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G = C2×C10×D12order 480 = 25·3·5

Direct product of C2×C10 and D12

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

Aliases: C2×C10×D12, C6012C23, C30.86C24, C61(D4×C10), (C2×C20)⋊36D6, (C2×C30)⋊28D4, C3012(C2×D4), C1513(C22×D4), (S3×C23)⋊3C10, C2010(C22×S3), (C22×C20)⋊16S3, (C22×C60)⋊19C2, C122(C22×C10), (C2×C60)⋊49C22, (C22×C12)⋊7C10, D61(C22×C10), C6.3(C23×C10), (S3×C10)⋊10C23, C23.40(S3×C10), C10.71(S3×C23), (C2×C30).443C23, (C22×C10).154D6, (C22×C30).183C22, C31(D4×C2×C10), C42(S3×C2×C10), (C2×C6)⋊6(C5×D4), (C2×C4)⋊9(S3×C10), (S3×C22×C10)⋊9C2, (C22×C4)⋊7(C5×S3), (C2×C12)⋊12(C2×C10), C2.4(S3×C22×C10), (S3×C2×C10)⋊21C22, C22.30(S3×C2×C10), (C22×S3)⋊5(C2×C10), (C22×C6).45(C2×C10), (C2×C6).64(C22×C10), (C2×C10).377(C22×S3), SmallGroup(480,1152)

Series: Derived Chief Lower central Upper central

C1C6 — C2×C10×D12
C1C3C6C30S3×C10S3×C2×C10S3×C22×C10 — C2×C10×D12
C3C6 — C2×C10×D12
C1C22×C10C22×C20

Generators and relations for C2×C10×D12
 G = < a,b,c,d | a2=b10=c12=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >

Subgroups: 1156 in 472 conjugacy classes, 210 normal (18 characteristic)
C1, C2, C2 [×6], C2 [×8], C3, C4 [×4], C22 [×7], C22 [×32], C5, S3 [×8], C6, C6 [×6], C2×C4 [×6], D4 [×16], C23, C23 [×20], C10, C10 [×6], C10 [×8], C12 [×4], D6 [×8], D6 [×24], C2×C6 [×7], C15, C22×C4, C2×D4 [×12], C24 [×2], C20 [×4], C2×C10 [×7], C2×C10 [×32], D12 [×16], C2×C12 [×6], C22×S3 [×12], C22×S3 [×8], C22×C6, C5×S3 [×8], C30, C30 [×6], C22×D4, C2×C20 [×6], C5×D4 [×16], C22×C10, C22×C10 [×20], C2×D12 [×12], C22×C12, S3×C23 [×2], C60 [×4], S3×C10 [×8], S3×C10 [×24], C2×C30 [×7], C22×C20, D4×C10 [×12], C23×C10 [×2], C22×D12, C5×D12 [×16], C2×C60 [×6], S3×C2×C10 [×12], S3×C2×C10 [×8], C22×C30, D4×C2×C10, C10×D12 [×12], C22×C60, S3×C22×C10 [×2], C2×C10×D12
Quotients: C1, C2 [×15], C22 [×35], C5, S3, D4 [×4], C23 [×15], C10 [×15], D6 [×7], C2×D4 [×6], C24, C2×C10 [×35], D12 [×4], C22×S3 [×7], C5×S3, C22×D4, C5×D4 [×4], C22×C10 [×15], C2×D12 [×6], S3×C23, S3×C10 [×7], D4×C10 [×6], C23×C10, C22×D12, C5×D12 [×4], S3×C2×C10 [×7], D4×C2×C10, C10×D12 [×6], S3×C22×C10, C2×C10×D12

