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G = C2×D303C4order 480 = 25·3·5

Direct product of C2 and D303C4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×D303C4, C22.16D60, C23.37D30, (C2×C4)⋊8D30, (C2×C20)⋊32D6, C2.3(C2×D60), C103(D6⋊C4), D3028(C2×C4), (C2×C12)⋊32D10, (C22×C20)⋊8S3, (C22×C60)⋊5C2, C6.44(C2×D20), (C2×C6).23D20, (C22×C12)⋊4D5, (C22×C4)⋊3D15, C307(C22⋊C4), (C2×C60)⋊42C22, C10.45(C2×D12), (C2×C30).143D4, (C2×C10).23D12, C30.272(C2×D4), (C22×D15)⋊8C4, C62(D10⋊C4), (C23×D15).2C2, C22.17(C4×D15), C30.170(C22×C4), (C2×C30).301C23, (C22×Dic15)⋊3C2, (C22×C6).118D10, (C22×C10).136D6, (C2×Dic15)⋊23C22, C22.20(C157D4), C22.23(C22×D15), (C22×C30).141C22, (C22×D15).85C22, C54(C2×D6⋊C4), C6.75(C2×C4×D5), C2.19(C2×C4×D15), C33(C2×D10⋊C4), C1517(C2×C22⋊C4), C10.107(S3×C2×C4), (C2×C6).36(C4×D5), C2.2(C2×C157D4), C6.99(C2×C5⋊D4), (C2×C10).61(C4×S3), C10.99(C2×C3⋊D4), (C2×C30).142(C2×C4), (C2×C6).75(C5⋊D4), (C2×C10).75(C3⋊D4), (C2×C6).297(C22×D5), (C2×C10).296(C22×S3), SmallGroup(480,892)

Series: Derived Chief Lower central Upper central

C1C30 — C2×D303C4
C1C5C15C30C2×C30C22×D15C23×D15 — C2×D303C4
C15C30 — C2×D303C4
C1C23C22×C4

Generators and relations for C2×D303C4
 G = < a,b,c,d | a2=b30=c2=d4=1, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, dcd-1=b15c >

Subgroups: 1716 in 264 conjugacy classes, 95 normal (31 characteristic)
C1, C2 [×3], C2 [×4], C2 [×4], C3, C4 [×4], C22, C22 [×6], C22 [×16], C5, S3 [×4], C6 [×3], C6 [×4], C2×C4 [×2], C2×C4 [×6], C23, C23 [×10], D5 [×4], C10 [×3], C10 [×4], Dic3 [×2], C12 [×2], D6 [×16], C2×C6, C2×C6 [×6], C15, C22⋊C4 [×4], C22×C4, C22×C4, C24, Dic5 [×2], C20 [×2], D10 [×16], C2×C10, C2×C10 [×6], C2×Dic3 [×4], C2×C12 [×2], C2×C12 [×2], C22×S3 [×10], C22×C6, D15 [×4], C30 [×3], C30 [×4], C2×C22⋊C4, C2×Dic5 [×4], C2×C20 [×2], C2×C20 [×2], C22×D5 [×10], C22×C10, D6⋊C4 [×4], C22×Dic3, C22×C12, S3×C23, Dic15 [×2], C60 [×2], D30 [×4], D30 [×12], C2×C30, C2×C30 [×6], D10⋊C4 [×4], C22×Dic5, C22×C20, C23×D5, C2×D6⋊C4, C2×Dic15 [×2], C2×Dic15 [×2], C2×C60 [×2], C2×C60 [×2], C22×D15 [×6], C22×D15 [×4], C22×C30, C2×D10⋊C4, D303C4 [×4], C22×Dic15, C22×C60, C23×D15, C2×D303C4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], D4 [×4], C23, D5, D6 [×3], C22⋊C4 [×4], C22×C4, C2×D4 [×2], D10 [×3], C4×S3 [×2], D12 [×2], C3⋊D4 [×2], C22×S3, D15, C2×C22⋊C4, C4×D5 [×2], D20 [×2], C5⋊D4 [×2], C22×D5, D6⋊C4 [×4], S3×C2×C4, C2×D12, C2×C3⋊D4, D30 [×3], D10⋊C4 [×4], C2×C4×D5, C2×D20, C2×C5⋊D4, C2×D6⋊C4, C4×D15 [×2], D60 [×2], C157D4 [×2], C22×D15, C2×D10⋊C4, D303C4 [×4], C2×C4×D15, C2×D60, C2×C157D4, C2×D303C4

