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G = C5×C4⋊D12order 480 = 25·3·5

Direct product of C5 and C4⋊D12

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

Aliases: C5×C4⋊D12, C206D12, C6025D4, C124(C5×D4), C41(C5×D12), (C4×C12)⋊4C10, (C4×C60)⋊16C2, (C4×C20)⋊14S3, C426(C5×S3), C6.3(D4×C10), (C2×D12)⋊1C10, C157(C41D4), C2.5(C10×D12), (C10×D12)⋊17C2, (C2×C20).429D6, C10.74(C2×D12), C30.290(C2×D4), (C2×C30).394C23, (C2×C60).526C22, C31(C5×C41D4), (C2×C4).78(S3×C10), C22.36(S3×C2×C10), (C2×C12).91(C2×C10), (S3×C2×C10).63C22, (C22×S3).1(C2×C10), (C2×C6).15(C22×C10), (C2×C10).328(C22×S3), SmallGroup(480,753)

Series: Derived Chief Lower central Upper central

C1C2×C6 — C5×C4⋊D12
C1C3C6C2×C6C2×C30S3×C2×C10C10×D12 — C5×C4⋊D12
C3C2×C6 — C5×C4⋊D12
C1C2×C10C4×C20

Generators and relations for C5×C4⋊D12
 G = < a,b,c,d | a5=b4=c12=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >

Subgroups: 660 in 216 conjugacy classes, 82 normal (14 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×6], C22, C22 [×12], C5, S3 [×4], C6 [×3], C2×C4 [×3], D4 [×12], C23 [×4], C10 [×3], C10 [×4], C12 [×6], D6 [×12], C2×C6, C15, C42, C2×D4 [×6], C20 [×6], C2×C10, C2×C10 [×12], D12 [×12], C2×C12 [×3], C22×S3 [×4], C5×S3 [×4], C30 [×3], C41D4, C2×C20 [×3], C5×D4 [×12], C22×C10 [×4], C4×C12, C2×D12 [×6], C60 [×6], S3×C10 [×12], C2×C30, C4×C20, D4×C10 [×6], C4⋊D12, C5×D12 [×12], C2×C60 [×3], S3×C2×C10 [×4], C5×C41D4, C4×C60, C10×D12 [×6], C5×C4⋊D12
Quotients: C1, C2 [×7], C22 [×7], C5, S3, D4 [×6], C23, C10 [×7], D6 [×3], C2×D4 [×3], C2×C10 [×7], D12 [×6], C22×S3, C5×S3, C41D4, C5×D4 [×6], C22×C10, C2×D12 [×3], S3×C10 [×3], D4×C10 [×3], C4⋊D12, C5×D12 [×6], S3×C2×C10, C5×C41D4, C10×D12 [×3], C5×C4⋊D12

