G = (C2×C10)⋊8Dic6 order 480 = 25·3·5
2nd semidirect product of C2×C10 and Dic6 acting via Dic6/Dic3=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C30)⋊3Q8, (C2×C10)⋊8Dic6, (C2×C6)⋊1Dic10, C22⋊2(C15⋊Q8), C30.63(C2×Q8), C10.166(S3×D4), C30.255(C2×D4), C15⋊23(C22⋊Q8), C23.35(S3×D5), C23.D5.4S3, C6.88(C4○D20), C3⋊3(C20.48D4), Dic15⋊5C4⋊40C2, C30.Q8⋊40C2, C6.Dic10⋊40C2, (C2×Dic5).67D6, (C5×Dic3).42D4, C6.30(C2×Dic10), C10.30(C2×Dic6), (C22×C6).50D10, C30.161(C4○D4), (C2×C30).217C23, C5⋊7(Dic3.D4), (C22×C10).113D6, C10.60(D4⋊2S3), (C22×Dic3).6D5, (C2×Dic3).167D10, C30.38D4.10C2, Dic3.19(C5⋊D4), (C22×C30).79C22, C2.31(Dic5.D6), (C6×Dic5).124C22, (C2×Dic15).146C22, (C10×Dic3).205C22, (C2×C15⋊Q8)⋊17C2, C2.12(C2×C15⋊Q8), C6.69(C2×C5⋊D4), C2.46(S3×C5⋊D4), (Dic3×C2×C10).7C2, C22.246(C2×S3×D5), (C3×C23.D5).5C2, (C2×C6).229(C22×D5), (C2×C10).229(C22×S3), SmallGroup(480,651)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C10)⋊8Dic6
G = < a,b,c,d | a2=b6=c20=1, d2=c10, ab=ba, ac=ca, dad-1=ab3, cbc-1=b-1, bd=db, dcd-1=c-1 >
Subgroups: 620 in 148 conjugacy classes, 56 normal (44 characteristic)
C1, C2, C2, C3, C4, C22, C22, C22, C5, C6, C6, C2×C4, Q8, C23, C10, C10, Dic3, Dic3, C12, C2×C6, C2×C6, C2×C6, C15, C22⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic5, C20, C2×C10, C2×C10, C2×C10, Dic6, C2×Dic3, C2×Dic3, C2×C12, C22×C6, C30, C30, C22⋊Q8, Dic10, C2×Dic5, C2×Dic5, C2×C20, C22×C10, Dic3⋊C4, C4⋊Dic3, C6.D4, C3×C22⋊C4, C2×Dic6, C22×Dic3, C5×Dic3, C5×Dic3, C3×Dic5, Dic15, C2×C30, C2×C30, C2×C30, C10.D4, C4⋊Dic5, C23.D5, C23.D5, C2×Dic10, C22×C20, Dic3.D4, C15⋊Q8, C6×Dic5, C10×Dic3, C10×Dic3, C2×Dic15, C22×C30, C20.48D4, C30.Q8, Dic15⋊5C4, C6.Dic10, C3×C23.D5, C30.38D4, C2×C15⋊Q8, Dic3×C2×C10, (C2×C10)⋊8Dic6
Quotients: C1, C2, C22, S3, D4, Q8, C23, D5, D6, C2×D4, C2×Q8, C4○D4, D10, Dic6, C22×S3, C22⋊Q8, Dic10, C5⋊D4, C22×D5, C2×Dic6, S3×D4, D4⋊2S3, S3×D5, C2×Dic10, C4○D20, C2×C5⋊D4, Dic3.D4, C15⋊Q8, C2×S3×D5, C20.48D4, Dic5.D6, C2×C15⋊Q8, S3×C5⋊D4, (C2×C10)⋊8Dic6
►On 240 points
Generators in S240
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(21 31)(22 32)(23 33)(24 34)(25 35)(26 36)(27 37)(28 38)(29 39)(30 40)(41 51)(42 52)(43 53)(44 54)(45 55)(46 56)(47 57)(48 58)(49 59)(50 60)(61 71)(62 72)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(81 209)(82 210)(83 211)(84 212)(85 213)(86 214)(87 215)(88 216)(89 217)(90 218)(91 219)(92 220)(93 201)(94 202)(95 203)(96 204)(97 205)(98 206)(99 207)(100 208)(101 187)(102 188)(103 189)(104 190)(105 191)(106 192)(107 193)(108 194)(109 195)(110 196)(111 197)(112 198)(113 199)(114 200)(115 181)(116 182)(117 183)(118 184)(119 185)(120 186)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(127 137)(128 138)(129 139)(130 140)(141 170)(142 171)(143 172)(144 173)(145 174)(146 175)(147 176)(148 177)(149 178)(150 179)(151 180)(152 161)(153 162)(154 163)(155 164)(156 165)(157 166)(158 167)(159 168)(160 169)(221 231)(222 232)(223 233)(224 234)(225 235)(226 236)(227 237)(228 238)(229 239)(230 240)
