direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C30.38D4, C24.2D15, C23⋊3Dic15, C23.30D30, (C23×C6).2D5, (C22×C30)⋊12C4, (C2×C30).151D4, C30.394(C2×D4), (C23×C30).2C2, (C23×C10).4S3, C6⋊2(C23.D5), (C22×C6)⋊4Dic5, C30⋊10(C22⋊C4), C22⋊3(C2×Dic15), C10⋊3(C6.D4), C30.218(C22×C4), (C2×C30).316C23, (C22×Dic15)⋊7C2, (C22×C10)⋊10Dic3, (C22×C6).122D10, (C22×C10).140D6, C6.29(C22×Dic5), C2.9(C22×Dic15), (C2×Dic15)⋊24C22, C22.25(C15⋊7D4), C10.42(C22×Dic3), C22.27(C22×D15), (C22×C30).145C22, (C2×C30)⋊40(C2×C4), C3⋊3(C2×C23.D5), C15⋊20(C2×C22⋊C4), (C2×C6)⋊8(C2×Dic5), C5⋊4(C2×C6.D4), C2.4(C2×C15⋊7D4), C6.121(C2×C5⋊D4), (C2×C10)⋊15(C2×Dic3), (C2×C6).83(C5⋊D4), C10.121(C2×C3⋊D4), (C2×C10).83(C3⋊D4), (C2×C6).312(C22×D5), (C2×C10).311(C22×S3), SmallGroup(480,917)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C30.38D4
G = < a,b,c,d | a2=b30=c4=1, d2=b15, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b15c-1 >
Subgroups: 916 in 264 conjugacy classes, 119 normal (21 characteristic)
C1, C2, C2 [×6], C2 [×4], C3, C4 [×4], C22, C22 [×10], C22 [×12], C5, C6, C6 [×6], C6 [×4], C2×C4 [×8], C23, C23 [×6], C23 [×4], C10, C10 [×6], C10 [×4], Dic3 [×4], C2×C6, C2×C6 [×10], C2×C6 [×12], C15, C22⋊C4 [×4], C22×C4 [×2], C24, Dic5 [×4], C2×C10, C2×C10 [×10], C2×C10 [×12], C2×Dic3 [×8], C22×C6, C22×C6 [×6], C22×C6 [×4], C30, C30 [×6], C30 [×4], C2×C22⋊C4, C2×Dic5 [×8], C22×C10, C22×C10 [×6], C22×C10 [×4], C6.D4 [×4], C22×Dic3 [×2], C23×C6, Dic15 [×4], C2×C30, C2×C30 [×10], C2×C30 [×12], C23.D5 [×4], C22×Dic5 [×2], C23×C10, C2×C6.D4, C2×Dic15 [×4], C2×Dic15 [×4], C22×C30, C22×C30 [×6], C22×C30 [×4], C2×C23.D5, C30.38D4 [×4], C22×Dic15 [×2], C23×C30, C2×C30.38D4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], D4 [×4], C23, D5, Dic3 [×4], D6 [×3], C22⋊C4 [×4], C22×C4, C2×D4 [×2], Dic5 [×4], D10 [×3], C2×Dic3 [×6], C3⋊D4 [×4], C22×S3, D15, C2×C22⋊C4, C2×Dic5 [×6], C5⋊D4 [×4], C22×D5, C6.D4 [×4], C22×Dic3, C2×C3⋊D4 [×2], Dic15 [×4], D30 [×3], C23.D5 [×4], C22×Dic5, C2×C5⋊D4 [×2], C2×C6.D4, C2×Dic15 [×6], C15⋊7D4 [×4], C22×D15, C2×C23.D5, C30.38D4 [×4], C22×Dic15, C2×C15⋊7D4 [×2], C2×C30.38D4
►On 240 points
Generators in S240
(1 182)(2 183)(3 184)(4 185)(5 186)(6 187)(7 188)(8 189)(9 190)(10 191)(11 192)(12 193)(13 194)(14 195)(15 196)(16 197)(17 198)(18 199)(19 200)(20 201)(21 202)(22 203)(23 204)(24 205)(25 206)(26 207)(27 208)(28 209)(29 210)(30 181)(31 109)(32 110)(33 111)(34 112)(35 113)(36 114)(37 115)(38 116)(39 117)(40 118)(41 119)(42 120)(43 91)(44 92)(45 93)(46 94)(47 95)(48 96)(49 97)(50 98)(51 99)(52 100)(53 101)(54 102)(55 103)(56 104)(57 105)(58 106)(59 107)(60 108)(61 153)(62 154)(63 155)(64 156)(65 157)(66 158)(67 159)(68 160)(69 161)(70 162)(71 163)(72 164)(73 165)(74 166)(75 167)(76 168)(77 169)(78 170)(79 171)(80 172)(81 173)(82 174)(83 175)(84 176)(85 177)(86 178)(87 179)(88 180)(89 151)(90 152)(121 212)(122 213)(123 214)(124 215)(125 216)(126 217)(127 218)(128 219)(129 220)(130 221)(131 222)(132 223)(133 224)(134 225)(135 226)(136 227)(137 228)(138 229)(139 230)(140 231)(141 232)(142 233)(143 234)(144 235)(145 236)(146 237)(147 238)(148 239)(149 240)(150 211)
