metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C30)⋊2Q8, (C2×C6)⋊5Dic10, (C2×C10)⋊4Dic6, C6.166(D4×D5), C22⋊3(C15⋊Q8), C30.62(C2×Q8), C30.254(C2×D4), C15⋊22(C22⋊Q8), C23.46(S3×D5), C5⋊3(C12.48D4), Dic15⋊5C4⋊39C2, C6.Dic10⋊39C2, C30.Q8⋊39C2, (C3×Dic5).74D4, C6.29(C2×Dic10), C10.29(C2×Dic6), C6.D4.4D5, (C22×C6).96D10, (C22×C10).65D6, C10.88(C4○D12), C30.160(C4○D4), C6.61(D4⋊2D5), (C2×C30).216C23, (C2×Dic5).196D6, (C2×Dic3).66D10, C30.38D4.9C2, (C22×Dic5).8S3, C3⋊7(Dic5.14D4), Dic5.35(C3⋊D4), (C22×C30).78C22, C2.31(Dic3.D10), (C6×Dic5).225C22, (C2×Dic15).145C22, (C10×Dic3).124C22, (C2×C15⋊Q8)⋊16C2, C2.11(C2×C15⋊Q8), C2.46(D5×C3⋊D4), (C2×C6×Dic5).7C2, C10.70(C2×C3⋊D4), C22.245(C2×S3×D5), (C5×C6.D4).5C2, (C2×C6).228(C22×D5), (C2×C10).228(C22×S3), SmallGroup(480,650)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C30)⋊Q8
G = < a,b,c,d | a2=b30=c4=1, d2=c2, ab=ba, cac-1=ab15, ad=da, cbc-1=b11, dbd-1=b19, dcd-1=c-1 >
Subgroups: 636 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, C12, C2×C6, C2×C6, C2×C6, C15, C22⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic5, 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, C6.D4, C2×Dic6, C22×C12, C5×Dic3, C3×Dic5, C3×Dic5, Dic15, C2×C30, C2×C30, C2×C30, C10.D4, C4⋊Dic5, C23.D5, C5×C22⋊C4, C2×Dic10, C22×Dic5, C12.48D4, C15⋊Q8, C6×Dic5, C6×Dic5, C10×Dic3, C2×Dic15, C22×C30, Dic5.14D4, C30.Q8, Dic15⋊5C4, C6.Dic10, C5×C6.D4, C30.38D4, C2×C15⋊Q8, C2×C6×Dic5, (C2×C30)⋊Q8
Quotients: C1, C2, C22, S3, D4, Q8, C23, D5, D6, C2×D4, C2×Q8, C4○D4, D10, Dic6, C3⋊D4, C22×S3, C22⋊Q8, Dic10, C22×D5, C2×Dic6, C4○D12, C2×C3⋊D4, S3×D5, C2×Dic10, D4×D5, D4⋊2D5, C12.48D4, C15⋊Q8, C2×S3×D5, Dic5.14D4, Dic3.D10, C2×C15⋊Q8, D5×C3⋊D4, (C2×C30)⋊Q8
►On 240 points
Generators in S240
(61 76)(62 77)(63 78)(64 79)(65 80)(66 81)(67 82)(68 83)(69 84)(70 85)(71 86)(72 87)(73 88)(74 89)(75 90)(91 106)(92 107)(93 108)(94 109)(95 110)(96 111)(97 112)(98 113)(99 114)(100 115)(101 116)(102 117)(103 118)(104 119)(105 120)(181 196)(182 197)(183 198)(184 199)(185 200)(186 201)(187 202)(188 203)(189 204)(190 205)(191 206)(192 207)(193 208)(194 209)(195 210)(211 226)(212 227)(213 228)(214 229)(215 230)(216 231)(217 232)(218 233)(219 234)(220 235)(221 236)(222 237)(223 238)(224 239)(225 240)
(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)
(1 112 45 75)(2 93 46 86)(3 104 47 67)(4 115 48 78)(5 96 49 89)(6 107 50 70)(7 118 51 81)(8 99 52 62)(9 110 53 73)(10 91 54 84)(11 102 55 65)(12 113 56 76)(13 94 57 87)(14 105 58 68)(15 116 59 79)(16 97 60 90)(17 108 31 71)(18 119 32 82)(19 100 33 63)(20 111 34 74)(21 92 35 85)(22 103 36 66)(23 114 37 77)(24 95 38 88)(25 106 39 69)(26 117 40 80)(27 98 41 61)(28 109 42 72)(29 120 43 83)(30 101 44 64)(121 186 156 221)(122 197 157 232)(123 