(1 35 239 72 140 49)(2 50 121 73 240 36)(3 37 221 74 122 51)(4 52 123 75 222 38)(5 39 223 76 124 53)(6 54 125 77 224 40)(7 21 225 78 126 55)(8 56 127 79 226 22)(9 23 227 80 128 57)(10 58 129 61 228 24)(11 25 229 62 130 59)(12 60 131 63 230 26)(13 27 231 64 132 41)(14 42 133 65 232 28)(15 29 233 66 134 43)(16 44 135 67 234 30)(17 31 235 68 136 45)(18 46 137 69 236 32)(19 33 237 70 138 47)(20 48 139 71 238 34)(81 154 185 219 173 109)(82 110 174 220 186 155)(83 156 187 201 175 111)(84 112 176 202 188 157)(85 158 189 203 177 113)(86 114 178 204 190 159)(87 160 191 205 179 115)(88 116 180 206 192 141)(89 142 193 207 161 117)(90 118 162 208 194 143)(91 144 195 209 163 119)(92 120 164 210 196 145)(93 146 197 211 165 101)(94 102 166 212 198 147)(95 148 199 213 167 103)(96 104 168 214 200 149)(97 150 181 215 169 105)(98 106 170 216 182 151)(99 152 183 217 171 107)(100 108 172 218 184 153)
(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)
(1 156 11 146)(2 155 12 145)(3 154 13 144)(4 153 14 143)(5 152 15 142)(6 151 16 141)(7 150 17 160)(8 149 18 159)(9 148 19 158)(10 147 20 157)(21 181 31 191)(22 200 32 190)(23 199 33 189)(24 198 34 188)(25 197 35 187)(26 196 36 186)(27 195 37 185)(28 194 38 184)(29 193 39 183)(30 192 40 182)(41 91 51 81)(42 90 52 100)(43 89 53 99)(44 88 54 98)(45 87 55 97)(46 86 56 96)(47 85 57 95)(48 84 58 94)(49 83 59 93)(50 82 60 92)(61 166 71 176)(62 165 72 175)(63 164 73 174)(64 163 74 173)(65 162 75 172)(66 161 76 171)(67 180 77 170)(68 179 78 169)(69 178 79 168)(70 177 80 167)(101 140 111 130)(102 139 112 129)(103 138 113 128)(104 137 114 127)(105 136 115 126)(106 135 116 125)(107 134 117 124)(108 133 118 123)(109 132 119 122)(110 131 120 121)(201 229 211 239)(202 228 212 238)(203 227 213 237)(204 226 214 236)(205 225 215 235)(206 224 216 234)(207 223 217 233)(208 222 218 232)(209 221 219 231)(210 240 220 230)
G:=sub<Sym(240)| (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,209)(82,210)(83,211)(84,212)(85,213)(86,214)(87,215)(88,216)(89,217)(90,218)(91,219)(92,220)(93,201)(94,202)(95,203)(96,204)(97,205)(98,206)(99,207)(100,208)(101,187)(102,188)(103,189)(104,190)(105,191)(106,192)(107,193)(108,194)(109,195)(110,196)(111,197)(112,198)(113,199)(114,200)(115,181)(116,182)(117,183)(118,184)(119,185)(120,186)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)(141,170)(142,171)(143,172)(144,173)(145,174)(146,175)(147,176)(148,177)(149,178)(150,179)(151,180)(152,161)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,169)(221,231)(222,232)(223,233)(224,234)(225,235)(226,236)(227,237)(228,238)(229,239)(230,240), (1,35,239,72,140,49)(2,50,121,73,240,36)(3,37,221,74,122,51)(4,52,123,75,222,38)(5,39,223,76,124,53)(6,54,125,77,224,40)(7,21,225,78,126,55)(8,56,127,79,226,22)(9,23,227,80,128,57)(10,58,129,61,228,24)(11,25,229,62,130,59)(12,60,131,63,230,26)(13,27,231,64,132,41)(14,42,133,65,232,28)(15,29,233,66,134,43)(16,44,135,67,234,30)(17,31,235,68,136,45)(18,46,137,69,236,32)(19,33,237,70,138,47)(20,48,139,71,238,34)(81,154,185,219,173,109)(82