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G = C2×C6×D20order 480 = 25·3·5

Direct product of C2×C6 and D20

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

Aliases: C2×C6×D20, C6011C23, C30.71C24, C101(C6×D4), (C2×C30)⋊26D4, C3011(C2×D4), (C2×C12)⋊36D10, C202(C22×C6), (C23×D5)⋊6C6, C1512(C22×D4), (C22×C20)⋊11C6, (C2×C60)⋊47C22, (C22×C60)⋊16C2, D101(C22×C6), (C6×D5)⋊10C23, (C22×C12)⋊12D5, C1210(C22×D5), C10.3(C23×C6), C23.40(C6×D5), C6.71(C23×D5), (C2×C30).381C23, (C22×C6).137D10, (C22×C30).166C22, C51(D4×C2×C6), C42(D5×C2×C6), (C2×C4)⋊9(C6×D5), (C2×C10)⋊9(C3×D4), (D5×C22×C6)⋊9C2, (C2×C20)⋊12(C2×C6), C2.4(D5×C22×C6), (D5×C2×C6)⋊21C22, (C22×C4)⋊7(C3×D5), C22.30(D5×C2×C6), (C22×D5)⋊6(C2×C6), (C22×C10).53(C2×C6), (C2×C10).64(C22×C6), (C2×C6).377(C22×D5), SmallGroup(480,1137)

Series: Derived Chief Lower central Upper central

C1C10 — C2×C6×D20
C1C5C10C30C6×D5D5×C2×C6D5×C22×C6 — C2×C6×D20
C5C10 — C2×C6×D20
C1C22×C6C22×C12

Generators and relations for C2×C6×D20
 G = < a,b,c,d | a2=b6=c20=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >

Subgroups: 1680 in 472 conjugacy classes, 210 normal (18 characteristic)
C1, C2, C2 [×6], C2 [×8], C3, C4 [×4], C22 [×7], C22 [×32], C5, C6, C6 [×6], C6 [×8], C2×C4 [×6], D4 [×16], C23, C23 [×20], D5 [×8], C10, C10 [×6], C12 [×4], C2×C6 [×7], C2×C6 [×32], C15, C22×C4, C2×D4 [×12], C24 [×2], C20 [×4], D10 [×8], D10 [×24], C2×C10 [×7], C2×C12 [×6], C3×D4 [×16], C22×C6, C22×C6 [×20], C3×D5 [×8], C30, C30 [×6], C22×D4, D20 [×16], C2×C20 [×6], C22×D5 [×12], C22×D5 [×8], C22×C10, C22×C12, C6×D4 [×12], C23×C6 [×2], C60 [×4], C6×D5 [×8], C6×D5 [×24], C2×C30 [×7], C2×D20 [×12], C22×C20, C23×D5 [×2], D4×C2×C6, C3×D20 [×16], C2×C60 [×6], D5×C2×C6 [×12], D5×C2×C6 [×8], C22×C30, C22×D20, C6×D20 [×12], C22×C60, D5×C22×C6 [×2], C2×C6×D20
Quotients: C1, C2 [×15], C3, C22 [×35], C6 [×15], D4 [×4], C23 [×15], D5, C2×C6 [×35], C2×D4 [×6], C24, D10 [×7], C3×D4 [×4], C22×C6 [×15], C3×D5, C22×D4, D20 [×4], C22×D5 [×7], C6×D4 [×6], C23×C6, C6×D5 [×7], C2×D20 [×6], C23×D5, D4×C2×C6, C3×D20 [×4], D5×C2×C6 [×7], C22×D20, C6×D20 [×6], D5×C22×C6, C2×C6×D20

