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G = Dic5.4D12order 480 = 25·3·5

4th non-split extension by Dic5 of D12 acting via D12/C6=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic5.4D12, (C2×Dic3).F5, C5⋊(C12.47D4), C15⋊(C4.10D4), C22.F5.S3, C22.6(S3×F5), C2.15(D6⋊F5), C10.15(D6⋊C4), (C10×Dic3).5C4, (C2×Dic15).6C4, (C3×Dic5).33D4, (C2×Dic5).72D6, C6.15(C22⋊F5), C30.15(C22⋊C4), Dic5.4(C3⋊D4), C31(Dic5.D4), C158M4(2).1C2, (C6×Dic5).139C22, (C2×C6).4(C2×F5), (C2×C30).9(C2×C4), (C2×C15⋊Q8).10C2, (C2×C10).11(C4×S3), (C3×C22.F5).1C2, SmallGroup(480,251)

Series: Derived Chief Lower central Upper central

C1C2×C30 — Dic5.4D12
C1C5C15C30C3×Dic5C6×Dic5C3×C22.F5 — Dic5.4D12
C15C30C2×C30 — Dic5.4D12
C1C2C22

Generators and relations for Dic5.4D12
 G = < a,b,c,d | a10=1, b2=c12=a5, d2=cbc-1=a5b, bab-1=a-1, cac-1=dad-1=a3, bd=db, dcd-1=a5bc11 >

Subgroups: 404 in 76 conjugacy classes, 26 normal (all characteristic)
C1, C2, C2, C3, C4 [×4], C22, C5, C6, C6, C8 [×2], C2×C4 [×3], Q8 [×2], C10, C10, Dic3 [×2], C12 [×2], C2×C6, C15, M4(2) [×2], C2×Q8, Dic5 [×2], Dic5, C20, C2×C10, C3⋊C8, C24, Dic6 [×2], C2×Dic3, C2×Dic3, C2×C12, C30, C30, C4.10D4, C5⋊C8 [×2], Dic10 [×2], C2×Dic5, C2×Dic5, C2×C20, C4.Dic3, C3×M4(2), C2×Dic6, C5×Dic3, C3×Dic5 [×2], Dic15, C2×C30, C22.F5, C22.F5, C2×Dic10, C12.47D4, C3×C5⋊C8, C15⋊C8, C15⋊Q8 [×2], C6×Dic5, C10×Dic3, C2×Dic15, Dic5.D4, C3×C22.F5, C158M4(2), C2×C15⋊Q8, Dic5.4D12
Quotients: C1, C2 [×3], C4 [×2], C22, S3, C2×C4, D4 [×2], D6, C22⋊C4, F5, C4×S3, D12, C3⋊D4, C4.10D4, C2×F5, D6⋊C4, C22⋊F5, C12.47D4, S3×F5, Dic5.D4, D6⋊F5, Dic5.4D12