,110,174,220,186,155)(83,156,187,201,175,111)(84,112,176,202,188,157)(85,158,189,203,177,113)(86,114,178,204,190,159)(87,160,191,205,179,115)(88,116,180,206,192,141)(89,142,193,207,161,117)(90,118,162,208,194,143)(91,144,195,209,163,119)(92,120,164,210,196,145)(93,146,197,211,165,101)(94,102,166,212,198,147)(95,148,199,213,167,103)(96,104,168,214,200,149)(97,150,181,215,169,105)(98,106,170,216,182,151)(99,152,183,217,171,107)(100,108,172,218,184,153), (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), (1,156,11,146)(2,155,12,145)(3,154,13,144)(4,153,14,143)(5,152,15,142)(6,151,16,141)(7,150,17,160)(8,149,18,159)(9,148,19,158)(10,147,20,157)(21,181,31,191)(22,200,32,190)(23,199,33,189)(24,198,34,188)(25,197,35,187)(26,196,36,186)(27,195,37,185)(28,194,38,184)(29,193,39,183)(30,192,40,182)(41,91,51,81)(42,90,52,100)(43,89,53,99)(44,88,54,98)(45,87,55,97)(46,86,56,96)(47,85,57,95)(48,84,58,94)(49,83,59,93)(50,82,60,92)(61,166,71,176)(62,165,72,175)(63,164,73,174)(64,163,74,173)(65,162,75,172)(66,161,76,171)(67,180,77,170)(68,179,78,169)(69,178,79,168)(70,177,80,167)(101,140,111,130)(102,139,112,129)(103,138,113,128)(104,137,114,127)(105,136,115,126)(106,135,116,125)(107,134,117,124)(108,133,118,123)(109,132,119,122)(110,131,120,121)(201,229,211,239)(202,228,212,238)(203,227,213,237)(204,226,214,236)(205,225,215,235)(206,224,216,234)(207,223,217,233)(208,222,218,232)(209,221,219,231)(210,240,220,230)>;
G:=Group( (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,209)(82,210)(83,211)(84,212)(85,213)(86,214)(87,215)(88,216)(89,217)(90,218)(91,219)(92,220)(93,201)(94,202)(95,203)(96,204)(97,205)(98,206)(99,207)(100,208)(101,187)(102,188)(103,189)(104,190)(105,191)(106,192)(107,193)(108,194)(109,195)(110,196)(111,197)(112,198)(113,199)(114,200)(115,181)(116,182)(117,183)(118,184)(119,185)(120,186)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)(141,170)(142,171)(143,172)(144,173)(145,174)(146,175)(147,176)(148,177)(149,178)(150,179)(151,180)(152,161)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,169)(221,231)(222,232)(223,233)(224,234)(225,235)(226,236)(227,237)(228,238)(229,239)(230,240), (1,35,239,72,140,49)(2,50,121,73,240,36)(3,37,221,74,122,51)(4,52,123,75,222,38)(5,39,223,76,124,53)(6,54,125,77,224,40)(7,21,225,78,126,55)(8,56,127,79,226,22)(9,23,227,80,128,57)(10,58,129,61,228,24)(11,25,229,62,130,59)(12,60,131,63,230,26)(13,27,231,64,132,41)(14,42,133,65,232,28)(15,29,233,66,134,43)(16,44,135,67,234,30)(17,31,235,68,136,45)(18,46,137,69,236,32)(19,33,237,70,138,47)(20,48,139,71,238,34)(81,154,185,219,173,109)(82,110,174,220,186,155)(83,156,187,201,175,111)(84,112,176,202,188,157)(85,158,189,203,177,113)(86,114,178,204,190,159)(87,160,191,205,179,115)(88,116,180,206,192,141)(89,142,193,207,161,117)(90,118,162,208,194,143)(91,144,195,209,163,119)(92,120,164,210,196,145)(93,146,197,211,165,101)(94,102,166,212,198,147)(95,148,199,213,167,103)(96,104,168,214,200,149)(97,150,181,215,169,105)(98,106,170,216,182,151)(99,152,183,217,171,107)