Smallest permutation representation of C2×C6×D20
On 240 points
Generators in S240
(1 107)(2 108)(3 109)(4 110)(5 111)(6 112)(7 113)(8 114)(9 115)(10 116)(11 117)(12 118)(13 119)(14 120)(15 101)(16 102)(17 103)(18 104)(19 105)(20 106)(21 171)(22 172)(23 173)(24 174)(25 175)(26 176)(27 177)(28 178)(29 179)(30 180)(31 161)(32 162)(33 163)(34 164)(35 165)(36 166)(37 167)(38 168)(39 169)(40 170)(41 158)(42 159)(43 160)(44 141)(45 142)(46 143)(47 144)(48 145)(49 146)(50 147)(51 148)(52 149)(53 150)(54 151)(55 152)(56 153)(57 154)(58 155)(59 156)(60 157)(61 88)(62 89)(63 90)(64 91)(65 92)(66 93)(67 94)(68 95)(69 96)(70 97)(71 98)(72 99)(73 100)(74 81)(75 82)(76 83)(77 84)(78 85)(79 86)(80 87)(121 214)(122 215)(123 216)(124 217)(125 218)(126 219)(127 220)(128 201)(129 202)(130 203)(131 204)(132 205)(133 206)(134 207)(135 208)(136 209)(137 210)(138 211)(139 212)(140 213)(181 222)(182 223)(183 224)(184 225)(185 226)(186 227)(187 228)(188 229)(189 230)(190 231)(191 232)(192 233)(193 234)(194 235)(195 236)(196 237)(197 238)(198 239)(199 240)(200 221)
(1 95 44 130 38 230)(2 96 45 131 39 231)(3 97 46 132 40 232)(4 98 47 133 21 233)(5 99 48 134 22 234)(6 100 49 135 23 235)(7 81 50 136 24 236)(8 82 51 137 25 237)(9 83 52 138 26 238)(10 84 53 139 27 239)(11 85 54 140 28 240)(12 86 55 121 29 221)(13 87 56 122 30 222)(14 88 57 123 31 223)(15 89 58 124 32 224)(16 90 59 125 33 225)(17 91 60 126 34 226)(18 92 41 127 35 227)(19 93 42 128 36 228)(20 94 43 129 37 229)(61 154 216 161 182 120)(62 155 217 162 183 101)(63 156 218 163 184 102)(64 157 219 164 185 103)(65 158 220 165 186 104)(66 159 201 166 187 105)(67 160 202 167 188 106)(68 141 203 168 189 107)(69 142 204 169 190 108)(70 143 205 170 191 109)(71 144 206 171 192 110)(72 145 207 172 193 111)(73 146 208 173 194 112)(74 147 209 174 195 113)(75 148 210 175 196 114)(76 149 211 176 197 115)(77 150 212 177 198 116)(78 151 213 178 199 117)(79 152 214 179 200 118)(80 153 215 180 181 119)
(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)
(1 124)(2 123)(3 122)(4 121)(5 140)(6 139)(7 138)(8 137)(9 136)(10 135)(11 134)(12 133)(13 132)(14 131)(15 130)(16 129)(17 128)(18 127)(19 126)(20 125)(21 86)(22 85)(23 84)(24 83)(25 82)(26 81)(27 100)(28 99)(29 98)(30 97)(31 96)(32 95)(33 94)(34 93)(35 92)(36 91)(37 90)(38 89)(39 88)(40 87)(41 227)(42 226)(43 225)(44 224)(45 223)(46 222)(47 221)(48 240)(49 239)(50 238)(51 237)(52 236)(53 235)(54 234)(55 233)(56 232)(57 231)(58 230)(59 229)(60 228)(61 169)(62 168)(63 167)(64 166)(65 165)(66 164)(67 163)(68 162)(69 161)(70 180)(71 179)(72 178)(73 177)(74 176)(75 175)(76 174)(77 173)(78 172)(79 171)(80 170)(101 203)(102 202)(103 201)(104 220)(105 219)(106 218)(107 217)(108 216)(109 215)(110 214)(111 213)(112 212)(113 211)(114 210)(115 209)(116 208)(117 207)(118 206)(119 205)(120 204)(141 183)(142 182)(143 181)(144 200)(145 199)(146 198)(147 197)(148 196)(149 195)(150 194)(151 193)(152 192)(153 191)(154 190)(155 189)(156 188)(157 187)(158 186)(159 185)(160 184)

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

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

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

156 conjugacy classes

class 1 2A···2G2H···2O3A3B4A4B4C4D5A5B6A···6N6O···6AD10A···10N12A···12H15A15B15C15D20A···20P30A···30AB60A···60AF
order12···22···2334444556···66···610···1012···121515151520···2030···3060···60
size11···110···10112222221···110···102···22···222222···22···22···2

156 irreducible representations

dim111111112222222222
type+++++++++
imageC1C2C2C2C3C6C6C6D4D5D10D10C3×D4C3×D5D20C6×D5C6×D5C3×D20
kernelC2×C6×D20C6×D20C22×C60D5×C22×C6C22×D20C2×D20C22×C20C23×D5C2×C30C22×C12C2×C12C22×C6C2×C10C22×C4C2×C6C2×C4C23C22
# reps112122242442122841624432

Matrix representation of C2×C6×D20 in GL4(𝔽61) generated by

60000
0100
0010
0001
,
60000
04800
00470
00047
,
1000
0100
005925
003432
,
1000
0100
0011
00060
G:=sub<GL(4,GF(61))| [60,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[60,0,0,0,0,48,0,0,0,0,47,0,0,0,0,47],[1,0,0,0,0,1,0,0,0,0,59,34,0,0,25,32],[1,0,0,0,0,1,0,0,0,0,1,0,0,0,1,60] >;

C2×C6×D20 in GAP, Magma, Sage, TeX

C_2\times C_6\times D_{20}
% in TeX

G:=Group("C2xC6xD20");
// GroupNames label

G:=SmallGroup(480,1137);
// by ID

G=gap.SmallGroup(480,1137);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-5,1571,192,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^6=c^20=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