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## G = C5×C12.10D4order 480 = 25·3·5

### Direct product of C5 and C12.10D4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C6 — C5×C12.10D4
 Chief series C1 — C3 — C6 — C2×C6 — C2×C12 — C2×C60 — C5×C4.Dic3 — C5×C12.10D4
 Lower central C3 — C6 — C2×C6 — C5×C12.10D4
 Upper central C1 — C10 — C2×C20 — Q8×C10

Generators and relations for C5×C12.10D4
G = < a,b,c,d | a5=b12=1, c4=b6, d2=b9, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b5, dcd-1=b9c3 >

Subgroups: 132 in 76 conjugacy classes, 42 normal (22 characteristic)
C1, C2, C2, C3, C4 [×2], C4 [×2], C22, C5, C6, C6, C8 [×2], C2×C4, C2×C4 [×2], Q8 [×2], C10, C10, C12 [×2], C12 [×2], C2×C6, C15, M4(2) [×2], C2×Q8, C20 [×2], C20 [×2], C2×C10, C3⋊C8 [×2], C2×C12, C2×C12 [×2], C3×Q8 [×2], C30, C30, C4.10D4, C40 [×2], C2×C20, C2×C20 [×2], C5×Q8 [×2], C4.Dic3 [×2], C6×Q8, C60 [×2], C60 [×2], C2×C30, C5×M4(2) [×2], Q8×C10, C12.10D4, C5×C3⋊C8 [×2], C2×C60, C2×C60 [×2], Q8×C15 [×2], C5×C4.10D4, C5×C4.Dic3 [×2], Q8×C30, C5×C12.10D4
Quotients: C1, C2 [×3], C4 [×2], C22, C5, S3, C2×C4, D4 [×2], C10 [×3], Dic3 [×2], D6, C22⋊C4, C20 [×2], C2×C10, C2×Dic3, C3⋊D4 [×2], C5×S3, C4.10D4, C2×C20, C5×D4 [×2], C6.D4, C5×Dic3 [×2], S3×C10, C5×C22⋊C4, C12.10D4, C10×Dic3, C5×C3⋊D4 [×2], C5×C4.10D4, C5×C6.D4, C5×C12.10D4

Smallest permutation representation of C5×C12.10D4
On 240 points
Generators in S240
(1 58 37 34 22)(2 59 38 35 23)(3 60 39 36 24)(4 49 40 25 13)(5 50 41 26 14)(6 51 42 27 15)(7 52 43 28 16)(8 53 44 29 17)(9 54 45 30 18)(10 55 46 31 19)(11 56 47 32 20)(12 57 48 33 21)(61 118 106 94 73)(62 119 107 95 74)(63 120 108 96 75)(64 109 97 85 76)(65 110 98 86 77)(66 111 99 87 78)(67 112 100 88 79)(68 113 101 89 80)(69 114 102 90 81)(70 115 103 91 82)(71 116 104 92 83)(72 117 105 93 84)(121 173 162 146 142)(122 174 163 147 143)(123 175 164 148 144)(124 176 165 149 133)(125 177 166 150 134)(126 178 167 151 135)(127 179 168 152 136)(128 180 157 153 137)(129 169 158 154 138)(130 170 159 155 139)(131 171 160 156 140)(132 172 161 145 141)(181 236 228 213 201)(182 237 217 214 202)(183 238 218 215 203)(184 239 219 216 204)(185 240 220 205 193)(186 229 221 206 194)(187 230 222 207 195)(188 231 223 208 196)(189 232 224 209 197)(190 233 225 210 198)(191 234 226 211 199)(192 235 227 212 200)
(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)
(1 188 4 185 7 182 10 191)(2 187 5 184 8 181 11 190)(3 186 6 183 9 192 12 189)(13 193 16 202 19 199 22 196)(14 204 17 201 20 198 23 195)(15 203 18 200 21 197 24 194)(25 205 28 214 31 211 34 208)(26 216 29 213 32 210 35 207)(27 215 30 212 33 209 36 206)(37 223 40 220 43 217 46 226)(38 222 41 219 44 228 47 225)(39 221 42 218 45 227 48 224)(49 240 52 237 55 234 58 231)(50 239 53 236 56 233 59 230)(51 238 54 235 57 232 60 229)(61 129 64 126 67 123 70 132)(62 128 65 125 68 122 71 131)(63 127 66 124 69 121 72 130)(73 138 76 135 79 144 82 141)(74 137 77 134 80 143 83 140)(75 136 78 133 81 142 84 139)(85 151 88 148 91 145 94 154)(86 150 89 147 92 156 95 153)(87 149 90 146 93 155 96 152)(97 167 100 164 103 161 106 158)(98 166 101 163 104 160 107 157)(99 165 102 162 105 159 108 168)(109 178 112 175 115 172 118 169)(110 177 113 174 116 171 119 180)(111 176 114 173 117 170 120 179)
(1 126 10 123 7 132 4 129)(2 131 11 128 8 125 5 122)(3 124 12 121 9 130 6 127)(13 138 22 135 19 144 16 141)(14 143 23 140 20 137 17 134)(15 136 24 133 21 142 18 139)(25 154 34 151 31 148 28 145)(26 147 35 156 32 153 29 150)(27 152 36 149 33 146 30 155)(37 167 46 164 43 161 40 158)(38 160 47 157 44 166 41 163)(39 165 48 162 45 159 42 168)(49 169 58 178 55 175 52 172)(50 174 59 171 56 180 53 177)(51 179 60 176 57 173 54 170)(61 191 70 188 67 185 64 182)(62 184 71 181 68 190 65 187)(63 189 72 186 69 183 66 192)(73 199 82 196 79 193 76 202)(74 204 83 201 80 198 77 195)(75 197 84 194 81 203 78 200)(85 214 94 211 91 208 88 205)(86 207 95 216 92 213 89 210)(87 212 96 209 93 206 90 215)(97 217 106 226 103 223 100 220)(98 222 107 219 104 228 101 225)(99 227 108 224 105 221 102 218)(109 237 118 234 115 231 112 240)(110 230 119 239 116 236 113 233)(111 235 120 232 117 229 114 238)