208 158 213)(124 189 159 224)(125 200 160 235)(126 181 161 216)(127 192 162 227)(128 203 163 238)(129 184 164 219)(130 195 165 230)(131 206 166 211)(132 187 167 222)(133 198 168 233)(134 209 169 214)(135 190 170 225)(136 201 171 236)(137 182 172 217)(138 193 173 228)(139 204 174 239)(140 185 175 220)(141 196 176 231)(142 207 177 212)(143 188 178 223)(144 199 179 234)(145 210 180 215)(146 191 151 226)(147 202 152 237)(148 183 153 218)(149 194 154 229)(150 205 155 240)
(1 166 45 131)(2 155 46 150)(3 174 47 139)(4 163 48 128)(5 152 49 147)(6 171 50 136)(7 160 51 125)(8 179 52 144)(9 168 53 133)(10 157 54 122)(11 176 55 141)(12 165 56 130)(13 154 57 149)(14 173 58 138)(15 162 59 127)(16 151 60 146)(17 170 31 135)(18 159 32 124)(19 178 33 143)(20 167 34 132)(21 156 35 121)(22 175 36 140)(23 164 37 129)(24 153 38 148)(25 172 39 137)(26 161 40 126)(27 180 41 145)(28 169 42 134)(29 158 43 123)(30 177 44 142)(61 215 98 210)(62 234 99 199)(63 223 100 188)(64 212 101 207)(65 231 102 196)(66 220 103 185)(67 239 104 204)(68 228 105 193)(69 217 106 182)(70 236 107 201)(71 225 108 190)(72 214 109 209)(73 233 110 198)(74 222 111 187)(75 211 112 206)(76 230 113 195)(77 219 114 184)(78 238 115 203)(79 227 116 192)(80 216 117 181)(81 235 118 200)(82 224 119 189)(83 213 120 208)(84 232 91 197)(85 221 92 186)(86 240 93 205)(87 229 94 194)(88 218 95 183)(89 237 96 202)(90 226 97 191)
G:=sub<Sym(240)| (61,76)(62,77)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90)(91,106)(92,107)(93,108)(94,109)(95,110)(96,111)(97,112)(98,113)(99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(181,196)(182,197)(183,198)(184,199)(185,200)(186,201)(187,202)(188,203)(189,204)(190,205)(191,206)(192,207)(193,208)(194,209)(195,210)(211,226)(212,227)(213,228)(214,229)(215,230)(216,231)(217,232)(218,233)(219,234)(220,235)(221,236)(222,237)(223,238)(224,239)(225,240), (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), (1,112,45,75)(2,93,46,86)(3,104,47,67)(4,115,48,78)(5,96,49,89)(6,107,50,70)(7,118,51,81)(8,99,52,62)(9,110,53,73)(10,91,54,84)(11,102,55,65)(12,113,56,76)(13,94,57,87)(14,105,58,68)(15,116,59,79)(16,97,60,90)(17,108,31,71)(18,119,32,82)(19,100,33,63)(20,111,34,74)(21,92,35,85)(22,103,36,66)(23,114,37,77)(24,95,38,88)(25,106,39,69)(26,117,40,80)(27,98,41,61)(28,109,42,72)(29,120,43,83)(30,101,44,64)(121,186,156,221)(122,197,157,232)(123,208,158,213)(124,189,159,224)(125,200,160,235)(126,181,161,216)(127,192,162,227)(128,203,163,238)(129,184,164,219)(130,195,165,230)(131,206,166,211)(132,187,167,222)(133,198,168,233)(134,209,169,214)(135,190,170,225)(136,201,171,236)(137,182,172,217)(138,193,173,228)(139,204,174,239)(140,185,175,220)(141,196,176,231)(142,207,177,212)(143,188,178,223)(144,199,179,234)(145,210,180