direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C20⋊7D4, C60⋊31D4, C20⋊7(C3×D4), (C2×C6)⋊4D20, (C2×D20)⋊6C6, (C2×C30)⋊25D4, C4⋊Dic5⋊9C6, (C6×D20)⋊22C2, C10.47(C6×D4), C6.88(C2×D20), C2.17(C6×D20), C22⋊2(C3×D20), D10⋊C4⋊3C6, C15⋊32(C4⋊D4), C12⋊15(C5⋊D4), (C22×C20)⋊10C6, (C22×C60)⋊15C2, C30.401(C2×D4), (C22×C12)⋊11D5, C23.29(C6×D5), (C2×C12).436D10, C6.126(C4○D20), C30.196(C4○D4), (C2×C60).514C22, (C2×C30).365C23, (C22×C6).109D10, (C22×C30).161C22, (C6×Dic5).163C22, C5⋊3(C3×C4⋊D4), C4⋊3(C3×C5⋊D4), (C2×C10)⋊8(C3×D4), (C2×C5⋊D4)⋊3C6, C2.7(C6×C5⋊D4), (C6×C5⋊D4)⋊18C2, (C2×C4).86(C6×D5), (C22×C4)⋊6(C3×D5), C22.56(D5×C2×C6), (C2×C20).97(C2×C6), (C3×C4⋊Dic5)⋊27C2, C10.17(C3×C4○D4), C2.19(C3×C4○D20), C6.128(C2×C5⋊D4), (C3×D10⋊C4)⋊3C2, (D5×C2×C6).82C22, (C2×C10).48(C22×C6), (C22×C10).48(C2×C6), (C2×Dic5).15(C2×C6), (C22×D5).12(C2×C6), (C2×C6).361(C22×D5), SmallGroup(480,723)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C20⋊7D4
G = < a,b,c,d | a3=b20=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Subgroups: 672 in 188 conjugacy classes, 74 normal (42 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C22, C5, C6, C6, C2×C4, C2×C4, D4, C23, C23, D5, C10, C10, C12, C12, C2×C6, C2×C6, C2×C6, C15, C22⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, C20, C20, D10, C2×C10, C2×C10, C2×C10, C2×C12, C2×C12, C3×D4, C22×C6, C22×C6, C3×D5, C30, C30, C4⋊D4, D20, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×C10, C3×C22⋊C4, C3×C4⋊C4, C22×C12, C6×D4, C3×Dic5, C60, C60, C6×D5, C2×C30, C2×C30, C2×C30, C4⋊Dic5, D10⋊C4, C2×D20, C2×C5⋊D4, C22×C20, C3×C4⋊D4, C3×D20, C6×Dic5, C3×C5⋊D4, C2×C60, C2×C60, D5×C2×C6, C22×C30, C20⋊7D4, C3×C4⋊Dic5, C3×D10⋊C4, C6×D20, C6×C5⋊D4, C22×C60, C3×C20⋊7D4
Quotients: C1, C2, C3, C22, C6, D4, C23, D5, C2×C6, C2×D4, C4○D4, D10, C3×D4, C22×C6, C3×D5, C4⋊D4, D20, C5⋊D4, C22×D5, C6×D4, C3×C4○D4, C6×D5, C2×D20, C4○D20, C2×C5⋊D4, C3×C4⋊D4, C3×D20, C3×C5⋊D4, D5×C2×C6, C20⋊7D4, C6×D20, C3×C4○D20, C6×C5⋊D4, C3×C20⋊7D4
►On 240 points
Generators in S240
(1 177 152)(2 178 153)(3 179 154)(4 180 155)(5 161 156)(6 162 157)(7 163 158)(8 164 159)(9 165 160)(10 166 141)(11 167 142)(12 168 143)(13 169 144)(14 170 145)(15 171 146)(16 172 147)(17 173 148)(18 174 149)(19 175 150)(20 176 151)(21 47 182)(22 48 183)(23 49 184)(24 50 185)(25 51 186)(26 52 187)(27 53 188)(28 54 189)(29 55 190)(30 56 191)(31 57 192)(32 58 193)(33 59 194)(34 60 195)(35 41 196)(36 42 197)(37 43 198)(38 44 199)(39 45 200)(40 46 181)(61 205 131)(62 206 132)(63 207 133)(64 208 134)(65 209 135)(66 210 136)(67 211 137)(68 212 138)(69 213 139)(70 214 140)(71 215 121)(72 216 122)(73 217 123)(74 218 124)(75 219 125)(76 220 126)(77 201 127)(78 202 128)(79 203 129)(80 204 130)(81 104 234)(82 105 235)(83 106 236)(84 107 237)(85 108 238)(86 109 239)(87 110 240)(88 111 221)(89 112 222)(90 113 223)(91 114 224)(92 115 225)(93 116 226)(94 117 227)(95 118 228)(96 119 229)(97 120 230)(98 101 231)(99 102 232)(100 103 233)
