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G = C5×C12.53D4order 480 = 25·3·5

Direct product of C5 and C12.53D4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C5×C12.53D4, C60.238D4, C3⋊C8.1C20, C4.13(S3×C20), C12.5(C2×C20), C12.53(C5×D4), C30.60(C4⋊C4), (C2×C30).10Q8, C20.115(C4×S3), C60.175(C2×C4), (C2×C20).348D6, (C2×C10).4Dic6, C1515(C8.C4), (C5×M4(2)).1S3, M4(2).1(C5×S3), C4.Dic3.2C10, C22.1(C5×Dic6), C20.121(C3⋊D4), (C2×C60).341C22, (C15×M4(2)).3C2, (C3×M4(2)).1C10, C10.25(Dic3⋊C4), (C2×C6).(C5×Q8), (C5×C3⋊C8).8C4, C6.8(C5×C4⋊C4), (C2×C3⋊C8).4C10, C32(C5×C8.C4), (C10×C3⋊C8).16C2, C4.28(C5×C3⋊D4), (C2×C4).36(S3×C10), C2.5(C5×Dic3⋊C4), (C2×C12).11(C2×C10), (C5×C4.Dic3).6C2, SmallGroup(480,141)

Series: Derived Chief Lower central Upper central

C1C12 — C5×C12.53D4
C1C3C6C12C2×C12C2×C60C10×C3⋊C8 — C5×C12.53D4
C3C6C12 — C5×C12.53D4
C1C20C2×C20C5×M4(2)

Generators and relations for C5×C12.53D4
 G = < a,b,c,d | a5=b12=1, c4=b6, d2=b9, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b5, dcd-1=b6c3 >

Subgroups: 100 in 60 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2, C3, C4 [×2], C22, C5, C6, C6, C8 [×4], C2×C4, C10, C10, C12 [×2], C2×C6, C15, C2×C8, M4(2), M4(2), C20 [×2], C2×C10, C3⋊C8 [×2], C3⋊C8, C24, C2×C12, C30, C30, C8.C4, C40 [×4], C2×C20, C2×C3⋊C8, C4.Dic3, C3×M4(2), C60 [×2], C2×C30, C2×C40, C5×M4(2), C5×M4(2), C12.53D4, C5×C3⋊C8 [×2], C5×C3⋊C8, C120, C2×C60, C5×C8.C4, C10×C3⋊C8, C5×C4.Dic3, C15×M4(2), C5×C12.53D4
Quotients: C1, C2 [×3], C4 [×2], C22, C5, S3, C2×C4, D4, Q8, C10 [×3], D6, C4⋊C4, C20 [×2], C2×C10, Dic6, C4×S3, C3⋊D4, C5×S3, C8.C4, C2×C20, C5×D4, C5×Q8, Dic3⋊C4, S3×C10, C5×C4⋊C4, C12.53D4, C5×Dic6, S3×C20, C5×C3⋊D4, C5×C8.C4, C5×Dic3⋊C4, C5×C12.53D4

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

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

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

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

120 conjugacy classes

class 1 2A2B 3 4A4B4C5A5B5C5D6A6B8A8B8C8D8E8F8G8H10A10B10C10D10E10F10G10H12A12B12C15A15B15C15D20A···20H20I20J20K20L24A24B24C24D30A30B30C30D30E30F30G30H40A···40H40I···40X40Y···40AF60A···60H60I60J60K60L120A···120P
order12234445555668888888810101010101010101212121515151520···202020202024242424303030303030303040···4040···4040···4060···6060606060120···120
size112211211112444666612121111222222422221···122224444222244444···46···612···122···244444···4

120 irreducible representations

dim1111111111222222222222222244
type++++++-+-
imageC1C2C2C2C4C5C10C10C10C20S3D4Q8D6C4×S3C3⋊D4Dic6C5×S3C8.C4C5×D4C5×Q8S3×C10S3×C20C5×C3⋊D4C5×Dic6C5×C8.C4C12.53D4C5×C12.53D4
kernelC5×C12.53D4C10×C3⋊C8C5×C4.Dic3C15×M4(2)C5×C3⋊C8C12.53D4C2×C3⋊C8C4.Dic3C3×M4(2)C3⋊C8C5×M4(2)C60C2×C30C2×C20C20C20C2×C10M4(2)C15C12C2×C6C2×C4C4C4C22C3C5C1
# reps111144444161111222444448881628

Matrix representation of C5×C12.53D4 in GL4(𝔽241) generated by

91000
09100
0010
0001
,
24024000
1000
001770
000177
,
1494800
1409200
002330
0013030
,
9219300
10114900
0014390
0015598
G:=sub<GL(4,GF(241))| [91,0,0,0,0,91,0,0,0,0,1,0,0,0,0,1],[240,1,0,0,240,0,0,0,0,0,177,0,0,0,0,177],[149,140,0,0,48,92,0,0,0,0,233,130,0,0,0,30],[92,101,0,0,193,149,0,0,0,0,143,155,0,0,90,98] >;

C5×C12.53D4 in GAP, Magma, Sage, TeX

C_5\times C_{12}._{53}D_4
% in TeX

G:=Group("C5xC12.53D4");
// GroupNames label

G:=SmallGroup(480,141);
// by ID

G=gap.SmallGroup(480,141);
# by ID

G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,280,589,148,136,2111,102,15686]);
// 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=d*b*d^-1=b^5,d*c*d^-1=b^6*c^3>;
// generators/relations

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