Copied to
clipboard

## G = C2×C20.D6order 480 = 25·3·5

### Direct product of C2 and C20.D6

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — C2×C20.D6
 Chief series C1 — C5 — C15 — C30 — C60 — C3×Dic10 — C20.D6 — C2×C20.D6
 Lower central C15 — C30 — C60 — C2×C20.D6
 Upper central C1 — C22 — C2×C4

Generators and relations for C2×C20.D6
G = < a,b,c,d | a2=b30=1, c4=d2=b15, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b19, dcd-1=c3 >

Subgroups: 572 in 136 conjugacy classes, 52 normal (30 characteristic)
C1, C2, C2 [×2], C2 [×2], C3, C4 [×2], C4 [×2], C22, C22 [×4], C5, S3 [×2], C6, C6 [×2], C8 [×2], C2×C4, C2×C4, D4 [×3], Q8 [×3], C23, C10, C10 [×2], C10 [×2], C12 [×2], C12 [×2], D6 [×4], C2×C6, C15, C2×C8, SD16 [×4], C2×D4, C2×Q8, Dic5 [×2], C20 [×2], C2×C10, C2×C10 [×4], C3⋊C8 [×2], D12 [×2], D12, C2×C12, C2×C12, C3×Q8 [×3], C22×S3, C5×S3 [×2], C30, C30 [×2], C2×SD16, C52C8 [×2], Dic10 [×2], Dic10, C2×Dic5, C2×C20, C5×D4 [×3], C22×C10, C2×C3⋊C8, Q82S3 [×4], C2×D12, C6×Q8, C3×Dic5 [×2], C60 [×2], S3×C10 [×4], C2×C30, C2×C52C8, D4.D5 [×4], C2×Dic10, D4×C10, C2×Q82S3, C153C8 [×2], C3×Dic10 [×2], C3×Dic10, C6×Dic5, C5×D12 [×2], C5×D12, C2×C60, S3×C2×C10, C2×D4.D5, C20.D6 [×4], C2×C153C8, C6×Dic10, C10×D12, C2×C20.D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], SD16 [×2], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C2×SD16, C5⋊D4 [×2], C22×D5, Q82S3 [×2], C2×C3⋊D4, S3×D5, D4.D5 [×2], C2×C5⋊D4, C2×Q82S3, C15⋊D4 [×2], C2×S3×D5, C2×D4.D5, C20.D6 [×2], C2×C15⋊D4, C2×C20.D6

Smallest permutation representation of C2×C20.D6
On 240 points
Generators in S240
(1 61)(2 62)(3 63)(4 64)(5 65)(6 66)(7 67)(8 68)(9 69)(10 70)(11 71)(12 72)(13 73)(14 74)(15 75)(16 76)(17 77)(18 78)(19 79)(20 80)(21 81)(22 82)(23 83)(24 84)(25 85)(26 86)(27 87)(28 88)(29 89)(30 90)(31 101)(32 102)(33 103)(34 104)(35 105)(36 106)(37 107)(38 108)(39 109)(40 110)(41 111)(42 112)(43 113)(44 114)(45 115)(46 116)(47 117)(48 118)(49 119)(50 120)(51 91)(52 92)(53 93)(54 94)(55 95)(56 96)(57 97)(58 98)(59 99)(60 100)(121 204)(122 205)(123 206)(124 207)(125 208)(126 209)(127 210)(128 181)(129 182)(130 183)(131 184)(132 185)(133 186)(134 187)(135 188)(136 189)(137 190)(138 191)(139 192)(140 193)(141 194)(142 195)(143 196)(144 197)(145 198)(146 199)(147 200)(148 201)(149 202)(150 203)(151 234)(152 235)(153 236)(154 237)(155 238)(156 239)(157 240)(158 211)(159 212)(160 213)(161 214)(162 215)(163 216)(164 217)(165 218)(166 219)(167 220)(168 221)(169 222)(170 223)(171 224)(172 225)(173 226)(174 227)(175 228)(176 229)(177 230)(178 231)(179 232)(180 233)
(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)
(1 180 31 149 16 165 46 134)(2 179 32 148 17 164 47 133)(3 178 33 147 18 163 48 132)(4 177 34 146 19 162 49 131)(5 176 35 145 20 161 50 130)(6 175 36 144 21 160 51 129)(7 174 37 143 22 159 52 128)(8 173 38 142 23 158 53 127)(9 172 39 141 24 157 54 126)(10 171 40 140 25 156 55 125)(11 170 41 139 26 155 56 124)(12 169 42 138 27 154 57 123)(13 168 43 137 28 153 58 122)(14 167 44 136 29 152 59 121)(15 166 45 135 30 151 60 150)(61 233 101 202 76 218 116 187)(62 232 102 201 77 217 117 186)(63 231 103 200 78 216 118 185)(64 230 104 199 79 215 119 184)(65 229 105 198 80 214 120 183)(66 228 106 197 81 213 91 182)(67 227 107 196 82 212 92 181)(68 226 108 195 83 211 93 210)(69 225 109 194 84 240 94 209)(70 224 110 193 85 239 95 208)(71 223 111 192 86 238 96 207)(72 222 112 191 87 237 97 206)(73 221 113 190 88 236 98 205)(74 220 114 189 89 235 99 204)(75 219 115 188 90 234 100 203)
(1 202 16 187)(2 191 17 206)(3 210 18 195)(4 199 19 184)(5 188 20 203)(6 207 21 192)(7 196 22 181)(8 185 23 200)(9 204 24 189)(10 193 25 208)(11 182 26 197)(12 201 27 186)(13 190 28 205)(14 209 29 194)(15 198 30 183)(31 233 46 218)(32 222 47 237)(33 211 48 226)(34 230 49 215)(35 219 50 234)(36 238 51 223)(37 227 52 212)(38 216 53 231)(39 235 54 220)(40 224 55 239)(41 213 56 228)(42 232 57 217)(43 221 58 236)(44 240 59 225)(45 229 60 214)(61 149 76 134)(62 138 77 123)(63 127 78 142)(64 146 79 131)(65 135 80 150)(66 124 81 139)(67 143 82 128)(68 132 83 147)(69 121 84 136)(70 140 85 125)(71 129 86 144)(72 148 87 133)(73 137 88 122)(74 126 89 141)(75 145 90 130)(91 170 106 155)(92 159 107 174)(93 178 108 163)(94 167 109 152)(95 156 110 171)(96 175 111 160)(97 164 112 179)(98 153 113 168)(99 172 114 157)(100 161 115 176)(101 180 116 165)(102 169 117 154)(103 158 118 173)(104 177 119 162)(105 166 120 151)