(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 58 83 76)(2 57 84 75)(3 56 85 74)(4 55 86 73)(5 54 87 72)(6 53 88 71)(7 52 89 70)(8 51 90 69)(9 50 91 68)(10 49 92 67)(11 48 93 66)(12 47 94 65)(13 46 95 64)(14 45 96 63)(15 44 97 62)(16 43 98 61)(17 42 99 80)(18 41 100 79)(19 60 81 78)(20 59 82 77)(21 227 135 143)(22 226 136 142)(23 225 137 141)(24 224 138 160)(25 223 139 159)(26 222 140 158)(27 221 121 157)(28 240 122 156)(29 239 123 155)(30 238 124 154)(31 237 125 153)(32 236 126 152)(33 235 127 151)(34 234 128 150)(35 233 129 149)(36 232 130 148)(37 231 131 147)(38 230 132 146)(39 229 133 145)(40 228 134 144)(101 205 172 198)(102 204 173 197)(103 203 174 196)(104 202 175 195)(105 201 176 194)(106 220 177 193)(107 219 178 192)(108 218 179 191)(109 217 180 190)(110 216 161 189)(111 215 162 188)(112 214 163 187)(113 213 164 186)(114 212 165 185)(115 211 166 184)(116 210 167 183)(117 209 168 182)(118 208 169 181)(119 207 170 200)(120 206 171 199)
(1 76)(2 75)(3 74)(4 73)(5 72)(6 71)(7 70)(8 69)(9 68)(10 67)(11 66)(12 65)(13 64)(14 63)(15 62)(16 61)(17 80)(18 79)(19 78)(20 77)(21 227)(22 226)(23 225)(24 224)(25 223)(26 222)(27 221)(28 240)(29 239)(30 238)(31 237)(32 236)(33 235)(34 234)(35 233)(36 232)(37 231)(38 230)(39 229)(40 228)(41 100)(42 99)(43 98)(44 97)(45 96)(46 95)(47 94)(48 93)(49 92)(50 91)(51 90)(52 89)(53 88)(54 87)(55 86)(56 85)(57 84)(58 83)(59 82)(60 81)(101 198)(102 197)(103 196)(104 195)(105 194)(106 193)(107 192)(108 191)(109 190)(110 189)(111 188)(112 187)(113 186)(114 185)(115 184)(116 183)(117 182)(118 181)(119 200)(120 199)(121 157)(122 156)(123 155)(124 154)(125 153)(126 152)(127 151)(128 150)(129 149)(130 148)(131 147)(132 146)(133 145)(134 144)(135 143)(136 142)(137 141)(138 160)(139 159)(140 158)(161 216)(162 215)(163 214)(164 213)(165 212)(166 211)(167 210)(168 209)(169 208)(170 207)(171 206)(172 205)(173 204)(174 203)(175 202)(176 201)(177 220)(178 219)(179 218)(180 217)
G:=sub<Sym(240)| (1,177,152)(2,178,153)(3,179,154)(4,180,155)(5,161,156)(6,162,157)(7,163,158)(8,164,159)(9,165,160)(10,166,141)(11,167,142)(12,168,143)(13,169,144)(14,170,145)(15,171,146)(16,172,147)(17,173,148)(18,174,149)(19,175,150)(20,176,151)(21,47,182)(22,48,183)(23,49,184)(24,50,185)(25,51,186)(26,52,187)(27,53,188)(28,54,189)(29,55,190)(30,56,191)(31,57,192)(32,58,193)(33,59,194)(34,60,195)(35,41,196)(36,42,197)(37,43,198)(38,44,199)(39,45,200)(40,46,181)(61,205,131)(62,206,132)(63,207,133)(64,208,134)(65,209,135)(66,210,136)(67,211,137)(68,212,138)(69,213,139)(70,214,140)(71,215,121)(72,216,122)(73,217,123)(74,218,124)(75,219,125)(76,220,126)(77,201,127)(78,202,128)(79,203,129)(80,204,130)(81,104,234)(82,105,235)(83,106,236)(84,107,237)(85,108,238)(86,109,239)(87,110,240)(88,111,221)(89,112,222)(90,113,223)(91,114,224)(92,115,225)(93,116,226)(94,117,227)(95,118,228)(96,119,229)(97,120,230)(98,101,231)(99,102,232)(100,103,233), (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), (1,58,83,76)(2,57,84,75)(3,56,85,74)(4,55,86,73)(5,54,87,72)(6,53,88,71)(7,52,89,70)(8,51,90,69)(9,50,91,68)(10,49,92,67)(11,48,93,66)(12,47,94,65)(13,46,95,64)(14,45,96,63)(15,44,97,62)(16,43,98,61)(17,42,99,80)(18,41,100,79)(19,60,81,78)(20,59,82,77)(21,227,135,143)(22,226,136,142)(23,225,137,141)(24,224,138,160)(25,223,139,159)(26,222,140,158)(27,221,121,157)(28,240