direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C20⋊4D4, C60⋊24D4, C12⋊6D20, C4⋊1(C3×D20), C20⋊4(C3×D4), (C4×C20)⋊10C6, (C4×C60)⋊12C2, (C2×D20)⋊1C6, (C4×C12)⋊12D5, C10.3(C6×D4), C2.5(C6×D20), C42⋊8(C3×D5), (C6×D20)⋊17C2, C15⋊6(C4⋊1D4), C6.74(C2×D20), C30.276(C2×D4), (C2×C12).427D10, (C2×C30).332C23, (C2×C60).507C22, C5⋊1(C3×C4⋊1D4), (C2×C4).77(C6×D5), C22.36(D5×C2×C6), (C2×C20).90(C2×C6), (D5×C2×C6).74C22, (C22×D5).2(C2×C6), (C2×C10).15(C22×C6), (C2×C6).328(C22×D5), SmallGroup(480,667)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C20⋊4D4
G = < a,b,c,d | a3=b4=c20=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >
Subgroups: 960 in 216 conjugacy classes, 82 normal (14 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, C6, C6, C2×C4, D4, C23, D5, C10, C12, C2×C6, C2×C6, C15, C42, C2×D4, C20, D10, C2×C10, C2×C12, C3×D4, C22×C6, C3×D5, C30, C4⋊1D4, D20, C2×C20, C22×D5, C4×C12, C6×D4, C60, C6×D5, C2×C30, C4×C20, C2×D20, C3×C4⋊1D4, C3×D20, C2×C60, D5×C2×C6, C20⋊4D4, C4×C60, C6×D20, C3×C20⋊4D4
Quotients: C1, C2, C3, C22, C6, D4, C23, D5, C2×C6, C2×D4, D10, C3×D4, C22×C6, C3×D5, C4⋊1D4, D20, C22×D5, C6×D4, C6×D5, C2×D20, C3×C4⋊1D4, C3×D20, D5×C2×C6, C20⋊4D4, C6×D20, C3×C20⋊4D4
►On 240 points
Generators in S240
(1 38 65)(2 39 66)(3 40 67)(4 21 68)(5 22 69)(6 23 70)(7 24 71)(8 25 72)(9 26 73)(10 27 74)(11 28 75)(12 29 76)(13 30 77)(14 31 78)(15 32 79)(16 33 80)(17 34 61)(18 35 62)(19 36 63)(20 37 64)(41 148 98)(42 149 99)(43 150 100)(44 151 81)(45 152 82)(46 153 83)(47 154 84)(48 155 85)(49 156 86)(50 157 87)(51 158 88)(52 159 89)(53 160 90)(54 141 91)(55 142 92)(56 143 93)(57 144 94)(58 145 95)(59 146 96)(60 147 97)(101 199 211)(102 200 212)(103 181 213)(104 182 214)(105 183 215)(106 184 216)(107 185 217)(108 186 218)(109 187 219)(110 188 220)(111 189 201)(112 190 202)(113 191 203)(114 192 204)(115 193 205)(116 194 206)(117 195 207)(118 196 208)(119 197 209)(120 198 210)(121 172 227)(122 173 228)(123 174 229)(124 175 230)(125 176 231)(126 177 232)(127 178 233)(128 179 234)(129 180 235)(130 161 236)(131 162 237)(132 163 238)(133 164 239)(134 165 240)(135 166 221)(136 167 222)(137 168 223)(138 169 224)(139 170 225)(140 171 226)
(1 115 227 90)(2 116 228 91)(3 117 229 92)(4 118 230 93)(5 119 231 94)(6 120 232 95)(7 101 233 96)(8 102 234 97)(9 103 235 98)(10 104 236 99)(11 105 237 100)(12 106 238 81)(13 107 239 82)(14 108 240 83)(15 109 221 84)(16 110 222 85)(17 111 223 86)(18 112 224 87)(19 113 225 88)(20 114 226 89)(21 196 124 56)(22 197 125 57)(23 198 126 58)(24 199 127 59)(25 200 128 60)(26 181 129 41)(27 182 130 42)(28 183 131 43)(29 184 132 44)(30 185 133 45)(31 186 134 46)(32 187 135 47)(33 188 136 48)(34 189 137 49)(35 190 138 50)(36 191 139 51)(37 192 140 52)(38 193 121 53)(39 194 122 54)(40 195 123 55)(61 201 168 156)(62 202 169 157)(63 203 170 158)(64 204 171 159)(65 205 172 160)(66 206 173 141)(67 207 174 142)(68 208 175 143)(69 209 176 144)(70 210 177 145)(71 211 178 146)(72 212 179 147)(73 213 180 148)(74 214 161 149)(75 215 162 150)(76 216 163 151)(77 217 164 152)(78 218 165 153)(79 219 166 154)(80 220 167 155)