(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)
(1 128 95 176)(2 127 96 175)(3 126 97 174)(4 125 98 173)(5 124 99 172)(6 123 100 171)(7 122 101 170)(8 121 102 169)(9 150 103 168)(10 149 104 167)(11 148 105 166)(12 147 106 165)(13 146 107 164)(14 145 108 163)(15 144 109 162)(16 143 110 161)(17 142 111 160)(18 141 112 159)(19 140 113 158)(20 139 114 157)(21 138 115 156)(22 137 116 155)(23 136 117 154)(24 135 118 153)(25 134 119 152)(26 133 120 151)(27 132 91 180)(28 131 92 179)(29 130 93 178)(30 129 94 177)(31 70 196 235)(32 69 197 234)(33 68 198 233)(34 67 199 232)(35 66 200 231)(36 65 201 230)(37 64 202 229)(38 63 203 228)(39 62 204 227)(40 61 205 226)(41 90 206 225)(42 89 207 224)(43 88 208 223)(44 87 209 222)(45 86 210 221)(46 85 181 220)(47 84 182 219)(48 83 183 218)(49 82 184 217)(50 81 185 216)(51 80 186 215)(52 79 187 214)(53 78 188 213)(54 77 189 212)(55 76 190 211)(56 75 191 240)(57 74 192 239)(58 73 193 238)(59 72 194 237)(60 71 195 236)
(1 234 16 219)(2 233 17 218)(3 232 18 217)(4 231 19 216)(5 230 20 215)(6 229 21 214)(7 228 22 213)(8 227 23 212)(9 226 24 211)(10 225 25 240)(11 224 26 239)(12 223 27 238)(13 222 28 237)(14 221 29 236)(15 220 30 235)(31 177 46 162)(32 176 47 161)(33 175 48 160)(34 174 49 159)(35 173 50 158)(36 172 51 157)(37 171 52 156)(38 170 53 155)(39 169 54 154)(40 168 55 153)(41 167 56 152)(42 166 57 151)(43 165 58 180)(44 164 59 179)(45 163 60 178)(61 118 76 103)(62 117 77 102)(63 116 78 101)(64 115 79 100)(65 114 80 99)(66 113 81 98)(67 112 82 97)(68 111 83 96)(69 110 84 95)(70 109 85 94)(71 108 86 93)(72 107 87 92)(73 106 88 91)(74 105 89 120)(75 104 90 119)(121 189 136 204)(122 188 137 203)(123 187 138 202)(124 186 139 201)(125 185 140 200)(126 184 141 199)(127 183 142 198)(128 182 143 197)(129 181 144 196)(130 210 145 195)(131 209 146 194)(132 208 147 193)(133 207 148 192)(134 206 149 191)(135 205 150 190)
G:=sub<Sym(240)| (1,182)(2,183)(3,184)(4,185)(5,186)(6,187)(7,188)(8,189)(9,190)(10,191)(11,192)(12,193)(13,194)(14,195)(15,196)(16,197)(17,198)(18,199)(19,200)(20,201)(21,202)(22,203)(23,204)(24,205)(25,206)(26,207)(27,208)(28,209)(29,210)(30,181)(31,109)(32,110)(33,111)(34,112)(35,113)(36,114)(37,115)(38,116)(39,117)(40,118)(41,119)(42,120)(43,91)(44,92)(45,93)(46,94)(47,95)(48,96)(49,97)(50,98)(51,99)(52,100)(53,101)(54,102)(55,103)(56,104)(57,105)(58,106)(59,107)(60,108)(61,153)(62,154)(63,155)(64,156)(65,157)(66,158)(67,159)(68,160)(69,161)(70,162)(71,163)(72,164)(73,165)(74,166)(75,167)(76,168)(77,169)(78,170)(79,171)(80,172)(81,173)(82,174)(83,175)(84,176)(85,177)(86,178)(87,179)(88,180)(89,151)(90,152)(121,212)(122,213)(123,214)(124,215)(125,216)(126,217)(127,218)(128,219)(129,220)(130,221)(131,222)(132,223)(133,224)(134,225)(135,226)(136,227)(137,228)(138,229)(139,230)(140,231)(141,232)(142,233)(143,234)(144,235)(145,236)(146,237)(147