,215)(146,191,151,226)(147,202,152,237)(148,183,153,218)(149,194,154,229)(150,205,155,240), (1,166,45,131)(2,155,46,150)(3,174,47,139)(4,163,48,128)(5,152,49,147)(6,171,50,136)(7,160,51,125)(8,179,52,144)(9,168,53,133)(10,157,54,122)(11,176,55,141)(12,165,56,130)(13,154,57,149)(14,173,58,138)(15,162,59,127)(16,151,60,146)(17,170,31,135)(18,159,32,124)(19,178,33,143)(20,167,34,132)(21,156,35,121)(22,175,36,140)(23,164,37,129)(24,153,38,148)(25,172,39,137)(26,161,40,126)(27,180,41,145)(28,169,42,134)(29,158,43,123)(30,177,44,142)(61,215,98,210)(62,234,99,199)(63,223,100,188)(64,212,101,207)(65,231,102,196)(66,220,103,185)(67,239,104,204)(68,228,105,193)(69,217,106,182)(70,236,107,201)(71,225,108,190)(72,214,109,209)(73,233,110,198)(74,222,111,187)(75,211,112,206)(76,230,113,195)(77,219,114,184)(78,238,115,203)(79,227,116,192)(80,216,117,181)(81,235,118,200)(82,224,119,189)(83,213,120,208)(84,232,91,197)(85,221,92,186)(86,240,93,205)(87,229,94,194)(88,218,95,183)(89,237,96,202)(90,226,97,191)>;
G:=Group( (61,76)(62,77)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90)(91,106)(92,107)(93,108)(94,109)(95,110)(96,111)(97,112)(98,113)(99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(181,196)(182,197)(183,198)(184,199)(185,200)(186,201)(187,202)(188,203)(189,204)(190,205)(191,206)(192,207)(193,208)(194,209)(195,210)(211,226)(212,227)(213,228)(214,229)(215,230)(216,231)(217,232)(218,233)(219,234)(220,235)(221,236)(222,237)(223,238)(224,239)(225,240), (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), (1,112,45,75)(2,93,46,86)(3,104,47,67)(4,115,48,78)(5,96,49,89)(6,107,50,70)(7,118,51,81)(8,99,52,62)(9,110,53,73)(10,91,54,84)(11,102,55,65)(12,113,56,76)(13,94,57,87)(14,105,58,68)(15,116,59,79)(16,97,60,90)(17,108,31,71)(18,119,32,82)(19,100,33,63)(20,111,34,74)(21,92,35,85)(22,103,36,66)(23,114,37,77)(24,95,38,88)(25,106,39,69)(26,117,40,80)(27,98,41,61)(28,109,42,72)(29,120,43,83)(30,101,44,64)(121,186,156,221)(122,197,157,232)(123,208,158,213)(124,189,159,224)(125,200,160,235)(126,181,161,216)(127,192,162,227)(128,203,163,238)(129,184,164,219)(130,195,165,230)(131,206,166,211)(132,187,167,222)(133,198,168,233)(134,209,169,214)(135,190,170,225)(136,201,171,236)(137,182,172,217)(138,193,173,228)(139,204,174,239)(140,185,175,220)(141,196,176,231)(142,207,177,212)(143,188,178,223)(144,199,179,234)(145,210,180,215)(146,191,151,226)(147,202,152,237)(148,183,153,218)(149,194,154,229)(150,205,155,240), (1,166,45,131)(2,155,46,150)(3,174,47,139)(4,163,48,128)(5,152,49,147)(6,171,50,136)(7,160,51,125)(8,179,52,144)(9,168,53,133)(10,157,54,122)(11,176,55,141)(12,165,56,130)(13,154,57,149)(14,173,58,138)(15,162,59,127)(16,151,60,146)(17,170,31,135)(18,159,32,124)(19,178,33,143)(20,167,34,132)