Smallest permutation representation of C5×C4⋊D12
On 240 points
Generators in S240
(1 83 40 188 214)(2 84 41 189 215)(3 73 42 190 216)(4 74 43 191 205)(5 75 44 192 206)(6 76 45 181 207)(7 77 46 182 208)(8 78 47 183 209)(9 79 48 184 210)(10 80 37 185 211)(11 81 38 186 212)(12 82 39 187 213)(13 127 101 119 162)(14 128 102 120 163)(15 129 103 109 164)(16 130 104 110 165)(17 131 105 111 166)(18 132 106 112 167)(19 121 107 113 168)(20 122 108 114 157)(21 123 97 115 158)(22 124 98 116 159)(23 125 99 117 160)(24 126 100 118 161)(25 133 153 224 59)(26 134 154 225 60)(27 135 155 226 49)(28 136 156 227 50)(29 137 145 228 51)(30 138 146 217 52)(31 139 147 218 53)(32 140 148 219 54)(33 141 149 220 55)(34 142 150 221 56)(35 143 151 222 57)(36 144 152 223 58)(61 175 235 94 196)(62 176 236 95 197)(63 177 237 96 198)(64 178 238 85 199)(65 179 239 86 200)(66 180 240 87 201)(67 169 229 88 202)(68 170 230 89 203)(69 171 231 90 204)(70 172 232 91 193)(71 173 233 92 194)(72 174 234 93 195)
(1 87 16 217)(2 88 17 218)(3 89 18 219)(4 90 19 220)(5 91 20 221)(6 92 21 222)(7 93 22 223)(8 94 23 224)(9 95 24 225)(10 96 13 226)(11 85 14 227)(12 86 15 228)(25 47 61 99)(26 48 62 100)(27 37 63 101)(28 38 64 102)(29 39 65 103)(30 40 66 104)(31 41 67 105)(32 42 68 106)(33 43 69 107)(34 44 70 108)(35 45 71 97)(36 46 72 98)(49 80 198 127)(50 81 199 128)(51 82 200 129)(52 83 201 130)(53 84 202 131)(54 73 203 132)(55 74 204 121)(56 75 193 122)(57 76 194 123)(58 77 195 124)(59 78 196 125)(60 79 197 126)(109 137 187 179)(110 138 188 180)(111 139 189 169)(112 140 190 170)(113 141 191 171)(114 142 192 172)(115 143 181 173)(116 144 182 174)(117 133 183 175)(118 134 184 176)(119 135 185 177)(120 136 186 178)(145 213 239 164)(146 214 240 165)(147 215 229 166)(148 216 230 167)(149 205 231 168)(150 206 232 157)(151 207 233 158)(152 208 234 159)(153 209 235 160)(154 210 236 161)(155 211 237 162)(156 212 238 163)
(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)
(1 219)(2 218)(3 217)(4 228)(5 227)(6 226)(7 225)(8 224)(9 223)(10 222)(11 221)(12 220)(13 92)(14 91)(15 90)(16 89)(17 88)(18 87)(19 86)(20 85)(21 96)(22 95)(23 94)(24 93)(25 47)(26 46)(27 45)(28 44)(29 43)(30 42)(31 41)(32 40)(33 39)(34 38)(35 37)(36 48)(49 76)(50 75)(51 74)(52 73)(53 84)(54 83)(55 82)(56 81)(57 80)(58 79)(59 78)(60 77)(61 99)(62 98)(63 97)(64 108)(65 107)(66 106)(67 105)(68 104)(69 103)(70 102)(71 101)(72 100)(109 171)(110 170)(111 169)(112 180)(113 179)(114 178)(115 177)(116 176)(117 175)(118 174)(119 173)(120 172)(121 200)(122 199)(123 198)(124 197)(125 196)(126 195)(127 194)(128 193)(129 204)(130 203)(131 202)(132 201)(133 183)(134 182)(135 181)(136 192)(137 191)(138 190)(139 189)(140 188)(141 187)(142 186)(143 185)(144 184)(145 205)(146 216)(147 215)(148 214)(149 213)(150 212)(151 211)(152 210)(153 209)(154 208)(155 207)(156 206)(157 238)(158 237)(159 236)(160 235)(161 234)(162 233)(163 232)(164 231)(165 230)(166 229)(167 240)(168 239)

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

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

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

150 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A···4F5A5B5C5D6A6B6C10A···10L10M···10AB12A···12L15A15B15C15D20A···20X30A···30L60A···60AV
order1222222234···4555566610···1010···1012···121515151520···2030···3060···60
size11111212121222···211112221···112···122···222222···22···22···2

150 irreducible representations

dim11111122222222
type+++++++
imageC1C2C2C5C10C10S3D4D6D12C5×S3C5×D4S3×C10C5×D12
kernelC5×C4⋊D12C4×C60C10×D12C4⋊D12C4×C12C2×D12C4×C20C60C2×C20C20C42C12C2×C4C4
# reps1164424163124241248

Matrix representation of C5×C4⋊D12 in GL4(𝔽61) generated by

1000
0100
00340
00034
,
8300
195300
00600
00060
,
8300
195300
002323
003846
,
535800
21800
0010
00160
G:=sub<GL(4,GF(61))| [1,0,0,0,0,1,0,0,0,0,34,0,0,0,0,34],[8,19,0,0,3,53,0,0,0,0,60,0,0,0,0,60],[8,19,0,0,3,53,0,0,0,0,23,38,0,0,23,46],[53,21,0,0,58,8,0,0,0,0,1,1,0,0,0,60] >;

C5×C4⋊D12 in GAP, Magma, Sage, TeX

C_5\times C_4\rtimes D_{12}
% in TeX

G:=Group("C5xC4:D12");
// GroupNames label

G:=SmallGroup(480,753);
// by ID

G=gap.SmallGroup(480,753);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-3,1149,568,926,226,15686]);
// Polycyclic

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

׿
×
𝔽