,238)(148,239)(149,240)(150,211), (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), (1,128,95,176)(2,127,96,175)(3,126,97,174)(4,125,98,173)(5,124,99,172)(6,123,100,171)(7,122,101,170)(8,121,102,169)(9,150,103,168)(10,149,104,167)(11,148,105,166)(12,147,106,165)(13,146,107,164)(14,145,108,163)(15,144,109,162)(16,143,110,161)(17,142,111,160)(18,141,112,159)(19,140,113,158)(20,139,114,157)(21,138,115,156)(22,137,116,155)(23,136,117,154)(24,135,118,153)(25,134,119,152)(26,133,120,151)(27,132,91,180)(28,131,92,179)(29,130,93,178)(30,129,94,177)(31,70,196,235)(32,69,197,234)(33,68,198,233)(34,67,199,232)(35,66,200,231)(36,65,201,230)(37,64,202,229)(38,63,203,228)(39,62,204,227)(40,61,205,226)(41,90,206,225)(42,89,207,224)(43,88,208,223)(44,87,209,222)(45,86,210,221)(46,85,181,220)(47,84,182,219)(48,83,183,218)(49,82,184,217)(50,81,185,216)(51,80,186,215)(52,79,187,214)(53,78,188,213)(54,77,189,212)(55,76,190,211)(56,75,191,240)(57,74,192,239)(58,73,193,238)(59,72,194,237)(60,71,195,236), (1,234,16,219)(2,233,17,218)(3,232,18,217)(4,231,19,216)(5,230,20,215)(6,229,21,214)(7,228,22,213)(8,227,23,212)(9,226,24,211)(10,225,25,240)(11,224,26,239)(12,223,27,238)(13,222,28,237)(14,221,29,236)(15,220,30,235)(31,177,46,162)(32,176,47,161)(33,175,48,160)(34,174,49,159)(35,173,50,158)(36,172,51,157)(37,171,52,156)(38,170,53,155)(39,169,54,154)(40,168,55,153)(41,167,56,152)(42,166,57,151)(43,165,58,180)(44,164,59,179)(45,163,60,178)(61,118,76,103)(62,117,77,102)(63,116,78,101)(64,115,79,100)(65,114,80,99)(66,113,81,98)(67,112,82,97)(68,111,83,96)(69,110,84,95)(70,109,85,94)(71,108,86,93)(72,107,87,92)(73,106,88,91)(74,105,89,120)(75,104,90,119)(121,189,136,204)(122,188,137,203)(123,187,138,202)(124,186,139,201)(125,185,140,200)(126,184,141,199)(127,183,142,198)(128,182,143,197)(129,181,144,196)(130,210,145,195)(131,209,146,194)(132,208,147,193)(133,207,148,192)(134,206,149,191)(135,205,150,190)>;
G:=Group( (1,182)(2,183)(3,184)(4,185)(5,186)(6,187)(7,188)(8,189)(9,190)(10,191)(11,192)(12,193)(13,194)(14,195)(15,196)(16,197)(17,198)(18,199)(19,200)(20,201)(21,202)(22,203)(23,204)(24,205)(25,206)(26,207)(27,208)(28,209)(29,210)(30,181)(31,109)(32,110)(33,111)(34,112)(35,113)(36,114)(37,115)(38,116)(39,117)(40,118)(41,119)(42,120)(43,91)(44,92)(45,93)(46,94)(47,95)(48,96)(49,97)(50,98)(51,99)(52,100)(53,101)(54,102)(55,103)(56,104)(57,105)(58,106)(59,107)(60,108)(61,153)(62,154)(63,155)(64,156)(65,157)(66,158)(67,159)(68,160)(69,161)(70,162)(71,163)(72,164)(73,165)(74,166)(75,167)(76,168)(77,169)(78,170)(79,171)(80,172)(81,173)(82,174)(83,175)(84,176)(85,177)(86,178)(87,179)(88,180)(89,151)(90,152)(121,212)(122,213)(123,214)(124,215)(125,216)(126,217)(127,218)(128,219)(129,220)(130,221)(131,222)(132,223)(133,224)(134,225)(135,226)(136,227)(137,228)(138,229)(139,230)(140,231)(141,232)(142,233)(143,234)(144,235)(145,236)(146,237)(147,238)(148,239)(149,240)(150,211), (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), (1,128,95,176)(2,127