Smallest permutation representation of C2×D303C4
On 240 points
Generators in S240
(1 154)(2 155)(3 156)(4 157)(5 158)(6 159)(7 160)(8 161)(9 162)(10 163)(11 164)(12 165)(13 166)(14 167)(15 168)(16 169)(17 170)(18 171)(19 172)(20 173)(21 174)(22 175)(23 176)(24 177)(25 178)(26 179)(27 180)(28 151)(29 152)(30 153)(31 132)(32 133)(33 134)(34 135)(35 136)(36 137)(37 138)(38 139)(39 140)(40 141)(41 142)(42 143)(43 144)(44 145)(45 146)(46 147)(47 148)(48 149)(49 150)(50 121)(51 122)(52 123)(53 124)(54 125)(55 126)(56 127)(57 128)(58 129)(59 130)(60 131)(61 212)(62 213)(63 214)(64 215)(65 216)(66 217)(67 218)(68 219)(69 220)(70 221)(71 222)(72 223)(73 224)(74 225)(75 226)(76 227)(77 228)(78 229)(79 230)(80 231)(81 232)(82 233)(83 234)(84 235)(85 236)(86 237)(87 238)(88 239)(89 240)(90 211)(91 196)(92 197)(93 198)(94 199)(95 200)(96 201)(97 202)(98 203)(99 204)(100 205)(101 206)(102 207)(103 208)(104 209)(105 210)(106 181)(107 182)(108 183)(109 184)(110 185)(111 186)(112 187)(113 188)(114 189)(115 190)(116 191)(117 192)(118 193)(119 194)(120 195)
(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)
(1 168)(2 167)(3 166)(4 165)(5 164)(6 163)(7 162)(8 161)(9 160)(10 159)(11 158)(12 157)(13 156)(14 155)(15 154)(16 153)(17 152)(18 151)(19 180)(20 179)(21 178)(22 177)(23 176)(24 175)(25 174)(26 173)(27 172)(28 171)(29 170)(30 169)(31 138)(32 137)(33 136)(34 135)(35 134)(36 133)(37 132)(38 131)(39 130)(40 129)(41 128)(42 127)(43 126)(44 125)(45 124)(46 123)(47 122)(48 121)(49 150)(50 149)(51 148)(52 147)(53 146)(54 145)(55 144)(56 143)(57 142)(58 141)(59 140)(60 139)(61 223)(62 222)(63 221)(64 220)(65 219)(66 218)(67 217)(68 216)(69 215)(70 214)(71 213)(72 212)(73 211)(74 240)(75 239)(76 238)(77 237)(78 236)(79 235)(80 234)(81 233)(82 232)(83 231)(84 230)(85 229)(86 228)(87 227)(88 226)(89 225)(90 224)(91 209)(92 208)(93 207)(94 206)(95 205)(96 204)(97 203)(98 202)(99 201)(100 200)(101 199)(102 198)(103 197)(104 196)(105 195)(106 194)(107 193)(108 192)(109 191)(110 190)(111 189)(112 188)(113 187)(114 186)(115 185)(116 184)(117 183)(118 182)(119 181)(120 210)
(1 98 42 82)(2 99 43 83)(3 100 44 84)(4 101 45 85)(5 102 46 86)(6 103 47 87)(7 104 48 88)(8 105 49 89)(9 106 50 90)(10 107 51 61)(11 108 52 62)(12 109 53 63)(13 110 54 64)(14 111 55 65)(15 112 56 66)(16 113 57 67)(17 114 58 68)(18 115 59 69)(19 116 60 70)(20 117 31 71)(21 118 32 72)(22 119 33 73)(23 120 34 74)(24 91 35 75)(25 92 36 76)(26 93 37 77)(27 94 38 78)(28 95 39 79)(29 96 40 80)(30 97 41 81)(121 211 162 181)(122 212 163 182)(123 213 164 183)(124 214 165 184)(125 215 166 185)(126 216 167 186)(127 217 168 187)(128 218 169 188)(129 219 170 189)(130 220 171 190)(131 221 172 191)(132 222 173 192)(133 223 174 193)(134 224 175 194)(135 225 176 195)(136 226 177 196)(137 227 178 197)(138 228 179 198)(139 229 180 199)(140 230 151 200)(141 231 152 201)(142 232 153 202)(143 233 154 203)(144 234 155 204)(145 235 156 205)(146 236 157 206)(147 237 158 207)(148 238 159 208)(149 239 160 209)(150 240 161 210)

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

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

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

132 conjugacy classes

class 1 2A···2G2H2I2J2K 3 4A4B4C4D4E4F4G4H5A5B6A···6G10A···10N12A···12H15A15B15C15D20A···20P30A···30AB60A···60AF
order12···22222344444444556···610···1012···121515151520···2030···3060···60
size11···1303030302222230303030222···22···22···222222···22···22···2

132 irreducible representations

dim1111112222222222222222222
type++++++++++++++++++
imageC1C2C2C2C2C4S3D4D5D6D6D10D10C4×S3D12C3⋊D4D15C4×D5D20C5⋊D4D30D30C4×D15D60C157D4
kernelC2×D303C4D303C4C22×Dic15C22×C60C23×D15C22×D15C22×C20C2×C30C22×C12C2×C20C22×C10C2×C12C22×C6C2×C10C2×C10C2×C10C22×C4C2×C6C2×C6C2×C6C2×C4C23C22C22C22
# reps1411181422142444488884161616

Matrix representation of C2×D303C4 in GL6(𝔽61)

6000000
0600000
001000
000100
0000600
0000060
,
60600000
100000
0037800
0063100
0000369
00002214
,
110000
0600000
00254500
00393600
00003716
0000624
,
1100000
0110000
0011000
0001100
0000324
0000329

G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[60,1,0,0,0,0,60,0,0,0,0,0,0,0,37,6,0,0,0,0,8,31,0,0,0,0,0,0,36,22,0,0,0,0,9,14],[1,0,0,0,0,0,1,60,0,0,0,0,0,0,25,39,0,0,0,0,45,36,0,0,0,0,0,0,37,6,0,0,0,0,16,24],[11,0,0,0,0,0,0,11,0,0,0,0,0,0,11,0,0,0,0,0,0,11,0,0,0,0,0,0,32,3,0,0,0,0,4,29] >;

C2×D303C4 in GAP, Magma, Sage, TeX

C_2\times D_{30}\rtimes_3C_4
% in TeX

G:=Group("C2xD30:3C4");
// GroupNames label

G:=SmallGroup(480,892);
// by ID

G=gap.SmallGroup(480,892);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,422,58,2693,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^30=c^2=d^4=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,b*d=d*b,d*c*d^-1=b^15*c>;
// generators/relations

׿
×
𝔽