(21,156,35,121)(22,175,36,140)(23,164,37,129)(24,153,38,148)(25,172,39,137)(26,161,40,126)(27,180,41,145)(28,169,42,134)(29,158,43,123)(30,177,44,142)(61,215,98,210)(62,234,99,199)(63,223,100,188)(64,212,101,207)(65,231,102,196)(66,220,103,185)(67,239,104,204)(68,228,105,193)(69,217,106,182)(70,236,107,201)(71,225,108,190)(72,214,109,209)(73,233,110,198)(74,222,111,187)(75,211,112,206)(76,230,113,195)(77,219,114,184)(78,238,115,203)(79,227,116,192)(80,216,117,181)(81,235,118,200)(82,224,119,189)(83,213,120,208)(84,232,91,197)(85,221,92,186)(86,240,93,205)(87,229,94,194)(88,218,95,183)(89,237,96,202)(90,226,97,191) );
G=PermutationGroup([[(61,76),(62,77),(63,78),(64,79),(65,80),(66,81),(67,82),(68,83),(69,84),(70,85),(71,86),(72,87),(73,88),(74,89),(75,90),(91,106),(92,107),(93,108),(94,109),(95,110),(96,111),(97,112),(98,113),(99,114),(100,115),(101,116),(102,117),(103,118),(104,119),(105,120),(181,196),(182,197),(183,198),(184,199),(185,200),(186,201),(187,202),(188,203),(189,204),(190,205),(191,206),(192,207),(193,208),(194,209),(195,210),(211,226),(212,227),(213,228),(214,229),(215,230),(216,231),(217,232),(218,233),(219,234),(220,235),(221,236),(222,237),(223,238),(224,239),(225,240)], [(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)], [(1,112,45,75),(2,93,46,86),(3,104,47,67),(4,115,48,78),(5,96,49,89),(6,107,50,70),(7,118,51,81),(8,99,52,62),(9,110,53,73),(10,91,54,84),(11,102,55,65),(12,113,56,76),(13,94,57,87),(14,105,58,68),(15,116,59,79),(16,97,60,90),(17,108,31,71),(18,119,32,82),(19,100,33,63),(20,111,34,74),(21,92,35,85),(22,103,36,66),(23,114,37,77),(24,95,38,88),(25,106,39,69),(26,117,40,80),(27,98,41,61),(28,109,42,72),(29,120,43,83),(30,101,44,64),(121,186,156,221),(122,197,157,232),(123,208,158,213),(124,189,159,224),(125,200,160,235),(126,181,161,216),(127,192,162,227),(128,203,163,238),(129,184,164,219),(130,195,165,230),(131,206,166,211),(132,187,167,222),(133,198,168,233),(134,209,169,214),(135,190,170,225),(136,201,171,236),(137,182,172,217),(138,193,173,228),(139,204,174,239),(140,185,175,220),(141,196,176,231),(142,207,177,212),(143,188,178,223),(144,199,179,234),(145,210,180,215),(146,191,151,226),(147,202,152,237),(148,183,153,218),(149,194,154,229),(150,205,155,240)], [(1,166,45,131),(2,155,46,150),(3,174,47,139),(4,163,48,128),(5,152,49,147),(6,171,50,136),(7,160,51,125),(8,179,52,144),(9,168,53,133),(10,157,54,122),(11,176,55,141),(12,165,56,130),(13,154,57,149),(14,173,58,138),(15,162,59,127),(16,151,60,146),(17,170,31,135),(18,159,32,124),(19,178,33,143),(20,167,34,132),(21,156,35,121),(22,175,36,140),(23,164,37,129),(24,153,38,148),(25,172,39,137),(26,161,40,126),(27,180,41,145),(28,169,42,134),(29,158,43,123),(30,177,44,142),(61,215,98,210),(62,234,99,199