(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 84)(2 83)(3 82)(4 81)(5 100)(6 99)(7 98)(8 97)(9 96)(10 95)(11 94)(12 93)(13 92)(14 91)(15 90)(16 89)(17 88)(18 87)(19 86)(20 85)(21 44)(22 43)(23 42)(24 41)(25 60)(26 59)(27 58)(28 57)(29 56)(30 55)(31 54)(32 53)(33 52)(34 51)(35 50)(36 49)(37 48)(38 47)(39 46)(40 45)(61 158)(62 157)(63 156)(64 155)(65 154)(66 153)(67 152)(68 151)(69 150)(70 149)(71 148)(72 147)(73 146)(74 145)(75 144)(76 143)(77 142)(78 141)(79 160)(80 159)(101 235)(102 234)(103 233)(104 232)(105 231)(106 230)(107 229)(108 228)(109 227)(110 226)(111 225)(112 224)(113 223)(114 222)(115 221)(116 240)(117 239)(118 238)(119 237)(120 236)(121 187)(122 186)(123 185)(124 184)(125 183)(126 182)(127 181)(128 200)(129 199)(130 198)(131 197)(132 196)(133 195)(134 194)(135 193)(136 192)(137 191)(138 190)(139 189)(140 188)(161 210)(162 209)(163 208)(164 207)(165 206)(166 205)(167 204)(168 203)(169 202)(170 201)(171 220)(172 219)(173 218)(174 217)(175 216)(176 215)(177 214)(178 213)(179 212)(180 211)
G:=sub<Sym(240)| (1,38,65)(2,39,66)(3,40,67)(4,21,68)(5,22,69)(6,23,70)(7,24,71)(8,25,72)(9,26,73)(10,27,74)(11,28,75)(12,29,76)(13,30,77)(14,31,78)(15,32,79)(16,33,80)(17,34,61)(18,35,62)(19,36,63)(20,37,64)(41,148,98)(42,149,99)(43,150,100)(44,151,81)(45,152,82)(46,153,83)(47,154,84)(48,155,85)(49,156,86)(50,157,87)(51,158,88)(52,159,89)(53,160,90)(54,141,91)(55,142,92)(56,143,93)(57,144,94)(58,145,95)(59,146,96)(60,147,97)(101,199,211)(102,200,212)(103,181,213)(104,182,214)(105,183,215)(106,184,216)(107,185,217)(108,186,218)(109,187,219)(110,188,220)(111,189,201)(112,190,202)(113,191,203)(114,192,204)(115,193,205)(116,194,206)(117,195,207)(118,196,208)(119,197,209)(120,198,210)(121,172,227)(122,173,228)(123,174,229)(124,175,230)(125,176,231)(126,177,232)(127,178,233)(128,179,234)(129,180,235)(130,161,236)(131,162,237)(132,163,238)(133,164,239)(134,165,240)(135,166,221)(136,167,222)(137,168,223)(138,169,224)(139,170,225)(140,171,226), (1,115,227,90)(2,116,228,91)(3,117,229,92)(4,118,230,93)(5,119,231,94)(6,120,232,95)(7,101,233,96)(8,102,234,97)(9,103,235,98)(10,104,236,99)(11,105,237,100)(12,106,238,81)(13,107,239,82)(14,108,240,83)(15,109,221,84)(16,110,222,85)(17,111,223,86)(18,112,224,87)(19,113,225,88)(20,114,226,89)(21,196,124,56)(22,197,125,57)(23,198,126,58)(24,199,127,59)(25,200,128,60)(26,181,129,41)(27,182,130,42)(28,183,131,43)(29,184,132,44)(30,185,133,45)(31,186,134,46)(32,187,135,47)(33,188,136,48)(34,189,137,49)(35,190,138,50)(36,191,139,51)(37,192,140,52)(38,193,121,53)(39,194,122,54)(40,195,123,55)(61,201,168,156)(62,202,169,157)(63,203,170,158)(64,204,171,159)(65,205,172,160)(66,206,173,141)(67,207,174,142)(68,208,175,143)(69,209,176,144)(70,210,177,145)(71,211,178,146)(72,212,179,147)(73,213,180,148)(74