Copied to
clipboard

## G = C10×C4.Dic3order 480 = 25·3·5

### Direct product of C10 and C4.Dic3

Series: Derived Chief Lower central Upper central

 Derived series C1 — C6 — C10×C4.Dic3
 Chief series C1 — C3 — C6 — C12 — C60 — C5×C3⋊C8 — C10×C3⋊C8 — C10×C4.Dic3
 Lower central C3 — C6 — C10×C4.Dic3
 Upper central C1 — C2×C20 — C22×C20

Generators and relations for C10×C4.Dic3
G = < a,b,c,d | a10=b4=1, c6=b2, d2=b2c3, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c5 >

Subgroups: 196 in 136 conjugacy classes, 98 normal (38 characteristic)
C1, C2, C2 [×2], C2 [×2], C3, C4 [×2], C4 [×2], C22, C22 [×2], C22 [×2], C5, C6, C6 [×2], C6 [×2], C8 [×4], C2×C4 [×2], C2×C4 [×4], C23, C10, C10 [×2], C10 [×2], C12 [×2], C12 [×2], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C2×C8 [×2], M4(2) [×4], C22×C4, C20 [×2], C20 [×2], C2×C10, C2×C10 [×2], C2×C10 [×2], C3⋊C8 [×4], C2×C12 [×2], C2×C12 [×4], C22×C6, C30, C30 [×2], C30 [×2], C2×M4(2), C40 [×4], C2×C20 [×2], C2×C20 [×4], C22×C10, C2×C3⋊C8 [×2], C4.Dic3 [×4], C22×C12, C60 [×2], C60 [×2], C2×C30, C2×C30 [×2], C2×C30 [×2], C2×C40 [×2], C5×M4(2) [×4], C22×C20, C2×C4.Dic3, C5×C3⋊C8 [×4], C2×C60 [×2], C2×C60 [×4], C22×C30, C10×M4(2), C10×C3⋊C8 [×2], C5×C4.Dic3 [×4], C22×C60, C10×C4.Dic3
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C5, S3, C2×C4 [×6], C23, C10 [×7], Dic3 [×4], D6 [×3], M4(2) [×2], C22×C4, C20 [×4], C2×C10 [×7], C2×Dic3 [×6], C22×S3, C5×S3, C2×M4(2), C2×C20 [×6], C22×C10, C4.Dic3 [×2], C22×Dic3, C5×Dic3 [×4], S3×C10 [×3], C5×M4(2) [×2], C22×C20, C2×C4.Dic3, C10×Dic3 [×6], S3×C2×C10, C10×M4(2), C5×C4.Dic3 [×2], Dic3×C2×C10, C10×C4.Dic3

Smallest permutation representation of C10×C4.Dic3
On 240 points
Generators in S240
(1 91 58 76 46 67 31 109 22 103)(2 92 59 77 47 68 32 110 23 104)(3 93 60 78 48 69 33 111 24 105)(4 94 49 79 37 70 34 112 13 106)(5 95 50 80 38 71 35 113 14 107)(6 96 51 81 39 72 36 114 15 108)(7 85 52 82 40 61 25 115 16 97)(8 86 53 83 41 62 26 116 17 98)(9 87 54 84 42 63 27 117 18 99)(10 88 55 73 43 64 28 118 19 100)(11 89 56 74 44 65 29 119 20 101)(12 90 57 75 45 66 30 120 21 102)(121 214 172 193 164 184 153 231 133 217)(122 215 173 194 165 185 154 232 134 218)(123 216 174 195 166 186 155 233 135 219)(124 205 175 196 167 187 156 234 136 220)(125 206 176 197 168 188 145 235 137 221)(126 207 177 198 157 189 146 236 138 222)(127 208 178 199 158 190 147 237 139 223)(128 209 179 200 159 191 148 238 140 224)(129 210 180 201 160 192 149 239 141 225)(130 211 169 202 161 181 150 240 142 226)(131 212 170 203 162 182 151 229 143 227)(132 213 171 204 163 183 152 230 144 228)
(1 64 7 70)(2 65 8 71)(3 66 9 72)(4 67 10 61)(5 68 11 62)(6 69 12 63)(13 76 19 82)(14 77 20 83)(15 78 21 84)(16 79 22 73)(17 80 23 74)(18 81 24 75)(25 94 31 88)(26 95 32 89)(27 96 33 90)(28 85 34 91)(29 86 35 92)(30 87 36 93)(37 103 43 97)(38 104 44 98)(39 105 45 99)(40 106 46 100)(41 107 47 101)(42 108 48 102)(49 109 55 115)(50 110 56 116)(51 111 57 117)(52 112 58 118)(53 113 59 119)(54 114 60 120)(121 187 127 181)(122 188 128 182)(123 189 129 183)(124 190 130 184)(125 191 131 185)(126 192 132 186)(133 196 139 202)(134 197 140 203)(135 198 141 204)(136 199 142 193)(137 200 143 194)(138 201 144 195)(145 209 151 215)(146 210 152 216)(147 211 153 205)(148 212 154 206)(149 213 155 207)(150 214 156 208)(157 225 163 219)(158 226 164 220)(159 227 165 221)(160 228 166 222)(161 217 167 223)(162 218 168 224)(169 231 175 237)(170 232 176 238)(171 233 177 239)(172 234 178 240)(173 235 179 229)(174 236 180 230)
(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)
(1 123 10 132 7 129 4 126)(2 128 11 125 8 122 5 131)(3 121 12 130 9 127 6 124)(13 138 22 135 19 144 16 141)(14 143 23 140 20 137 17 134)(15 136 24 133 21 142 18 139)(25 149 34 146 31 155 28 152)(26 154 35 151 32 148 29 145)(27 147 36 156 33 153 30 150)(37 157 46 166 43 163 40 160)(38 162 47 159 44 168 41 165)(39 167 48 164 45 161 42 158)(49 177 58 174 55 171 52 180)(50 170 59 179 56 176 53 173)(51 175 60 172 57 169 54 178)(61 192 70 189 67 186 64 183)(62 185 71 182 68 191 65 188)(63 190 72 187 69 184 66 181)(73 204 82 201 79 198 76 195)(74 197 83 194 80 203 77 200)(75 202 84 199 81 196 78 193)(85 210 94 207 91 216 88 213)(86 215 95 212 92 209 89 206)(87 208 96 205 93 214 90 211)(97 225 106 222 103 219 100 228)(98 218 107 227 104 224 101 221)(99 223 108 220 105 217 102 226)(109 233 118 230 115 239 112 236)(110 238 119 235 116 232 113 229)(111 231 120 240 117 237 114 234)