),(63,223,100,188),(64,212,101,207),(65,231,102,196),(66,220,103,185),(67,239,104,204),(68,228,105,193),(69,217,106,182),(70,236,107,201),(71,225,108,190),(72,214,109,209),(73,233,110,198),(74,222,111,187),(75,211,112,206),(76,230,113,195),(77,219,114,184),(78,238,115,203),(79,227,116,192),(80,216,117,181),(81,235,118,200),(82,224,119,189),(83,213,120,208),(84,232,91,197),(85,221,92,186),(86,240,93,205),(87,229,94,194),(88,218,95,183),(89,237,96,202),(90,226,97,191)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 6A | ··· | 6G | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 12A | ··· | 12H | 15A | 15B | 20A | ··· | 20H | 30A | ··· | 30N |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 12 | ··· | 12 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 12 | 12 | 60 | 60 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 12 | ··· | 12 | 4 | ··· | 4 |
66 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 | C3⋊D4 | Dic6 | Dic10 | C4○D12 | S3×D5 | D4×D5 | D4⋊2D5 | C15⋊Q8 | C2×S3×D5 | Dic3.D10 | D5×C3⋊D4 |
| kernel | (C2×C30)⋊Q8 | C30.Q8 | Dic15⋊5C4 | C6.Dic10 | C5×C6.D4 | C30.38D4 | C2×C15⋊Q8 | C2×C6×Dic5 | C22×Dic5 | C3×Dic5 | C2×C30 | C6.D4 | C2×Dic5 | C22×C10 | C30 | C2×Dic3 | C22×C6 | Dic5 | C2×C10 | C2×C6 | C10 | C23 | C6 | C6 | C22 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 4 | 2 | 4 | 4 | 8 | 4 | 2 | 2 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of (C2×C30)⋊Q8 ►in GL6(𝔽61)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 14 | 60 | 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 | 8 | 60 |
| 14 | 0 | 0 | 0 | 0 | 0 |
| 6 | 48 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 1 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 48 | 0 |
| 0 | 0 | 0 | 0 | 14 | 14 |
| 14 | 59 | 0 | 0 | 0 | 0 |
| 6 | 47 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 46 |
| 0 | 0 | 0 | 0 | 53 | 1 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 50 | 0 |
| 0 | 0 | 0 | 0 | 34 | 11 |
G:=sub<GL(6,GF(61))| [1,14,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,8,0,0,0,0,0,60],[14,6,0,0,0,0,0,48,0,0,0,0,0,0,17,60,0,0,0,0,1,0,0,0,0,0,0,0,48,14,0,0,0,0,0,14],[14,6,0,0,0,0,59,47,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,53,0,0,0,0,46,1],[60,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,60,0,0,0,0,0,0,0,50,34,0,0,0,0,0,11] >;
(C2×C30)⋊Q8 in GAP, Magma, Sage, TeX
(C_2\times C_{30})\rtimes Q_8 % in TeX
G:=Group("(C2xC30):Q8"); // GroupNames label
G:=SmallGroup(480,650);
// by ID
G=gap.SmallGroup(480,650);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,64,219,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^30=c^4=1,d^2=c^2,a*b=b*a,c*a*c^-1=a*b^15,a*d=d*a,c*b*c^-1=b^11,d*b*d^-1=b^19,d*c*d^-1=c^-1>;
// generators/relations