,214,161,149)(75,215,162,150)(76,216,163,151)(77,217,164,152)(78,218,165,153)(79,219,166,154)(80,220,167,155), (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), (1,84)(2,83)(3,82)(4,81)(5,100)(6,99)(7,98)(8,97)(9,96)(10,95)(11,94)(12,93)(13,92)(14,91)(15,90)(16,89)(17,88)(18,87)(19,86)(20,85)(21,44)(22,43)(23,42)(24,41)(25,60)(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(61,158)(62,157)(63,156)(64,155)(65,154)(66,153)(67,152)(68,151)(69,150)(70,149)(71,148)(72,147)(73,146)(74,145)(75,144)(76,143)(77,142)(78,141)(79,160)(80,159)(101,235)(102,234)(103,233)(104,232)(105,231)(106,230)(107,229)(108,228)(109,227)(110,226)(111,225)(112,224)(113,223)(114,222)(115,221)(116,240)(117,239)(118,238)(119,237)(120,236)(121,187)(122,186)(123,185)(124,184)(125,183)(126,182)(127,181)(128,200)(129,199)(130,198)(131,197)(132,196)(133,195)(134,194)(135,193)(136,192)(137,191)(138,190)(139,189)(140,188)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203)(169,202)(170,201)(171,220)(172,219)(173,218)(174,217)(175,216)(176,215)(177,214)(178,213)(179,212)(180,211)>;
G:=Group( (1,38,65)(2,39,66)(3,40,67)(4,21,68)(5,22,69)(6,23,70)(7,24,71)(8,25,72)(9,26,73)(10,27,74)(11,28,75)(12,29,76)(13,30,77)(14,31,78)(15,32,79)(16,33,80)(17,34,61)(18,35,62)(19,36,63)(20,37,64)(41,148,98)(42,149,99)(43,150,100)(44,151,81)(45,152,82)(46,153,83)(47,154,84)(48,155,85)(49,156,86)(50,157,87)(51,158,88)(52,159,89)(53,160,90)(54,141,91)(55,142,92)(56,143,93)(57,144,94)(58,145,95)(59,146,96)(60,147,97)(101,199,211)(102,200,212)(103,181,213)(104,182,214)(105,183,215)(106,184,216)(107,185,217)(108,186,218)(109,187,219)(110,188,220)(111,189,201)(112,190,202)(113,191,203)(114,192,204)(115,193,205)(116,194,206)(117,195,207)(118,196,208)(119,197,209)(120,198,210)(121,172,227)(122,173,228)(123,174,229)(124,175,230)(125,176,231)(126,177,232)(127,178,233)(128,179,234)(129,180,235)(130,161,236)(131,162,237)(132,163,238)(133,164,239)(134,165,240)(135,166,221)(136,167,222)(137,168,223)(138,169,224)(139,170,225)(140,171,226), (1,115,227,90)(2,116,228,91)(3,117,229,92)(4,118,230,93)(5,119,231,94)(6,120,232,95)(7,101,233,96)(8,102,234,97)(9,103,235,98)(10,104,236,99)(11,105,237,100)(12,106,238,81)(13,107,239,82)(14,108,240,83)(15,109,221,84)(16,110,222,85)(17,111,223,86)(18,112,224,87)(19,113,225,88)(20,114,226,89)(21,196,124,56)(22,197,125,57)(23,198,126,58)(24,199,127,59)(25,200,128,60)(26,181,129,41)(27,182,130,42)(28,183,131,43)(29,184,132,44)(30,185,133,45)(31,186,134,46)(32,187,135,47)(33,188,136,48)(34,189,137,49)(35,190,138,50)(36,191,139,51)(37,192,140,52)(38,193,121,53)(39,194,122,54)(40,195,123,55)(61,201,168,156)(62,202,169,157)(63,203,170,158)(64,204,171,159)(65,205,172,160)(66,206,173,141)(67,207,174,142)(68,208,175,143)(69,209,176,144)(70,210,177,145)(71,211,178,146)(72,212,179,147)(73,213,180,148)(74,214,161,149)(75,215,162,150)(76,216,163,151)(77,217,164,152)(78,218,165,153)(79,219,166,154)(80,220,167,155), (