,117,69,126,230,105)(58,98,231,143,70,110,219,131)(59,124,220,103,71,136,232,115)(60,108,233,129,72,120,221,141) );
G=PermutationGroup([[(1,56,43,164,223,13,68,31,152,235),(2,165,69,236,44,14,153,57,224,32),(3,237,154,33,70,15,225,166,45,58),(4,34,226,59,155,16,46,238,71,167),(5,60,47,168,227,17,72,35,156,239),(6,145,49,240,48,18,157,61,228,36),(7,217,158,37,50,19,229,146,25,62),(8,38,230,63,159,20,26,218,51,147),(9,64,27,148,231,21,52,39,160,219),(10,149,53,220,28,22,161,65,232,40),(11,221,162,41,54,23,233,150,29,66),(12,42,234,67,163,24,30,222,55,151),(73,126,111,188,212,85,138,99,176,200),(74,189,139,201,112,86,177,127,213,100),(75,202,178,101,140,87,214,190,113,128),(76,102,215,129,179,88,114,203,141,191),(77,130,115,192,216,89,142,103,180,204),(78,169,143,205,116,90,181,131,193,104),(79,206,182,105,144,91,194,170,117,132),(80,106,195,133,183,92,118,207,121,171),(81,134,119,172,196,93,122,107,184,208),(82,173,123,209,120,94,185,135,197,108),(83,210,186,109,124,95,198,174,97,136),(84,110,199,137,187,96,98,211,125,175)], [(1,235),(2,44),(3,58),(4,155),(5,239),(6,48),(7,62),(8,159),(9,219),(10,28),(11,66),(12,163),(13,223),(14,32),(15,70),(16,167),(17,227),(18,36),(19,50),(20,147),(21,231),(22,40),(23,54),(24,151),(25,217),(26,51),(27,39),(29,221),(30,55),(31,43),(33,225),(34,59),(35,47),(37,229),(38,63),(41,233),(42,67),(45,237),(46,71),(52,148),(56,152),(60,156),(64,160),(68,164),(72,168),(73,111),(74,86),(75,214),(76,129),(77,115),(78,90),(79,194),(80,133),(81,119),(82,94),(83,198),(84,137),(85,99),(87,202),(88,141),(89,103),(91,206),(92,121),(93,107),(95,210),(96,125),(98,211),(100,177),(102,215),(104,181),(106,195),(108,185),(110,199),(112,189),(114,203),(116,169),(118,207),(120,173),(123,209),(124,186),(127,213),(128,190),(131,193),(132,170),(135,197),(136,174),(139,201),(140,178),(143,205),(144,182),(145,240),(146,158),(149,220),(150,162),(153,224),(154,166),(157,228),(161,232),(165,236),(171,183),(172,208),(175,187),(176,212),(179,191),(180,216),(184,196),(188,200),(192,204)], [(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)], [(1,201,19,195,13,213,7,207),(2,200,8,206,14,212,20,194),(3,211,21,205,15,199,9,193),(4,210,10,216,16,198,22,204),(5,197,23,215,17,209,11,203),(6,196,12,202,18,208,24,214),(25,92,152,189,37,80,164,177),(26,170,165,73,38,182,153,85),(27,78,154,175,39,90,166,187),(28,180,167,83,40,192,155,95),(29,88,156,185,41,76,168,173),(30,190,145,93,42,178,157,81),(31,74,158,171,43,86,146,183),(32,176,147,79,44,188,159,91),(33,84,160,181,45,96,148,169),(34,186,149,89,46,174,161,77),(35,94,162,191,47,82,150,179),(36,172,151,75,48,184,163,87),(49,122,234,101,61,134,222,113),(50,106,223,127,62,118,235,139),(51,132,236,111,63,144,224,99),(52,116,225,137,64,104,237,125),(53,142,238,97,65,130,226,109),(54,102,227,123,66,114,239,135),(55,128,240,107,67,140,228,119),(56,112,229,133,68,100,217,121),(57,138,218,117,69,126,230,105),(58,98,231,143,70,110,219,131),(59,124,220,103,71,136,232,115),(60,108,233,129,72,120,221,141)]])
