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G = (C2×C30)⋊Q8order 480 = 25·3·5

2nd semidirect product of C2×C30 and Q8 acting via Q8/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C2×C30)⋊2Q8, (C2×C6)⋊5Dic10, (C2×C10)⋊4Dic6, C6.166(D4×D5), C223(C15⋊Q8), C30.62(C2×Q8), C30.254(C2×D4), C1522(C22⋊Q8), C23.46(S3×D5), C53(C12.48D4), Dic155C439C2, C6.Dic1039C2, C30.Q839C2, (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(D42D5), (C2×C30).216C23, (C2×Dic5).196D6, (C2×Dic3).66D10, C30.38D4.9C2, (C22×Dic5).8S3, C37(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

C1C2×C30 — (C2×C30)⋊Q8
C1C5C15C30C2×C30C6×Dic5C2×C15⋊Q8 — (C2×C30)⋊Q8
C15C2×C30 — (C2×C30)⋊Q8
C1C22C23

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 [×3], C2 [×2], C3, C4 [×7], C22, C22 [×2], C22 [×2], C5, C6 [×3], C6 [×2], C2×C4 [×8], Q8 [×2], C23, C10 [×3], C10 [×2], Dic3 [×4], C12 [×3], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C22⋊C4 [×2], C4⋊C4 [×3], C22×C4, C2×Q8, Dic5 [×2], Dic5 [×3], C20 [×2], C2×C10, C2×C10 [×2], C2×C10 [×2], Dic6 [×2], C2×Dic3 [×2], C2×Dic3 [×2], C2×C12 [×4], C22×C6, C30 [×3], C30 [×2], C22⋊Q8, Dic10 [×2], C2×Dic5 [×2], C2×Dic5 [×4], C2×C20 [×2], C22×C10, Dic3⋊C4 [×2], C4⋊Dic3, C6.D4, C6.D4, C2×Dic6, C22×C12, C5×Dic3 [×2], C3×Dic5 [×2], C3×Dic5, Dic15 [×2], C2×C30, C2×C30 [×2], C2×C30 [×2], C10.D4 [×2], C4⋊Dic5, C23.D5, C5×C22⋊C4, C2×Dic10, C22×Dic5, C12.48D4, C15⋊Q8 [×2], C6×Dic5 [×2], C6×Dic5 [×2], C10×Dic3 [×2], C2×Dic15 [×2], C22×C30, Dic5.14D4, C30.Q8, Dic155C4, C6.Dic10, C5×C6.D4, C30.38D4, C2×C15⋊Q8, C2×C6×Dic5, (C2×C30)⋊Q8
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], Q8 [×2], C23, D5, D6 [×3], C2×D4, C2×Q8, C4○D4, D10 [×3], Dic6 [×2], C3⋊D4 [×2], C22×S3, C22⋊Q8, Dic10 [×2], C22×D5, C2×Dic6, C4○D12, C2×C3⋊D4, S3×D5, C2×Dic10, D4×D5, D42D5, C12.48D4, C15⋊Q8 [×2], C2×S3×D5, Dic5.14D4, Dic3.D10, C2×C15⋊Q8, D5×C3⋊D4, (C2×C30)⋊Q8

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

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

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

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

66 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D4E4F4G4H5A5B6A···6G10A···10F10G10H10I10J12A···12H15A15B20A···20H30A···30N
order122222344444444556···610···101010101012···12151520···2030···30
size11112221010101012126060222···22···2444410···104412···124···4

66 irreducible representations

dim1111111122222222222224444444
type++++++++++-+++++--++--+
imageC1C2C2C2C2C2C2C2S3D4Q8D5D6D6C4○D4D10D10C3⋊D4Dic6Dic10C4○D12S3×D5D4×D5D42D5C15⋊Q8C2×S3×D5Dic3.D10D5×C3⋊D4
kernel(C2×C30)⋊Q8C30.Q8Dic155C4C6.Dic10C5×C6.D4C30.38D4C2×C15⋊Q8C2×C6×Dic5C22×Dic5C3×Dic5C2×C30C6.D4C2×Dic5C22×C10C30C2×Dic3C22×C6Dic5C2×C10C2×C6C10C23C6C6C22C22C2C2
# reps1111111112222124244842224244

Matrix representation of (C2×C30)⋊Q8 in GL6(𝔽61)

100000
14600000
001000
000100
000010
0000860
,
1400000
6480000
0017100
0060000
0000480
00001414
,
14590000
6470000
0060000
0006000
00006046
0000531
,
6000000
0600000
0006000
0060000
0000500
00003411

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

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