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), (1,84)(2,83)(3,82)(4,81)(5,100)(6,99)(7,98)(8,97)(9,96)(10,95)(11,94)(12,93)(13,92)(14,91)(15,90)(16,89)(17,88)(18,87)(19,86)(20,85)(21,44)(22,43)(23,42)(24,41)(25,60)(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(61,158)(62,157)(63,156)(64,155)(65,154)(66,153)(67,152)(68,151)(69,150)(70,149)(71,148)(72,147)(73,146)(74,145)(75,144)(76,143)(77,142)(78,141)(79,160)(80,159)(101,235)(102,234)(103,233)(104,232)(105,231)(106,230)(107,229)(108,228)(109,227)(110,226)(111,225)(112,224)(113,223)(114,222)(115,221)(116,240)(117,239)(118,238)(119,237)(120,236)(121,187)(122,186)(123,185)(124,184)(125,183)(126,182)(127,181)(128,200)(129,199)(130,198)(131,197)(132,196)(133,195)(134,194)(135,193)(136,192)(137,191)(138,190)(139,189)(140,188)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203)(169,202)(170,201)(171,220)(172,219)(173,218)(174,217)(175,216)(176,215)(177,214)(178,213)(179,212)(180,211) );
G=PermutationGroup([[(1,38,65),(2,39,66),(3,40,67),(4,21,68),(5,22,69),(6,23,70),(7,24,71),(8,25,72),(9,26,73),(10,27,74),(11,28,75),(12,29,76),(13,30,77),(14,31,78),(15,32,79),(16,33,80),(17,34,61),(18,35,62),(19,36,63),(20,37,64),(41,148,98),(42,149,99),(43,150,100),(44,151,81),(45,152,82),(46,153,83),(47,154,84),(48,155,85),(49,156,86),(50,157,87),(51,158,88),(52,159,89),(53,160,90),(54,141,91),(55,142,92),(56,143,93),(57,144,94),(58,145,95),(59,146,96),(60,147,97),(101,199,211),(102,200,212),(103,181,213),(104,182,214),(105,183,215),(106,184,216),(107,185,217),(108,186,218),(109,187,219),(110,188,220),(111,189,201),(112,190,202),(113,191,203),(114,192,204),(115,193,205),(116,194,206),(117,195,207),(118,196,208),(119,197,209),(120,198,210),(121,172,227),(122,173,228),(123,174,229),(124,175,230),(125,176,231),(126,177,232),(127,178,233),(128,179,234),(129,180,235),(130,161,236),(131,162,237),(132,163,238),(133,164,239),(134,165,240),(135,166,221),(136,167,222),(137,168,223),(138,169,224),(139,170,225),(140,171,226)], [(1,115,227,90),(2,116,228,91),(3,117,229,92),(4,118,230,93),(5,119,231,94),(6,120,232,95),(7,101,233,96),(8,102,234,97),(9,103,235,98),(10,104,236,99),(11,105,237,100),(12,106,238,81),(13,107,239,82),(14,108,240,83),(15,109,221,84),(16,110,222,85),(17,111,223,86),(18,112,224,87),(19,113,225,88),(20,114,226,89),(21,196,124,56),(22,197,125,57),(23,198,126,58),(24,199,127,59),(25,200,128,60),(26,181,129,41),(27,182,130,42),(28,183,131,43),(29,184,132,44),(30,185,133,45),(31,186,134,46),(32,187,135,47),(33,188,136,48),(34,189,137,49),(35,190,138,50),(36,191,139,51),(37,192,140,52),(38,193,121,53),(39,194,122,54),(40,195,123,55),(61,201,168,156),(62,202,169,157),(63,203,170,158),(64,204,171,159),(65,205,172,160),(66,206,173,141),(67,207,174,142),(68,208,175,143),(69,209,176,144),(70,210,177,145),(71,211,178,146),(72,212,179,147),(73,213,180,148),(74,214,161,149),(75,215,162,150),(76,216,163,151),(77,217,164,152),(78,218,165,