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G = (C2×C10)⋊4D12order 480 = 25·3·5

1st semidirect product of C2×C10 and D12 acting via D12/C6=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C2×C30)⋊6D4, (C2×C10)⋊4D12, C54(C127D4), C6.164(D4×D5), C1522(C4⋊D4), D6⋊Dic534C2, (C3×Dic5)⋊16D4, C10.69(C2×D12), C30.246(C2×D4), D304C434C2, C23.45(S3×D5), Dic55(C3⋊D4), C34(Dic5⋊D4), C222(C5⋊D12), C30.Q838C2, (C22×C6).95D10, (C22×C10).60D6, C30.157(C4○D4), C10.87(C4○D12), C6.60(D42D5), (C2×C30).208C23, (C2×Dic5).195D6, (C2×Dic3).64D10, (C22×Dic5)⋊10S3, (C22×S3).29D10, (C22×C30).70C22, C2.30(Dic3.D10), (C6×Dic5).224C22, (C22×D15).68C22, (C2×Dic15).142C22, (C10×Dic3).121C22, (C2×C3⋊D4)⋊6D5, (C2×C6×Dic5)⋊7C2, (C10×C3⋊D4)⋊6C2, (C2×C6)⋊8(C5⋊D4), C6.23(C2×C5⋊D4), C2.44(D5×C3⋊D4), (C2×C157D4)⋊17C2, (C2×C5⋊D12)⋊13C2, C2.24(C2×C5⋊D12), C10.68(C2×C3⋊D4), C22.237(C2×S3×D5), (S3×C2×C10).54C22, (C2×C6).220(C22×D5), (C2×C10).220(C22×S3), SmallGroup(480,642)

Series: Derived Chief Lower central Upper central

C1C2×C30 — (C2×C10)⋊4D12
C1C5C15C30C2×C30C6×Dic5C2×C5⋊D12 — (C2×C10)⋊4D12
C15C2×C30 — (C2×C10)⋊4D12
C1C22C23

Generators and relations for (C2×C10)⋊4D12
 G = < a,b,c,d | a2=b10=c12=d2=1, ab=ba, ac=ca, dad=ab5, cbc-1=dbd=b-1, dcd=c-1 >

Subgroups: 1020 in 188 conjugacy classes, 56 normal (44 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×5], C22, C22 [×2], C22 [×8], C5, S3 [×2], C6 [×3], C6 [×2], C2×C4 [×6], D4 [×6], C23, C23 [×2], D5, C10 [×3], C10 [×3], Dic3 [×2], C12 [×3], D6 [×6], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C22⋊C4 [×2], C4⋊C4, C22×C4, C2×D4 [×3], Dic5 [×2], Dic5 [×2], C20, D10 [×3], C2×C10, C2×C10 [×2], C2×C10 [×5], D12 [×2], C2×Dic3, C2×Dic3, C3⋊D4 [×4], C2×C12 [×4], C22×S3, C22×S3, C22×C6, C5×S3, D15, C30 [×3], C30 [×2], C4⋊D4, C2×Dic5 [×2], C2×Dic5 [×3], C5⋊D4 [×4], C2×C20, C5×D4 [×2], C22×D5, C22×C10, C22×C10, C4⋊Dic3, D6⋊C4 [×2], C2×D12, C2×C3⋊D4, C2×C3⋊D4, C22×C12, C5×Dic3, C3×Dic5 [×2], C3×Dic5, Dic15, S3×C10 [×3], D30 [×3], C2×C30, C2×C30 [×2], C2×C30 [×2], C10.D4, D10⋊C4, C23.D5, C22×Dic5, C2×C5⋊D4 [×2], D4×C10, C127D4, C5⋊D12 [×2], C6×Dic5 [×2], C6×Dic5 [×2], C10×Dic3, C5×C3⋊D4 [×2], C2×Dic15, C157D4 [×2], S3×C2×C10, C22×D15, C22×C30, Dic5⋊D4, D6⋊Dic5, D304C4, C30.Q8, C2×C5⋊D12, C2×C6×Dic5, C10×C3⋊D4, C2×C157D4, (C2×C10)⋊4D12
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×4], C23, D5, D6 [×3], C2×D4 [×2], C4○D4, D10 [×3], D12 [×2], C3⋊D4 [×2], C22×S3, C4⋊D4, C5⋊D4 [×2], C22×D5, C2×D12, C4○D12, C2×C3⋊D4, S3×D5, D4×D5, D42D5, C2×C5⋊D4, C127D4, C5⋊D12 [×2], C2×S3×D5, Dic5⋊D4, Dic3.D10, C2×C5⋊D12, D5×C3⋊D4, (C2×C10)⋊4D12

Smallest permutation representation of (C2×C10)⋊4D12
On 240 points
Generators in S240
(25 106)(26 107)(27 108)(28 97)(29 98)(30 99)(31 100)(32 101)(33 102)(34 103)(35 104)(36 105)(49 77)(50 78)(51 79)(52 80)(53 81)(54 82)(55 83)(56 84)(57 73)(58 74)(59 75)(60 76)(61 153)(62 154)(63 155)(64 156)(65 145)(66 146)(67 147)(68 148)(69 149)(70 150)(71 151)(72 152)(121 190)(122 191)(123 192)(124 181)(125 182)(126 183)(127 184)(128 185)(129 186)(130 187)(131 188)(132 189)(157 227)(158 228)(159 217)(160 218)(161 219)(162 220)(163 221)(164 222)(165 223)(166 224)(167 225)(168 226)
(1 238 211 94 42 173 112 202 140 24)(2 13 141 203 113 174 43 95 212 239)(3 240 213 96 44 175 114 204 142 14)(4 15 143 193 115 176 45 85 214 229)(5 230 215 86 46 177 116 194 144 16)(6 17 133 195 117 178 47 87 216 231)(7 232 205 88 48 179 118 196 134 18)(8 19 135 197 119 180 37 89 206 233)(9 234 207 90 38 169 120 198 136 20)(10 21 137 199 109 170 39 91 208 235)(11 236 209 92 40 171 110 200 138 22)(12 23 139 201 111 172 41 93 210 237)(25 80 163 131 61 106 52 221 188 153)(26 154 189 222 53 107 62 132 164 81)(27 82 165 121 63 108 54 223 190 155)(28 156 191 224 55 97 64 122 166 83)(29 84 167 123 65 98 56 225 192 145)(30 146 181 226 57 99 66 124 168 73)(31 74 157 125 67 100 58 227 182 147)(32 148 183 228 59 101 68 126 158 75)(33 76 159 127 69 102 60 217 184 149)(34 150 185 218 49 103 70 128 160 77)(35 78 161 129 71 104 50 219 186 151)(36 152 187 220 51 105 72 130 162 79)
(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)
(1 181)(2 192)(3 191)(4 190)(5 189)(6 188)(7 187)(8 186)(9 185)(10 184)(11 183)(12 182)(13 225)(14 224)(15 223)(16 222)(17 221)(18 220)(19 219)(20 218)(21 217)(22 228)(23 227)(24 226)(25 216)(26 215)(27 214)(28 213)(29 212)(30 211)(31 210)(32 209)(33 208)(34 207)(35 206)(36 205)(37 161)(38 160)(39 159)(40 158)(41 157)(42 168)(43 167)(44 166)(45 165)(46 164)(47 163)(48 162)(49 136)(50 135)(51 134)(52 133)(53 144)(54 143)(55 142)(56 141)(57 140)(58 139)(59 138)(60 137)(61 117)(62 116)(63 115)(64 114)(65 113)(66 112)(67 111)(68 110)(69 109)(70 120)(71 119)(72 118)(73 94)(74 93)(75 92)(76 91)(77 90)(78 89)(79 88)(80 87)(81 86)(82 85)(83 96)(84 95)(97 204)(98 203)(99 202)(100 201)(101 200)(102 199)(103 198)(104 197)(105 196)(106 195)(107 194)(108 193)(121 176)(122 175)(123 174)(124 173)(125 172)(126 171)(127 170)(128 169)(129 180)(130 179)(131 178)(132 177)(145 239)(146 238)(147 237)(148 236)(149 235)(150 234)(151 233)(152 232)(153 231)(154 230)(155 229)(156 240)

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

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

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

66 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B4C4D4E4F5A5B6A···6G10A···10F10G10H10I10J10K10L10M10N12A···12H15A15B20A20B20C20D30A···30N
order122222223444444556···610···10101010101010101012···1215152020202030···30
size11112212602101010101260222···22···244441212121210···1044121212124···4

66 irreducible representations

dim11111111222222222222224444444
type++++++++++++++++++++-++
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6C4○D4D10D10D10C3⋊D4D12C5⋊D4C4○D12S3×D5D4×D5D42D5C5⋊D12C2×S3×D5Dic3.D10D5×C3⋊D4
kernel(C2×C10)⋊4D12D6⋊Dic5D304C4C30.Q8C2×C5⋊D12C2×C6×Dic5C10×C3⋊D4C2×C157D4C22×Dic5C3×Dic5C2×C30C2×C3⋊D4C2×Dic5C22×C10C30C2×Dic3C22×S3C22×C6Dic5C2×C10C2×C6C10C23C6C6C22C22C2C2
# reps11111111122221222244842224244

Matrix representation of (C2×C10)⋊4D12 in GL6(𝔽61)

100000
010000
0011700
0006000
000010
000001
,
18180000
43600000
0060000
0006000
000010
000001
,
3490000
7270000
0011400
0005000
0000290
00004740
,
47550000
2140000
00215900
00374000
00005315
000088

G:=sub<GL(6,GF(61))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,17,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[18,43,0,0,0,0,18,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[34,7,0,0,0,0,9,27,0,0,0,0,0,0,11,0,0,0,0,0,4,50,0,0,0,0,0,0,29,47,0,0,0,0,0,40],[47,2,0,0,0,0,55,14,0,0,0,0,0,0,21,37,0,0,0,0,59,40,0,0,0,0,0,0,53,8,0,0,0,0,15,8] >;

(C2×C10)⋊4D12 in GAP, Magma, Sage, TeX

(C_2\times C_{10})\rtimes_4D_{12}
% in TeX

G:=Group("(C2xC10):4D12");
// GroupNames label

G:=SmallGroup(480,642);
// by ID

G=gap.SmallGroup(480,642);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,219,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^10=c^12=d^2=1,a*b=b*a,a*c=c*a,d*a*d=a*b^5,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations

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