,122,156)(29,239,123,155)(30,238,124,154)(31,237,125,153)(32,236,126,152)(33,235,127,151)(34,234,128,150)(35,233,129,149)(36,232,130,148)(37,231,131,147)(38,230,132,146)(39,229,133,145)(40,228,134,144)(101,205,172,198)(102,204,173,197)(103,203,174,196)(104,202,175,195)(105,201,176,194)(106,220,177,193)(107,219,178,192)(108,218,179,191)(109,217,180,190)(110,216,161,189)(111,215,162,188)(112,214,163,187)(113,213,164,186)(114,212,165,185)(115,211,166,184)(116,210,167,183)(117,209,168,182)(118,208,169,181)(119,207,170,200)(120,206,171,199), (1,76)(2,75)(3,74)(4,73)(5,72)(6,71)(7,70)(8,69)(9,68)(10,67)(11,66)(12,65)(13,64)(14,63)(15,62)(16,61)(17,80)(18,79)(19,78)(20,77)(21,227)(22,226)(23,225)(24,224)(25,223)(26,222)(27,221)(28,240)(29,239)(30,238)(31,237)(32,236)(33,235)(34,234)(35,233)(36,232)(37,231)(38,230)(39,229)(40,228)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(101,198)(102,197)(103,196)(104,195)(105,194)(106,193)(107,192)(108,191)(109,190)(110,189)(111,188)(112,187)(113,186)(114,185)(115,184)(116,183)(117,182)(118,181)(119,200)(120,199)(121,157)(122,156)(123,155)(124,154)(125,153)(126,152)(127,151)(128,150)(129,149)(130,148)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,160)(139,159)(140,158)(161,216)(162,215)(163,214)(164,213)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,206)(172,205)(173,204)(174,203)(175,202)(176,201)(177,220)(178,219)(179,218)(180,217)>;
G:=Group( (1,177,152)(2,178,153)(3,179,154)(4,180,155)(5,161,156)(6,162,157)(7,163,158)(8,164,159)(9,165,160)(10,166,141)(11,167,142)(12,168,143)(13,169,144)(14,170,145)(15,171,146)(16,172,147)(17,173,148)(18,174,149)(19,175,150)(20,176,151)(21,47,182)(22,48,183)(23,49,184)(24,50,185)(25,51,186)(26,52,187)(27,53,188)(28,54,189)(29,55,190)(30,56,191)(31,57,192)(32,58,193)(33,59,194)(34,60,195)(35,41,196)(36,42,197)(37,43,198)(38,44,199)(39,45,200)(40,46,181)(61,205,131)(62,206,132)(63,207,133)(64,208,134)(65,209,135)(66,210,136)(67,211,137)(68,212,138)(69,213,139)(70,214,140)(71,215,121)(72,216,122)(73,217,123)(74,218,124)(75,219,125)(76,220,126)(77,201,127)(78,202,128)(79,203,129)(80,204,130)(81,104,234)(82,105,235)(83,106,236)(84,107,237)(85,108,238)(86,109,239)(87,110,240)(88,111,221)(89,112,222)(90,113,223)(91,114,224)(92,115,225)(93,116,226)(94,117,227)(95,118,228)(96,119,229)(97,120,230)(98,101,231)(99,102,232)(100,103,233), (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), (1,58,83,76)(2,57,84,75)(3,56,85,74)(4,55,86,73)(5,54,87,72)(6,53,88,71)(7,52,89,70)(8,51,90,69)(9,50,91,68)(10,49,92,67)(11,48,93,66)(12,47,94,65)(13,46,95,64)(14,45,96,63)(15,44,97,62)(16,43,98,61)(17,42,99,80)(18,41,100,79)(19,60,81,78)(20,59,82,77)(21,227,135,143)(22,226,136,142)(23,225,137,141)(24,224,138,160)(25,223,139,159)(26,222,140,158)(27,221,121,157)(28,240,122,156)(29,239,123,155)(30,238,124,154)(31,237,125,153)(32,236,126,152)(33,235,127,151)(34,234,128,150)(35,233,129,149)(36,232,130,148)(37,231,131,147)(38,230,132,146)(39,229,133,145)(40,228,134,144)(101,205,172,198)(102,204,173,197)(103,203,174,196)(104,202,175,195)(105,201,176,194)(106,220,177,193)(107,219,178,192)(108,218,179,191)(109,217,180