Smallest permutation representation of Dic5.4D12
On 240 points
Generators in S240
(1 133 169 82 57 13 121 181 94 69)(2 83 122 70 170 14 95 134 58 182)(3 71 96 183 123 15 59 84 171 135)(4 184 60 136 73 16 172 72 124 85)(5 137 173 86 61 17 125 185 74 49)(6 87 126 50 174 18 75 138 62 186)(7 51 76 187 127 19 63 88 175 139)(8 188 64 140 77 20 176 52 128 89)(9 141 177 90 65 21 129 189 78 53)(10 91 130 54 178 22 79 142 66 190)(11 55 80 191 131 23 67 92 179 143)(12 192 68 144 81 24 180 56 132 93)(25 207 239 118 167 37 195 227 106 155)(26 119 196 156 240 38 107 208 168 228)(27 157 108 229 197 39 145 120 217 209)(28 230 146 210 109 40 218 158 198 97)(29 211 219 98 147 41 199 231 110 159)(30 99 200 160 220 42 111 212 148 232)(31 161 112 233 201 43 149 100 221 213)(32 234 150 214 113 44 222 162 202 101)(33 215 223 102 151 45 203 235 114 163)(34 103 204 164 224 46 115 216 152 236)(35 165 116 237 205 47 153 104 225 193)(36 238 154 194 117 48 226 166 206 105)
(1 19 13 7)(2 8 14 20)(3 21 15 9)(4 10 16 22)(5 23 17 11)(6 12 18 24)(25 43 37 31)(26 32 38 44)(27 45 39 33)(28 34 40 46)(29 47 41 35)(30 36 42 48)(49 67 61 55)(50 56 62 68)(51 69 63 57)(52 58 64 70)(53 71 65 59)(54 60 66 72)(73 79 85 91)(74 92 86 80)(75 81 87 93)(76 94 88 82)(77 83 89 95)(78 96 90 84)(97 103 109 115)(98 116 110 104)(99 105 111 117)(100 118 112 106)(101 107 113 119)(102 120 114 108)(121 139 133 127)(122 128 134 140)(123 141 135 129)(124 130 136 142)(125 143 137 131)(126 132 138 144)(145 163 157 151)(146 152 158 164)(147 165 159 153)(148 154 160 166)(149 167 161 155)(150 156 162 168)(169 187 181 175)(170 176 182 188)(171 189 183 177)(172 178 184 190)(173 191 185 179)(174 180 186 192)(193 211 205 199)(194 200 206 212)(195 213 207 201)(196 202 208 214)(197 215 209 203)(198 204 210 216)(217 235 229 223)(218 224 230 236)(219 237 231 225)(220 226 232 238)(221 239 233 227)(222 228 234 240)
(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)
(1 162 7 156 13 150 19 168)(2 155 20 161 14 167 8 149)(3 160 9 154 15 148 21 166)(4 153 22 159 16 165 10 147)(5 158 11 152 17 146 23 164)(6 151 24 157 18 163 12 145)(25 64 31 58 37 52 43 70)(26 57 44 63 38 69 32 51)(27 62 33 56 39 50 45 68)(28 55 46 61 40 67 34 49)(29 60 35 54 41 72 47 66)(30 53 48 59 42 65 36 71)(73 205 91 211 85 193 79 199)(74 210 80 204 86 198 92 216)(75 203 93 209 87 215 81 197)(76 208 82 202 88 196 94 214)(77 201 95 207 89 213 83 195)(78 206 84 200 90 194 96 212)(97 131 115 137 109 143 103 125)(98 136 104 130 110 124 116 142)(99 129 117 135 111 141 105 123)(100 134 106 128 112 122 118 140)(101 127 119 133 113 139 107 121)(102 132 108 126 114 144 120 138)(169 234 175 228 181 222 187 240)(170 227 188 233 182 239 176 221)(171 232 177 226 183 220 189 238)(172 225 190 231 184 237 178 219)(173 230 179 224 185 218 191 236)(174 223 192 229 186 235 180 217)

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

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

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

33 conjugacy classes

class 1 2A2B 3 4A4B4C4D 5 6A6B8A8B8C8D10A10B10C12A12B12C 15 20A20B20C20D24A24B24C24D30A30B30C
order122344445668888101010121212152020202024242424303030
size1122101012604242020606044410102081212121220202020888

33 irreducible representations

dim111111222222444444888
type+++++++++-++--++-
imageC1C2C2C2C4C4S3D4D6D12C3⋊D4C4×S3F5C4.10D4C2×F5C22⋊F5C12.47D4Dic5.D4S3×F5D6⋊F5Dic5.4D12
kernelDic5.4D12C3×C22.F5C158M4(2)C2×C15⋊Q8C10×Dic3C2×Dic15C22.F5C3×Dic5C2×Dic5Dic5Dic5C2×C10C2×Dic3C15C2×C6C6C5C3C22C2C1
# reps111122121222111224112

Matrix representation of Dic5.4D12 in GL6(𝔽241)

100000
010000
00124000
001915100
00110177152
00128131189189
,
24000000
02400000
009110600
003115000
008150135228
0013714197106
,
1051200000
1201050000
00002401
0019564239189
001922121770
0042771770
,
1051210000
1201360000
0054103126126
0096760207
00126187214138
004954214138

G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,191,110,128,0,0,240,51,177,131,0,0,0,0,1,189,0,0,0,0,52,189],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,91,31,81,137,0,0,106,150,50,14,0,0,0,0,135,197,0,0,0,0,228,106],[105,120,0,0,0,0,120,105,0,0,0,0,0,0,0,195,192,42,0,0,0,64,212,77,0,0,240,239,177,177,0,0,1,189,0,0],[105,120,0,0,0,0,121,136,0,0,0,0,0,0,54,96,126,49,0,0,103,76,187,54,0,0,126,0,214,214,0,0,126,207,138,138] >;

Dic5.4D12 in GAP, Magma, Sage, TeX

{\rm Dic}_5._4D_{12}
% in TeX

G:=Group("Dic5.4D12");
// GroupNames label

G:=SmallGroup(480,251);
// by ID

G=gap.SmallGroup(480,251);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,141,120,219,100,675,1356,9414,4724]);
// Polycyclic

G:=Group<a,b,c,d|a^10=1,b^2=c^12=a^5,d^2=c*b*c^-1=a^5*b,b*a*b^-1=a^-1,c*a*c^-1=d*a*d^-1=a^3,b*d=d*b,d*c*d^-1=a^5*b*c^11>;
// generators/relations

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