(100,108,172,218,184,153), (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), (1,156,11,146)(2,155,12,145)(3,154,13,144)(4,153,14,143)(5,152,15,142)(6,151,16,141)(7,150,17,160)(8,149,18,159)(9,148,19,158)(10,147,20,157)(21,181,31,191)(22,200,32,190)(23,199,33,189)(24,198,34,188)(25,197,35,187)(26,196,36,186)(27,195,37,185)(28,194,38,184)(29,193,39,183)(30,192,40,182)(41,91,51,81)(42,90,52,100)(43,89,53,99)(44,88,54,98)(45,87,55,97)(46,86,56,96)(47,85,57,95)(48,84,58,94)(49,83,59,93)(50,82,60,92)(61,166,71,176)(62,165,72,175)(63,164,73,174)(64,163,74,173)(65,162,75,172)(66,161,76,171)(67,180,77,170)(68,179,78,169)(69,178,79,168)(70,177,80,167)(101,140,111,130)(102,139,112,129)(103,138,113,128)(104,137,114,127)(105,136,115,126)(106,135,116,125)(107,134,117,124)(108,133,118,123)(109,132,119,122)(110,131,120,121)(201,229,211,239)(202,228,212,238)(203,227,213,237)(204,226,214,236)(205,225,215,235)(206,224,216,234)(207,223,217,233)(208,222,218,232)(209,221,219,231)(210,240,220,230) );
G=PermutationGroup([[(1,11),(2,12),(3,13),(4,14),(5,15),(6,16),(7,17),(8,18),(9,19),(10,20),(21,31),(22,32),(23,33),(24,34),(25,35),(26,36),(27,37),(28,38),(29,39),(30,40),(41,51),(42,52),(43,53),(44,54),(45,55),(46,56),(47,57),(48,58),(49,59),(50,60),(61,71),(62,72),(63,73),(64,74),(65,75),(66,76),(67,77),(68,78),(69,79),(70,80),(81,209),(82,210),(83,211),(84,212),(85,213),(86,214),(87,215),(88,216),(89,217),(90,218),(91,219),(92,220),(93,201),(94,202),(95,203),(96,204),(97,205),(98,206),(99,207),(100,208),(101,187),(102,188),(103,189),(104,190),(105,191),(106,192),(107,193),(108,194),(109,195),(110,196),(111,197),(112,198),(113,199),(114,200),(115,181),(116,182),(117,183),(118,184),(119,185),(120,186),(121,131),(122,132),(123,133),(124,134),(125,135),(126,136),(127,137),(128,138),(129,139),(130,140),(141,170),(142,171),(143,172),(144,173),(145,174),(146,175),(147,176),(148,177),(149,178),(150,179),(151,180),(152,161),(153,162),(154,163),(155,164),(156,165),(157,166),(158,167),(159,168),(160,169),(221,231),(222,232),(223,233),(224,234),(225,235),(226,236),(227,237),(228,238),(229,239),(230,240)], [(1,35,239,72,140,49),(2,50,121,73,240,36),(3,37,221,74,122,51),(4,52,123,75,222,38),(5,39,223,76,124,53),(6,54,125,77,224,40),(7,21,225,78,126,55),(8,56,127,79,226,22),(9,23,227,80,128,57),(10,58,129,61,228,24),(11,25,229,62,130,59),(12,60,131,63,230,26),(13,27,231,64,132,41),(14,42,133,65,232,28),(15,29,233,66,134,43),(16,44,135,67,234,30),(17,31,235,68,136,45),(18,46,137,69,236,32),(19,33,237,70,138,47),(20,48,139,71,238,34),(81,154,185,219,173,109),(82,110,174,220,186,155),(83,156,187,201,175,111),(84,112,176,202,188,157),(85,158,189,203,177,113),(86,114,178,204,190,159),(87,160,191,205,179,115),(88,116,180,206,192,141),(89,142,193,207,161,117),(90,118,162,208,194,143),(91,144,195,209,163,119),(92,120,164,210,196,145),(93,146,197,211,165,101),(94,102,166,212,198,147),(95,148,199,213,167,103),(96,104,168,214,200,149),(97,150,181,215,169,105),(98,106,170,216,182,151),(99,152,183,