36 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 4C | 5 | 6A | 6B | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 10 | 12A | 12B | 12C | 15 | 20A | 20B | 24A | 24B | 24C | 24D | 30 | 40A | 40B | 40C | 40D | 60A | 60B |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 4 | 5 | 6 | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | 12 | 12 | 12 | 15 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 40 | 40 | 40 | 40 | 60 | 60 |
| size | 1 | 1 | 10 | 2 | 2 | 5 | 5 | 4 | 2 | 20 | 6 | 6 | 20 | 20 | 30 | 30 | 60 | 60 | 4 | 4 | 10 | 10 | 8 | 4 | 4 | 20 | 20 | 20 | 20 | 8 | 12 | 12 | 12 | 12 | 8 | 8 |
36 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 |
| type | + | + | + | + | + | + | - | + | - | + | + | + | - | |||||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | S3 | D4 | Q8 | D6 | C3⋊D4 | C4×S3 | Dic6 | C8.C4 | F5 | C2×F5 | C4⋊F5 | C12.53D4 | D10.Q8 | S3×F5 | Dic3⋊F5 | D10.2Dic6 |
| kernel | D10.2Dic6 | D5×C3⋊C8 | C3×C4.F5 | C12.F5 | C5×C3⋊C8 | C15⋊3C8 | C4.F5 | C3×Dic5 | C6×D5 | C4×D5 | Dic5 | C20 | D10 | C15 | C3⋊C8 | C12 | C6 | C5 | C3 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 1 | 1 | 2 | 2 | 4 | 1 | 1 | 2 |
Matrix representation of D10.2Dic6 ►in GL6(𝔽241)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 0 | 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 101 | 171 | 0 | 0 | 0 | 0 |
| 70 | 171 | 0 | 0 | 0 | 0 |
| 0 | 0 | 87 | 174 | 104 | 70 |
| 0 | 0 | 171 | 137 | 67 | 154 |
| 0 | 0 | 171 | 17 | 104 | 34 |
| 0 | 0 | 87 | 17 | 224 | 154 |
| 76 | 176 | 0 | 0 | 0 | 0 |
| 100 | 165 | 0 | 0 | 0 | 0 |
| 0 | 0 | 65 | 0 | 108 | 108 |
| 0 | 0 | 133 | 198 | 133 | 0 |
| 0 | 0 | 0 | 133 | 198 | 133 |
| 0 | 0 | 108 | 108 | 0 | 65 |
G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,240,0,0,0,0,1,0,240,0,0,0,1,0,0,0,0,240,1,0,0],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,0,240,0,0,0,0,240,0,0,0,0,240,0,0,0,0,240,0,0,0],[101,70,0,0,0,0,171,171,0,0,0,0,0,0,87,171,171,87,0,0,174,137,17,17,0,0,104,67,104,224,0,0,70,154,34,154],[76,100,0,0,0,0,176,165,0,0,0,0,0,0,65,133,0,108,0,0,0,198,133,108,0,0,108,133,198,0,0,0,108,0,133,65] >;
D10.2Dic6 in GAP, Magma, Sage, TeX
D_{10}._2{\rm Dic}_6 % in TeX
G:=Group("D10.2Dic6"); // GroupNames label
G:=SmallGroup(480,238);
// by ID
G=gap.SmallGroup(480,238);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,141,176,100,675,80,1356,9414,4724]);
// Polycyclic
G:=Group<a,b,c,d|a^10=b^2=1,c^12=a^5,d^2=a^4*b*c^6,b*a*b=a^-1,c*a*c^-1=a^3,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=a^-1*b*c^11>;
// generators/relations