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

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

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

60 conjugacy classes

 class 1 2A 2B 2C 2D 2E 3 4A 4B 4C 4D 5A 5B 6A 6B 6C 8A 8B 8C 8D 10A ··· 10F 10G ··· 10N 12A 12B 12C 12D 12E 12F 15A 15B 20A 20B 20C 20D 30A ··· 30F 60A ··· 60H order 1 2 2 2 2 2 3 4 4 4 4 5 5 6 6 6 8 8 8 8 10 ··· 10 10 ··· 10 12 12 12 12 12 12 15 15 20 20 20 20 30 ··· 30 60 ··· 60 size 1 1 1 1 12 12 2 2 2 20 20 2 2 2 2 2 30 30 30 30 2 ··· 2 12 ··· 12 4 4 20 20 20 20 4 4 4 4 4 4 4 ··· 4 4 ··· 4

60 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 type + + + + + + + + + + + + + + + - - + - image C1 C2 C2 C2 C2 S3 D4 D4 D5 D6 D6 SD16 D10 D10 C3⋊D4 C3⋊D4 C5⋊D4 C5⋊D4 Q8⋊2S3 S3×D5 D4.D5 C15⋊D4 C2×S3×D5 C15⋊D4 C20.D6 kernel C2×C20.D6 C20.D6 C2×C15⋊3C8 C6×Dic10 C10×D12 C2×Dic10 C60 C2×C30 C2×D12 Dic10 C2×C20 C30 D12 C2×C12 C20 C2×C10 C12 C2×C6 C10 C2×C4 C6 C4 C4 C22 C2 # reps 1 4 1 1 1 1 1 1 2 2 1 4 4 2 2 2 4 4 2 2 4 2 2 2 8

Matrix representation of C2×C20.D6 in GL6(𝔽241)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 240 0 0 0 0 0 0 240
,
 87 0 0 0 0 0 191 205 0 0 0 0 0 0 240 0 0 0 0 0 0 240 0 0 0 0 0 0 239 54 0 0 0 0 174 1
,
 119 18 0 0 0 0 204 122 0 0 0 0 0 0 236 13 0 0 0 0 124 208 0 0 0 0 0 0 240 54 0 0 0 0 0 1
,
 119 18 0 0 0 0 97 122 0 0 0 0 0 0 208 36 0 0 0 0 117 33 0 0 0 0 0 0 240 0 0 0 0 0 0 240

G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[87,191,0,0,0,0,0,205,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,239,174,0,0,0,0,54,1],[119,204,0,0,0,0,18,122,0,0,0,0,0,0,236,124,0,0,0,0,13,208,0,0,0,0,0,0,240,0,0,0,0,0,54,1],[119,97,0,0,0,0,18,122,0,0,0,0,0,0,208,117,0,0,0,0,36,33,0,0,0,0,0,0,240,0,0,0,0,0,0,240] >;

C2×C20.D6 in GAP, Magma, Sage, TeX

C_2\times C_{20}.D_6
% in TeX

G:=Group("C2xC20.D6");
// GroupNames label

G:=SmallGroup(480,384);
// by ID

G=gap.SmallGroup(480,384);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,141,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^30=1,c^4=d^2=b^15,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^19,d*c*d^-1=c^3>;
// generators/relations

׿
×
𝔽