Smallest permutation representation of C2×C10×D12
On 240 points
Generators in S240
(1 96)(2 85)(3 86)(4 87)(5 88)(6 89)(7 90)(8 91)(9 92)(10 93)(11 94)(12 95)(13 135)(14 136)(15 137)(16 138)(17 139)(18 140)(19 141)(20 142)(21 143)(22 144)(23 133)(24 134)(25 116)(26 117)(27 118)(28 119)(29 120)(30 109)(31 110)(32 111)(33 112)(34 113)(35 114)(36 115)(37 101)(38 102)(39 103)(40 104)(41 105)(42 106)(43 107)(44 108)(45 97)(46 98)(47 99)(48 100)(49 62)(50 63)(51 64)(52 65)(53 66)(54 67)(55 68)(56 69)(57 70)(58 71)(59 72)(60 61)(73 129)(74 130)(75 131)(76 132)(77 121)(78 122)(79 123)(80 124)(81 125)(82 126)(83 127)(84 128)(145 221)(146 222)(147 223)(148 224)(149 225)(150 226)(151 227)(152 228)(153 217)(154 218)(155 219)(156 220)(157 209)(158 210)(159 211)(160 212)(161 213)(162 214)(163 215)(164 216)(165 205)(166 206)(167 207)(168 208)(169 204)(170 193)(171 194)(172 195)(173 196)(174 197)(175 198)(176 199)(177 200)(178 201)(179 202)(180 203)(181 230)(182 231)(183 232)(184 233)(185 234)(186 235)(187 236)(188 237)(189 238)(190 239)(191 240)(192 229)
(1 168 169 134 220 240 99 30 121 53)(2 157 170 135 221 229 100 31 122 54)(3 158 171 136 222 230 101 32 123 55)(4 159 172 137 223 231 102 33 124 56)(5 160 173 138 224 232 103 34 125 57)(6 161 174 139 225 233 104 35 126 58)(7 162 175 140 226 234 105 36 127 59)(8 163 176 141 227 235 106 25 128 60)(9 164 177 142 228 236 107 26 129 49)(10 165 178 143 217 237 108 27 130 50)(11 166 179 144 218 238 97 28 131 51)(12 167 180 133 219 239 98 29 132 52)(13 145 192 48 110 78 67 85 209 193)(14 146 181 37 111 79 68 86 210 194)(15 147 182 38 112 80 69 87 211 195)(16 148 183 39 113 81 70 88 212 196)(17 149 184 40 114 82 71 89 213 197)(18 150 185 41 115 83 72 90 214 198)(19 151 186 42 116 84 61 91 215 199)(20 152 187 43 117 73 62 92 216 200)(21 153 188 44 118 74 63 93 205 201)(22 154 189 45 119 75 64 94 206 202)(23 155 190 46 120 76 65 95 207 203)(24 156 191 47 109 77 66 96 208 204)
(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)
(1 230)(2 229)(3 240)(4 239)(5 238)(6 237)(7 236)(8 235)(9 234)(10 233)(11 232)(12 231)(13 78)(14 77)(15 76)(16 75)(17 74)(18 73)(19 84)(20 83)(21 82)(22 81)(23 80)(24 79)(25 176)(26 175)(27 174)(28 173)(29 172)(30 171)(31 170)(32 169)(33 180)(34 179)(35 178)(36 177)(37 208)(38 207)(39 206)(40 205)(41 216)(42 215)(43 214)(44 213)(45 212)(46 211)(47 210)(48 209)(49 226)(50 225)(51 224)(52 223)(53 222)(54 221)(55 220)(56 219)(57 218)(58 217)(59 228)(60 227)(61 151)(62 150)(63 149)(64 148)(65 147)(66 146)(67 145)(68 156)(69 155)(70 154)(71 153)(72 152)(85 192)(86 191)(87 190)(88 189)(89 188)(90 187)(91 186)(92 185)(93 184)(94 183)(95 182)(96 181)(97 160)(98 159)(99 158)(100 157)(101 168)(102 167)(103 166)(104 165)(105 164)(106 163)(107 162)(108 161)(109 194)(110 193)(111 204)(112 203)(113 202)(114 201)(115 200)(116 199)(117 198)(118 197)(119 196)(120 195)(121 136)(122 135)(123 134)(124 133)(125 144)(126 143)(127 142)(128 141)(129 140)(130 139)(131 138)(132 137)

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

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

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

180 conjugacy classes

class 1 2A···2G2H···2O 3 4A4B4C4D5A5B5C5D6A···6G10A···10AB10AC···10BH12A···12H15A15B15C15D20A···20P30A···30AB60A···60AF
order12···22···23444455556···610···1010···1012···121515151520···2030···3060···60
size11···16···62222211112···21···16···62···222222···22···22···2

180 irreducible representations

dim111111112222222222
type+++++++++
imageC1C2C2C2C5C10C10C10S3D4D6D6D12C5×S3C5×D4S3×C10S3×C10C5×D12
kernelC2×C10×D12C10×D12C22×C60S3×C22×C10C22×D12C2×D12C22×C12S3×C23C22×C20C2×C30C2×C20C22×C10C2×C10C22×C4C2×C6C2×C4C23C22
# reps11212448481461841624432

Matrix representation of C2×C10×D12 in GL4(𝔽61) generated by

60000
06000
0010
0001
,
27000
0100
0010
0001
,
60000
06000
003823
003815
,
1000
06000
0011
00060
G:=sub<GL(4,GF(61))| [60,0,0,0,0,60,0,0,0,0,1,0,0,0,0,1],[27,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[60,0,0,0,0,60,0,0,0,0,38,38,0,0,23,15],[1,0,0,0,0,60,0,0,0,0,1,0,0,0,1,60] >;

C2×C10×D12 in GAP, Magma, Sage, TeX

C_2\times C_{10}\times D_{12}
% in TeX

G:=Group("C2xC10xD12");
// GroupNames label

G:=SmallGroup(480,1152);
// by ID

G=gap.SmallGroup(480,1152);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-3,2467,304,15686]);
// Polycyclic

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

׿
×
𝔽