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

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

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

105 conjugacy classes

 class 1 2A 2B 3 4A 4B 4C 4D 5A 5B 5C 5D 6A 6B 6C 8A 8B 8C 8D 10A 10B 10C 10D 10E 10F 10G 10H 12A ··· 12F 15A 15B 15C 15D 20A ··· 20H 20I ··· 20P 30A ··· 30L 40A ··· 40P 60A ··· 60X order 1 2 2 3 4 4 4 4 5 5 5 5 6 6 6 8 8 8 8 10 10 10 10 10 10 10 10 12 ··· 12 15 15 15 15 20 ··· 20 20 ··· 20 30 ··· 30 40 ··· 40 60 ··· 60 size 1 1 2 2 2 2 4 4 1 1 1 1 2 2 2 12 12 12 12 1 1 1 1 2 2 2 2 4 ··· 4 2 2 2 2 2 ··· 2 4 ··· 4 2 ··· 2 12 ··· 12 4 ··· 4

105 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 4 4 4 4 type + + + + + - + - image C1 C2 C2 C4 C5 C10 C10 C20 S3 D4 Dic3 D6 C3⋊D4 C5×S3 C5×D4 C5×Dic3 S3×C10 C5×C3⋊D4 C4.10D4 C12.10D4 C5×C4.10D4 C5×C12.10D4 kernel C5×C12.10D4 C5×C4.Dic3 Q8×C30 C2×C60 C12.10D4 C4.Dic3 C6×Q8 C2×C12 Q8×C10 C60 C2×C20 C2×C20 C20 C2×Q8 C12 C2×C4 C2×C4 C4 C15 C5 C3 C1 # reps 1 2 1 4 4 8 4 16 1 2 2 1 4 4 8 8 4 16 1 2 4 8

Matrix representation of C5×C12.10D4 in GL6(𝔽241)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 87 0 0 0 0 0 0 87 0 0 0 0 0 0 87 0 0 0 0 0 0 87
,
 226 0 0 0 0 0 0 16 0 0 0 0 0 0 0 1 0 0 0 0 240 0 0 0 0 0 240 240 240 239 0 0 1 0 1 1
,
 0 84 0 0 0 0 66 0 0 0 0 0 0 0 61 61 141 122 0 0 80 80 19 160 0 0 61 80 0 0 0 0 100 161 161 100
,
 0 84 0 0 0 0 175 0 0 0 0 0 0 0 0 0 1 0 0 0 240 240 240 239 0 0 0 1 0 0 0 0 1 0 0 1

G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,87,0,0,0,0,0,0,87,0,0,0,0,0,0,87,0,0,0,0,0,0,87],[226,0,0,0,0,0,0,16,0,0,0,0,0,0,0,240,240,1,0,0,1,0,240,0,0,0,0,0,240,1,0,0,0,0,239,1],[0,66,0,0,0,0,84,0,0,0,0,0,0,0,61,80,61,100,0,0,61,80,80,161,0,0,141,19,0,161,0,0,122,160,0,100],[0,175,0,0,0,0,84,0,0,0,0,0,0,0,0,240,0,1,0,0,0,240,1,0,0,0,1,240,0,0,0,0,0,239,0,1] >;

C5×C12.10D4 in GAP, Magma, Sage, TeX

C_5\times C_{12}._{10}D_4
% in TeX

G:=Group("C5xC12.10D4");
// GroupNames label

G:=SmallGroup(480,155);
// by ID

G=gap.SmallGroup(480,155);
# by ID

G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,140,589,568,1410,136,4204,15686]);
// Polycyclic

G:=Group<a,b,c,d|a^5=b^12=1,c^4=b^6,d^2=b^9,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^5,d*c*d^-1=b^9*c^3>;
// generators/relations

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