,190)(110,216,161,189)(111,215,162,188)(112,214,163,187)(113,213,164,186)(114,212,165,185)(115,211,166,184)(116,210,167,183)(117,209,168,182)(118,208,169,181)(119,207,170,200)(120,206,171,199), (1,76)(2,75)(3,74)(4,73)(5,72)(6,71)(7,70)(8,69)(9,68)(10,67)(11,66)(12,65)(13,64)(14,63)(15,62)(16,61)(17,80)(18,79)(19,78)(20,77)(21,227)(22,226)(23,225)(24,224)(25,223)(26,222)(27,221)(28,240)(29,239)(30,238)(31,237)(32,236)(33,235)(34,234)(35,233)(36,232)(37,231)(38,230)(39,229)(40,228)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(101,198)(102,197)(103,196)(104,195)(105,194)(106,193)(107,192)(108,191)(109,190)(110,189)(111,188)(112,187)(113,186)(114,185)(115,184)(116,183)(117,182)(118,181)(119,200)(120,199)(121,157)(122,156)(123,155)(124,154)(125,153)(126,152)(127,151)(128,150)(129,149)(130,148)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,160)(139,159)(140,158)(161,216)(162,215)(163,214)(164,213)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,206)(172,205)(173,204)(174,203)(175,202)(176,201)(177,220)(178,219)(179,218)(180,217) );
G=PermutationGroup([[(1,177,152),(2,178,153),(3,179,154),(4,180,155),(5,161,156),(6,162,157),(7,163,158),(8,164,159),(9,165,160),(10,166,141),(11,167,142),(12,168,143),(13,169,144),(14,170,145),(15,171,146),(16,172,147),(17,173,148),(18,174,149),(19,175,150),(20,176,151),(21,47,182),(22,48,183),(23,49,184),(24,50,185),(25,51,186),(26,52,187),(27,53,188),(28,54,189),(29,55,190),(30,56,191),(31,57,192),(32,58,193),(33,59,194),(34,60,195),(35,41,196),(36,42,197),(37,43,198),(38,44,199),(39,45,200),(40,46,181),(61,205,131),(62,206,132),(63,207,133),(64,208,134),(65,209,135),(66,210,136),(67,211,137),(68,212,138),(69,213,139),(70,214,140),(71,215,121),(72,216,122),(73,217,123),(74,218,124),(75,219,125),(76,220,126),(77,201,127),(78,202,128),(79,203,129),(80,204,130),(81,104,234),(82,105,235),(83,106,236),(84,107,237),(85,108,238),(86,109,239),(87,110,240),(88,111,221),(89,112,222),(90,113,223),(91,114,224),(92,115,225),(93,116,226),(94,117,227),(95,118,228),(96,119,229),(97,120,230),(98,101,231),(99,102,232),(100,103,233)], [(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)], [(1,58,83,76),(2,57,84,75),(3,56,85,74),(4,55,86,73),(5,54,87,72),(6,53,88,71),(7,52,89,70),(8,51,90,69),(9,50,91,68),(10,49,92,67),(11,48,93,66),(12,47,94,65),(13,46,95,64),(14,45,96,63),(15,44,97,62),(16,43,98,61),(17,42,99,80),(18,41,100,79),(19,60,81,78),(20,59,82,77),(21,227,135,143),(22,226,136,142),(23,225,137,141),(24,224,138,160),(25,223,139,159),(26,222,140,158),(27,221,121,157),(28,240,122,156),(29,239,123,155),(30,238,124,154),(31,237,125,153),(32,236,126,152),(33,235,127,151),(34,234,128,150),(35,233,129,149),(36,232,130,148),(37,231,131,147),(38,230,132,146),(39,229,133,145),(40,228,134,144),(101,205,172,198),(102,204,173,197),(103,203,174,196),(104,202,175,195),(105,201,176,194),(106,220,177,193),(107,219,178,192),(108,218,179,191),(109,217,180,190),(110,216,161,189),(111,215,162,188),(112,214,163,187),(113,213,164,186),(114,212,165,185),(115,211,166,184),(116,210,167,183),(117,209,168,182),(118,208,169,181),(119,207,170,200),(120,206,171,199)], [(1,76),(2,75),(3,74),(4,73),(5,72),(6,71),(7,70),(8,69),(9,68),(10,67),(11,66),(12,65),(13,64),(14,63),(15,62),(16,61),(17,80),(18,79),(19,78),(20,77),(21,227),(22,226),(23,225),(24,224),(25,223),(26,222),(27,221),(28,240),(29,239),(30,238),(31,237),(32,236),(33,235),(34,234),(35,233),(36,232),(37,231),(38,230),(39,229),(40,228),(41,100),(42,99),(43,98),(44,97),(45,96),(46,95),(47,94),(48,93),(49,92),(50,91),(51,90),(52,89),(53,88),(54,87),(55,86),(56,85),(57,84),(58,83),(59,82),(60,81),(101,198),(102,197),(103,196),(104,195),(105,194),(106,193),(107,192),(108,191),(109,190),(110,189),(111,188),(112,187),(113,186),(114,185),(115,184),(116,183),(117,182),(118,181),(119,200),(120,199),(121,157),(122,156),(123,155),(124,154),(125,153),(126,152),(127,151),(128,150),(129,149),(130,148),(131,147),(132,146),(133,145),(134,144),(135,143),(136,142),(137,141),(138,160),(139,159),(140,158),(161,216),(162,215),(163,214),(164,213),(165,212),(166,211),(167,210),(168,209),(169,208),(170,207),(171,206),(172,205),(173,204),(174,203),(175,202),(176,201),(177,220),(178,219),(179,218),(180,217)]])
138 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 6A | ··· | 6F | 6G | 6H | 6I | 6J | 6K | 6L | 6M | 6N | 10A | ··· | 10N | 12A | ··· | 12H | 12I | 12J | 12K | 12L | 15A | 15B | 15C | 15D | 20A | ··· | 20P | 30A | ··· | 30AB | 60A | ··· | 60AF |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 20 | 20 | 1 | 1 | 2 | 2 | 2 | 2 | 20 | 20 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | ··· | 2 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
138 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||||||||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | C6 | C6 | D4 | D4 | D5 | C4○D4 | D10 | D10 | C3×D4 | C3×D4 | C3×D5 | C5⋊D4 | D20 | C3×C4○D4 | C6×D5 | C6×D5 | C4○D20 | C3×C5⋊D4 | C3×D20 | C3×C4○D20 |
| kernel | C3×C20⋊7D4 | C3×C4⋊Dic5 | C3×D10⋊C4 | C6×D20 | C6×C5⋊D4 | C22×C60 | C20⋊7D4 | C4⋊Dic5 | D10⋊C4 | C2×D20 | C2×C5⋊D4 | C22×C20 | C60 | C2×C30 | C22×C12 | C30 | C2×C12 | C22×C6 | C20 | C2×C10 | C22×C4 | C12 | C2×C6 | C10 | C2×C4 | C23 | C6 | C4 | C22 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 2 | 2 | 4 | 2 | 4 | 2 | 2 | 2 | 2 | 2 | 4 | 2 | 4 | 4 | 4 | 8 | 8 | 4 | 8 | 4 | 8 | 16 | 16 | 16 |
Matrix representation of C3×C20⋊7D4 ►in GL4(𝔽61) generated by
| 13 | 0 | 0 | 0 |
| 0 | 13 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 23 | 0 | 0 | 0 |
| 0 | 8 | 0 | 0 |
| 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 34 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 60 | 0 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
G:=sub<GL(4,GF(61))| [13,0,0,0,0,13,0,0,0,0,1,0,0,0,0,1],[23,0,0,0,0,8,0,0,0,0,9,0,0,0,0,34],[0,1,0,0,1,0,0,0,0,0,0,60,0,0,1,0],[0,1,0,0,1,0,0,0,0,0,0,1,0,0,1,0] >;
C3×C20⋊7D4 in GAP, Magma, Sage, TeX
C_3\times C_{20}\rtimes_7D_4 % in TeX
G:=Group("C3xC20:7D4"); // GroupNames label
G:=SmallGroup(480,723);
// by ID
G=gap.SmallGroup(480,723);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-2,-2,-5,701,344,590,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^20=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations