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G = D10.2Dic6order 480 = 25·3·5

2nd non-split extension by D10 of Dic6 acting via Dic6/Dic3=C2

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, C153C8.2C4, C20.18(C4×S3), C4.F5.2S3, C60.18(C2×C4), (C4×D5).63D6, C6.11(C4⋊F5), C32(D10.Q8), C152(C8.C4), C12.F5.2C2, C52(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

C1C60 — D10.2Dic6
C1C5C15C30C3×Dic5D5×C12C3×C4.F5 — D10.2Dic6
C15C30C60 — D10.2Dic6
C1C2C4

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 [×4], C2×C4, D5, C10, C12, C12, C2×C6, C15, C2×C8, M4(2) [×2], Dic5, C20, D10, C3⋊C8, C3⋊C8 [×2], C24, C2×C12, C3×D5, C30, C8.C4, C52C8, C40, C5⋊C8 [×2], 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, C153C8, C3×C5⋊C8, C15⋊C8, D5×C12, D10.Q8, D5×C3⋊C8, C3×C4.F5, C12.F5, D10.2Dic6
Quotients: C1, C2 [×3], C4 [×2], 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

Smallest permutation representation of D10.2Dic6
On 240 points
Generators in S240
(1 59 202 80 138 13 71 214 92 126)(2 81 72 127 203 14 93 60 139 215)(3 128 94 216 49 15 140 82 204 61)(4 193 141 62 95 16 205 129 50 83)(5 63 206 84 142 17 51 194 96 130)(6 85 52 131 207 18 73 64 143 195)(7 132 74 196 53 19 144 86 208 65)(8 197 121 66 75 20 209 133 54 87)(9 67 210 88 122 21 55 198 76 134)(10 89 56 135 211 22 77 68 123 199)(11 136 78 200 57 23 124 90 212 69)(12 201 125 70 79 24 213 137 58 91)(25 162 171 109 222 37 150 183 97 234)(26 110 151 235 172 38 98 163 223 184)(27 236 99 185 152 39 224 111 173 164)(28 186 225 165 100 40 174 237 153 112)(29 166 175 113 226 41 154 187 101 238)(30 114 155 239 176 42 102 167 227 188)(31 240 103 189 156 43 228 115 177 168)(32 190 229 145 104 44 178 217 157 116)(33 146 179 117 230 45 158 191 105 218)(34 118 159 219 180 46 106 147 231 192)(35 220 107 169 160 47 232 119 181 148)(36 170 233 149 108 48 182 221 161 120)
(1 126)(2 203)(3 61)(4 95)(5 130)(6 207)(7 65)(8 75)(9 134)(10 211)(11 69)(12 79)(13 138)(14 215)(15 49)(16 83)(17 142)(18 195)(19 53)(20 87)(21 122)(22 199)(23 57)(24 91)(25 150)(26 235)(27 99)(28 40)(29 154)(30 239)(31 103)(32 44)(33 158)(34 219)(35 107)(36 48)(37 162)(38 223)(39 111)(41 166)(42 227)(43 115)(45 146)(46 231)(47 119)(50 205)(51 84)(54 209)(55 88)(58 213)(59 92)(62 193)(63 96)(66 197)(67 76)(70 201)(71 80)(73 143)(74 86)(77 123)(78 90)(81 127)(82 94)(85 131)(89 135)(93 139)(98 163)(100 186)(102 167)(104 190)(106 147)(108 170)(110 151)(112 174)(114 155)(116 178)(118 159)(120 182)(124 200)(128 204)(132 208)(136 212)(140 216)(144 196)(145 229)(148 169)(149 233)(152 173)(153 237)(156 177)(157 217)(160 181)(161 221)(164 185)(165 225)(168 189)(171 222)(172 184)(175 226)(176 188)(179 230)(180 192)(183 234)(187 238)(191 218)(194 206)(198 210)(202 214)
(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)
(1 153 19 147 13 165 7 159)(2 152 8 158 14 164 20 146)(3 163 21 157 15 151 9 145)(4 162 10 168 16 150 22 156)(5 149 23 167 17 161 11 155)(6 148 12 154 18 160 24 166)(25 199 177 95 37 211 189 83)(26 76 190 204 38 88 178 216)(27 209 179 81 39 197 191 93)(28 86 192 214 40 74 180 202)(29 195 181 91 41 207 169 79)(30 96 170 200 42 84 182 212)(31 205 183 77 43 193 171 89)(32 82 172 210 44 94 184 198)(33 215 185 87 45 203 173 75)(34 92 174 196 46 80 186 208)(35 201 187 73 47 213 175 85)(36 78 176 206 48 90 188 194)(49 110 134 229 61 98 122 217)(50 234 123 115 62 222 135 103)(51 120 136 239 63 108 124 227)(52 220 125 101 64 232 137 113)(53 106 138 225 65 118 126 237)(54 230 127 111 66 218 139 99)(55 116 140 235 67 104 128 223)(56 240 129 97 68 228 141 109)(57 102 142 221 69 114 130 233)(58 226 131 107 70 238 143 119)(59 112 144 231 71 100 132 219)(60 236 133 117 72 224 121 105)

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

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

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

36 conjugacy classes

class 1 2A2B 3 4A4B4C 5 6A6B8A8B8C8D8E8F8G8H 10 12A12B12C 15 20A20B24A24B24C24D 30 40A40B40C40D60A60B
order122344456688888888101212121520202424242430404040406060
size111022554220662020303060604410108442020202081212121288

36 irreducible representations

dim1111112222222244444888
type++++++-+-+++-
imageC1C2C2C2C4C4S3D4Q8D6C3⋊D4C4×S3Dic6C8.C4F5C2×F5C4⋊F5C12.53D4D10.Q8S3×F5Dic3⋊F5D10.2Dic6
kernelD10.2Dic6D5×C3⋊C8C3×C4.F5C12.F5C5×C3⋊C8C153C8C4.F5C3×Dic5C6×D5C4×D5Dic5C20D10C15C3⋊C8C12C6C5C3C4C2C1
# reps1111221111222411224112

Matrix representation of D10.2Dic6 in GL6(𝔽241)

100000
010000
00000240
001111
00240000
00024000
,
24000000
02400000
00000240
00002400
00024000
00240000
,
1011710000
701710000
008717410470
0017113767154
001711710434
008717224154
,
761760000
1001650000
00650108108
001331981330
000133198133
00108108065

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

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