217,171,107),(100,108,172,218,184,153)], [(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)], [(1,156,11,146),(2,155,12,145),(3,154,13,144),(4,153,14,143),(5,152,15,142),(6,151,16,141),(7,150,17,160),(8,149,18,159),(9,148,19,158),(10,147,20,157),(21,181,31,191),(22,200,32,190),(23,199,33,189),(24,198,34,188),(25,197,35,187),(26,196,36,186),(27,195,37,185),(28,194,38,184),(29,193,39,183),(30,192,40,182),(41,91,51,81),(42,90,52,100),(43,89,53,99),(44,88,54,98),(45,87,55,97),(46,86,56,96),(47,85,57,95),(48,84,58,94),(49,83,59,93),(50,82,60,92),(61,166,71,176),(62,165,72,175),(63,164,73,174),(64,163,74,173),(65,162,75,172),(66,161,76,171),(67,180,77,170),(68,179,78,169),(69,178,79,168),(70,177,80,167),(101,140,111,130),(102,139,112,129),(103,138,113,128),(104,137,114,127),(105,136,115,126),(106,135,116,125),(107,134,117,124),(108,133,118,123),(109,132,119,122),(110,131,120,121),(201,229,211,239),(202,228,212,238),(203,227,213,237),(204,226,214,236),(205,225,215,235),(206,224,216,234),(207,223,217,233),(208,222,218,232),(209,221,219,231),(210,240,220,230)]])
72 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 10A | ··· | 10N | 12A | 12B | 12C | 12D | 15A | 15B | 20A | ··· | 20P | 30A | ··· | 30N |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 6 | 6 | 6 | 6 | 20 | 20 | 60 | 60 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | ··· | 2 | 20 | 20 | 20 | 20 | 4 | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
72 irreducible representations
| dim | 1 | 1 | 1 | 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 | C2 | C2 | C2 | S3 | D4 | Q8 | D5 | D6 | D6 | C4○D4 | D10 | D10 | Dic6 | C5⋊D4 | Dic10 | C4○D20 | S3×D4 | D4⋊2S3 | S3×D5 | C15⋊Q8 | C2×S3×D5 | Dic5.D6 | S3×C5⋊D4 |
| kernel | (C2×C10)⋊8Dic6 | C30.Q8 | Dic15⋊5C4 | C6.Dic10 | C3×C23.D5 | C30.38D4 | C2×C15⋊Q8 | Dic3×C2×C10 | C23.D5 | C5×Dic3 | C2×C30 | C22×Dic3 | C2×Dic5 | C22×C10 | C30 | C2×Dic3 | C22×C6 | C2×C10 | Dic3 | C2×C6 | C6 | C10 | C10 | C23 | C22 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 4 | 2 | 4 | 8 | 8 | 8 | 1 | 1 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of (C2×C10)⋊8Dic6 ►in GL4(𝔽61) generated by
| 1 | 0 | 0 | 0 |
| 60 | 60 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 60 |
| 0 | 0 | 1 | 60 |
| 34 | 0 | 0 | 0 |
| 18 | 9 | 0 | 0 |
| 0 | 0 | 36 | 51 |
| 0 | 0 | 26 | 25 |
| 54 | 47 | 0 | 0 |
| 47 | 7 | 0 | 0 |
| 0 | 0 | 38 | 46 |
| 0 | 0 | 15 | 23 |
G:=sub<GL(4,GF(61))| [1,60,0,0,0,60,0,0,0,0,60,0,0,0,0,60],[60,0,0,0,0,60,0,0,0,0,0,1,0,0,60,60],[34,18,0,0,0,9,0,0,0,0,36,26,0,0,51,25],[54,47,0,0,47,7,0,0,0,0,38,15,0,0,46,23] >;
(C2×C10)⋊8Dic6 in GAP, Magma, Sage, TeX
(C_2\times C_{10})\rtimes_8{\rm Dic}_6 % in TeX
G:=Group("(C2xC10):8Dic6"); // GroupNames label
G:=SmallGroup(480,651);
// by ID
G=gap.SmallGroup(480,651);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,64,422,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^6=c^20=1,d^2=c^10,a*b=b*a,a*c=c*a,d*a*d^-1=a*b^3,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations