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G = (C2×C12).D10order 480 = 25·3·5

10th non-split extension by C2×C12 of D10 acting via D10/C5=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C4⋊Dic35D5, (C2×C20).222D6, (C2×C12).10D10, C6.Dic105C2, (C22×D5).6D6, C155(C422C2), (Dic3×Dic5)⋊9C2, D10⋊C4.7S3, C6.65(C4○D20), (C2×C30).51C23, C30.4Q817C2, (C2×Dic5).95D6, C54(C23.8D6), C30.106(C4○D4), C10.52(C4○D12), C6.21(D42D5), C10.6(D42S3), C2.9(D125D5), C2.9(D20⋊S3), (C2×C60).315C22, C6.25(Q82D5), (C2×Dic3).12D10, D10⋊Dic3.5C2, (C6×Dic5).29C22, C2.13(Dic5.D6), (C2×Dic15).53C22, (C10×Dic3).31C22, C34(C4⋊C4⋊D5), (C2×C4).34(S3×D5), (D5×C2×C6).4C22, (C5×C4⋊Dic3)⋊16C2, C22.138(C2×S3×D5), (C2×C6).63(C22×D5), (C2×C10).63(C22×S3), (C3×D10⋊C4).10C2, SmallGroup(480,437)

Series: Derived Chief Lower central Upper central

C1C2×C30 — (C2×C12).D10
C1C5C15C30C2×C30D5×C2×C6D10⋊Dic3 — (C2×C12).D10
C15C2×C30 — (C2×C12).D10
C1C22C2×C4

Generators and relations for (C2×C12).D10
 G = < a,b,c,d | a2=b12=1, c10=a, d2=ab6, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=ab-1, dcd-1=b6c9 >

Subgroups: 556 in 120 conjugacy classes, 44 normal (all characteristic)
C1, C2 [×3], C2, C3, C4 [×6], C22, C22 [×3], C5, C6 [×3], C6, C2×C4, C2×C4 [×5], C23, D5, C10 [×3], Dic3 [×4], C12 [×2], C2×C6, C2×C6 [×3], C15, C42, C22⋊C4 [×3], C4⋊C4 [×3], Dic5 [×3], C20 [×3], D10 [×3], C2×C10, C2×Dic3 [×2], C2×Dic3 [×2], C2×C12, C2×C12, C22×C6, C3×D5, C30 [×3], C422C2, C2×Dic5, C2×Dic5 [×2], C2×C20, C2×C20 [×2], C22×D5, C4×Dic3, Dic3⋊C4 [×2], C4⋊Dic3, C6.D4 [×2], C3×C22⋊C4, C5×Dic3 [×2], C3×Dic5, Dic15 [×2], C60, C6×D5 [×3], C2×C30, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, D10⋊C4 [×2], C5×C4⋊C4, C23.8D6, C6×Dic5, C10×Dic3 [×2], C2×Dic15 [×2], C2×C60, D5×C2×C6, C4⋊C4⋊D5, Dic3×Dic5, D10⋊Dic3 [×2], C6.Dic10, C3×D10⋊C4, C5×C4⋊Dic3, C30.4Q8, (C2×C12).D10
Quotients: C1, C2 [×7], C22 [×7], S3, C23, D5, D6 [×3], C4○D4 [×3], D10 [×3], C22×S3, C422C2, C22×D5, C4○D12, D42S3 [×2], S3×D5, C4○D20, D42D5, Q82D5, C23.8D6, C2×S3×D5, C4⋊C4⋊D5, D20⋊S3, D125D5, Dic5.D6, (C2×C12).D10

Smallest permutation representation of (C2×C12).D10
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 91)(82 92)(83 93)(84 94)(85 95)(86 96)(87 97)(88 98)(89 99)(90 100)(101 111)(102 112)(103 113)(104 114)(105 115)(106 116)(107 117)(108 118)(109 119)(110 120)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(127 137)(128 138)(129 139)(130 140)(141 151)(142 152)(143 153)(144 154)(145 155)(146 156)(147 157)(148 158)(149 159)(150 160)(161 171)(162 172)(163 173)(164 174)(165 175)(166 176)(167 177)(168 178)(169 179)(170 180)(181 191)(182 192)(183 193)(184 194)(185 195)(186 196)(187 197)(188 198)(189 199)(190 200)(201 211)(202 212)(203 213)(204 214)(205 215)(206 216)(207 217)(208 218)(209 219)(210 220)(221 231)(222 232)(223 233)(224 234)(225 235)(226 236)(227 237)(228 238)(229 239)(230 240)
(1 77 93 226 205 122 199 34 172 48 154 102)(2 103 155 49 173 35 200 123 206 227 94 78)(3 79 95 228 207 124 181 36 174 50 156 104)(4 105 157 51 175 37 182 125 208 229 96 80)(5 61 97 230 209 126 183 38 176 52 158 106)(6 107 159 53 177 39 184 127 210 231 98 62)(7 63 99 232 211 128 185 40 178 54 160 108)(8 109 141 55 179 21 186 129 212 233 100 64)(9 65 81 234 213 130 187 22 180 56 142 110)(10 111 143 57 161 23 188 131 214 235 82 66)(11 67 83 236 215 132 189 24 162 58 144 112)(12 113 145 59 163 25 190 133 216 237 84 68)(13 69 85 238 217 134 191 26 164 60 146 114)(14 115 147 41 165 27 192 135 218 239 86 70)(15 71 87 240 219 136 193 28 166 42 148 116)(16 117 149 43 167 29 194 137 220 221 88 72)(17 73 89 222 201 138 195 30 168 44 150 118)(18 119 151 45 169 31 196 139 202 223 90 74)(19 75 91 224 203 140 197 32 170 46 152 120)(20 101 153 47 171 33 198 121 204 225 92 76)
(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 10 189 198)(2 197 190 9)(3 8 191 196)(4 195 192 7)(5 6 193 194)(11 20 199 188)(12 187 200 19)(13 18 181 186)(14 185 182 17)(15 16 183 184)(21 79 74 26)(22 25 75 78)(23 77 76 24)(27 73 80 40)(28 39 61 72)(29 71 62 38)(30 37 63 70)(31 69 64 36)(32 35 65 68)(33 67 66 34)(41 222 229 54)(42 53 230 221)(43 240 231 52)(44 51 232 239)(45 238 233 50)(46 49 234 237)(47 236 235 48)(55 228 223 60)(56 59 224 227)(57 226 225 58)(81 94 170 163)(82 162 171 93)(83 92 172 161)(84 180 173 91)(85 90 174 179)(86 178 175 89)(87 88 176 177)(95 100 164 169)(96 168 165 99)(97 98 166 167)(101 132 131 102)(103 130 133 120)(104 119 134 129)(105 128 135 118)(106 117 136 127)(107 126 137 116)(108 115 138 125)(109 124 139 114)(110 113 140 123)(111 122 121 112)(141 217 202 156)(142 155 203 216)(143 215 204 154)(144 153 205 214)(145 213 206 152)(146 151 207 212)(147 211 208 150)(148 149 209 210)(157 201 218 160)(158 159 219 220)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E4F4G4H4I5A5B6A6B6C6D6E10A···10F12A12B12C12D15A15B20A20B20C20D20E···20L30A···30F60A···60H
order122223444444444556666610···101212121215152020202020···2030···3060···60
size11112024661010123030602222220202···244202044444412···124···44···4

60 irreducible representations

dim1111111222222222244444444
type++++++++++++++-+-++-
imageC1C2C2C2C2C2C2S3D5D6D6D6C4○D4D10D10C4○D12C4○D20D42S3S3×D5D42D5Q82D5C2×S3×D5D20⋊S3D125D5Dic5.D6
kernel(C2×C12).D10Dic3×Dic5D10⋊Dic3C6.Dic10C3×D10⋊C4C5×C4⋊Dic3C30.4Q8D10⋊C4C4⋊Dic3C2×Dic5C2×C20C22×D5C30C2×Dic3C2×C12C10C6C10C2×C4C6C6C22C2C2C2
# reps1121111121116424822222444

Matrix representation of (C2×C12).D10 in GL6(𝔽61)

6000000
0600000
0060000
0006000
000010
000001
,
11400000
0500000
00471600
00451400
0000215
00001260
,
60130000
2810000
00575700
0045000
00001950
0000542
,
1480000
0600000
00575700
0050400
00001950
0000542

G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[11,0,0,0,0,0,40,50,0,0,0,0,0,0,47,45,0,0,0,0,16,14,0,0,0,0,0,0,2,12,0,0,0,0,15,60],[60,28,0,0,0,0,13,1,0,0,0,0,0,0,57,4,0,0,0,0,57,50,0,0,0,0,0,0,19,5,0,0,0,0,50,42],[1,0,0,0,0,0,48,60,0,0,0,0,0,0,57,50,0,0,0,0,57,4,0,0,0,0,0,0,19,5,0,0,0,0,50,42] >;

(C2×C12).D10 in GAP, Magma, Sage, TeX

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

G:=Group("(C2xC12).D10");
// GroupNames label

G:=SmallGroup(480,437);
// by ID

G=gap.SmallGroup(480,437);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,64,254,219,100,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^12=1,c^10=a,d^2=a*b^6,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=a*b^-1,d*c*d^-1=b^6*c^9>;
// generators/relations

׿
×
𝔽