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

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

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

180 conjugacy classes

 class 1 2A 2B 2C 2D 2E 3 4A 4B 4C 4D 4E 4F 5A 5B 5C 5D 6A ··· 6G 8A ··· 8H 10A ··· 10L 10M ··· 10T 12A ··· 12H 15A 15B 15C 15D 20A ··· 20P 20Q ··· 20X 30A ··· 30AB 40A ··· 40AF 60A ··· 60AF order 1 2 2 2 2 2 3 4 4 4 4 4 4 5 5 5 5 6 ··· 6 8 ··· 8 10 ··· 10 10 ··· 10 12 ··· 12 15 15 15 15 20 ··· 20 20 ··· 20 30 ··· 30 40 ··· 40 60 ··· 60 size 1 1 1 1 2 2 2 1 1 1 1 2 2 1 1 1 1 2 ··· 2 6 ··· 6 1 ··· 1 2 ··· 2 2 ··· 2 2 2 2 2 1 ··· 1 2 ··· 2 2 ··· 2 6 ··· 6 2 ··· 2

180 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 type + + + + + - + - image C1 C2 C2 C2 C4 C4 C5 C10 C10 C10 C20 C20 S3 Dic3 D6 Dic3 M4(2) C5×S3 C4.Dic3 C5×Dic3 S3×C10 C5×Dic3 C5×M4(2) C5×C4.Dic3 kernel C10×C4.Dic3 C10×C3⋊C8 C5×C4.Dic3 C22×C60 C2×C60 C22×C30 C2×C4.Dic3 C2×C3⋊C8 C4.Dic3 C22×C12 C2×C12 C22×C6 C22×C20 C2×C20 C2×C20 C22×C10 C30 C22×C4 C10 C2×C4 C2×C4 C23 C6 C2 # reps 1 2 4 1 6 2 4 8 16 4 24 8 1 3 3 1 4 4 8 12 12 4 16 32

Matrix representation of C10×C4.Dic3 in GL4(𝔽241) generated by

 150 0 0 0 0 150 0 0 0 0 87 0 0 0 0 87
,
 64 0 0 0 0 177 0 0 0 0 64 0 0 0 0 177
,
 177 0 0 0 0 177 0 0 0 0 181 0 0 0 0 237
,
 0 1 0 0 177 0 0 0 0 0 0 1 0 0 64 0
G:=sub<GL(4,GF(241))| [150,0,0,0,0,150,0,0,0,0,87,0,0,0,0,87],[64,0,0,0,0,177,0,0,0,0,64,0,0,0,0,177],[177,0,0,0,0,177,0,0,0,0,181,0,0,0,0,237],[0,177,0,0,1,0,0,0,0,0,0,64,0,0,1,0] >;

C10×C4.Dic3 in GAP, Magma, Sage, TeX

C_{10}\times C_4.{\rm Dic}_3
% in TeX

G:=Group("C10xC4.Dic3");
// GroupNames label

G:=SmallGroup(480,800);
// by ID

G=gap.SmallGroup(480,800);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-3,280,1766,102,15686]);
// Polycyclic

G:=Group<a,b,c,d|a^10=b^4=1,c^6=b^2,d^2=b^2*c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^5>;
// generators/relations

׿
×
𝔽