153),(79,219,166,154),(80,220,167,155)], [(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)], [(1,84),(2,83),(3,82),(4,81),(5,100),(6,99),(7,98),(8,97),(9,96),(10,95),(11,94),(12,93),(13,92),(14,91),(15,90),(16,89),(17,88),(18,87),(19,86),(20,85),(21,44),(22,43),(23,42),(24,41),(25,60),(26,59),(27,58),(28,57),(29,56),(30,55),(31,54),(32,53),(33,52),(34,51),(35,50),(36,49),(37,48),(38,47),(39,46),(40,45),(61,158),(62,157),(63,156),(64,155),(65,154),(66,153),(67,152),(68,151),(69,150),(70,149),(71,148),(72,147),(73,146),(74,145),(75,144),(76,143),(77,142),(78,141),(79,160),(80,159),(101,235),(102,234),(103,233),(104,232),(105,231),(106,230),(107,229),(108,228),(109,227),(110,226),(111,225),(112,224),(113,223),(114,222),(115,221),(116,240),(117,239),(118,238),(119,237),(120,236),(121,187),(122,186),(123,185),(124,184),(125,183),(126,182),(127,181),(128,200),(129,199),(130,198),(131,197),(132,196),(133,195),(134,194),(135,193),(136,192),(137,191),(138,190),(139,189),(140,188),(161,210),(162,209),(163,208),(164,207),(165,206),(166,205),(167,204),(168,203),(169,202),(170,201),(171,220),(172,219),(173,218),(174,217),(175,216),(176,215),(177,214),(178,213),(179,212),(180,211)]])
138 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 4A | ··· | 4F | 5A | 5B | 6A | ··· | 6F | 6G | ··· | 6N | 10A | ··· | 10F | 12A | ··· | 12L | 15A | 15B | 15C | 15D | 20A | ··· | 20X | 30A | ··· | 30L | 60A | ··· | 60AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | ··· | 4 | 5 | 5 | 6 | ··· | 6 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 20 | 20 | 20 | 20 | 1 | 1 | 2 | ··· | 2 | 2 | 2 | 1 | ··· | 1 | 20 | ··· | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
138 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | |||||||
| image | C1 | C2 | C2 | C3 | C6 | C6 | D4 | D5 | D10 | C3×D4 | C3×D5 | D20 | C6×D5 | C3×D20 |
| kernel | C3×C20⋊4D4 | C4×C60 | C6×D20 | C20⋊4D4 | C4×C20 | C2×D20 | C60 | C4×C12 | C2×C12 | C20 | C42 | C12 | C2×C4 | C4 |
| # reps | 1 | 1 | 6 | 2 | 2 | 12 | 6 | 2 | 6 | 12 | 4 | 24 | 12 | 48 |
Matrix representation of C3×C20⋊4D4 ►in GL4(𝔽61) generated by
| 13 | 0 | 0 | 0 |
| 0 | 13 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 36 | 4 |
| 0 | 0 | 57 | 25 |
| 6 | 5 | 0 | 0 |
| 17 | 55 | 0 | 0 |
| 0 | 0 | 34 | 36 |
| 0 | 0 | 25 | 57 |
| 60 | 0 | 0 | 0 |
| 39 | 1 | 0 | 0 |
| 0 | 0 | 34 | 36 |
| 0 | 0 | 34 | 27 |
G:=sub<GL(4,GF(61))| [13,0,0,0,0,13,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,36,57,0,0,4,25],[6,17,0,0,5,55,0,0,0,0,34,25,0,0,36,57],[60,39,0,0,0,1,0,0,0,0,34,34,0,0,36,27] >;
C3×C20⋊4D4 in GAP, Magma, Sage, TeX
C_3\times C_{20}\rtimes_4D_4 % in TeX
G:=Group("C3xC20:4D4"); // GroupNames label
G:=SmallGroup(480,667);
// by ID
G=gap.SmallGroup(480,667);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-2,-2,-5,701,344,590,142,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^4=c^20=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