,96,175)(3,126,97,174)(4,125,98,173)(5,124,99,172)(6,123,100,171)(7,122,101,170)(8,121,102,169)(9,150,103,168)(10,149,104,167)(11,148,105,166)(12,147,106,165)(13,146,107,164)(14,145,108,163)(15,144,109,162)(16,143,110,161)(17,142,111,160)(18,141,112,159)(19,140,113,158)(20,139,114,157)(21,138,115,156)(22,137,116,155)(23,136,117,154)(24,135,118,153)(25,134,119,152)(26,133,120,151)(27,132,91,180)(28,131,92,179)(29,130,93,178)(30,129,94,177)(31,70,196,235)(32,69,197,234)(33,68,198,233)(34,67,199,232)(35,66,200,231)(36,65,201,230)(37,64,202,229)(38,63,203,228)(39,62,204,227)(40,61,205,226)(41,90,206,225)(42,89,207,224)(43,88,208,223)(44,87,209,222)(45,86,210,221)(46,85,181,220)(47,84,182,219)(48,83,183,218)(49,82,184,217)(50,81,185,216)(51,80,186,215)(52,79,187,214)(53,78,188,213)(54,77,189,212)(55,76,190,211)(56,75,191,240)(57,74,192,239)(58,73,193,238)(59,72,194,237)(60,71,195,236), (1,234,16,219)(2,233,17,218)(3,232,18,217)(4,231,19,216)(5,230,20,215)(6,229,21,214)(7,228,22,213)(8,227,23,212)(9,226,24,211)(10,225,25,240)(11,224,26,239)(12,223,27,238)(13,222,28,237)(14,221,29,236)(15,220,30,235)(31,177,46,162)(32,176,47,161)(33,175,48,160)(34,174,49,159)(35,173,50,158)(36,172,51,157)(37,171,52,156)(38,170,53,155)(39,169,54,154)(40,168,55,153)(41,167,56,152)(42,166,57,151)(43,165,58,180)(44,164,59,179)(45,163,60,178)(61,118,76,103)(62,117,77,102)(63,116,78,101)(64,115,79,100)(65,114,80,99)(66,113,81,98)(67,112,82,97)(68,111,83,96)(69,110,84,95)(70,109,85,94)(71,108,86,93)(72,107,87,92)(73,106,88,91)(74,105,89,120)(75,104,90,119)(121,189,136,204)(122,188,137,203)(123,187,138,202)(124,186,139,201)(125,185,140,200)(126,184,141,199)(127,183,142,198)(128,182,143,197)(129,181,144,196)(130,210,145,195)(131,209,146,194)(132,208,147,193)(133,207,148,192)(134,206,149,191)(135,205,150,190) );
G=PermutationGroup([(1,182),(2,183),(3,184),(4,185),(5,186),(6,187),(7,188),(8,189),(9,190),(10,191),(11,192),(12,193),(13,194),(14,195),(15,196),(16,197),(17,198),(18,199),(19,200),(20,201),(21,202),(22,203),(23,204),(24,205),(25,206),(26,207),(27,208),(28,209),(29,210),(30,181),(31,109),(32,110),(33,111),(34,112),(35,113),(36,114),(37,115),(38,116),(39,117),(40,118),(41,119),(42,120),(43,91),(44,92),(45,93),(46,94),(47,95),(48,96),(49,97),(50,98),(51,99),(52,100),(53,101),(54,102),(55,103),(56,104),(57,105),(58,106),(59,107),(60,108),(61,153),(62,154),(63,155),(64,156),(65,157),(66,158),(67,159),(68,160),(69,161),(70,162),(71,163),(72,164),(73,165),(74,166),(75,167),(76,168),(77,169),(78,170),(79,171),(80,172),(81,173),(82,174),(83,175),(84,176),(85,177),(86,178),(87,179),(88,180),(89,151),(90,152),(121,212),(122,213),(123,214),(124,215),(125,216),(126,217),(127,218),(128,219),(129,220),(130,221),(131,222),(132,223),(133,224),(134,225),(135,226),(136,227),(137,228),(138,229),(139,230),(140,231),(141,232),(142,233),(143,234),(144,235),(145,236),(146,237),(147,238),(148,239),(149,240),(150,211)], [(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)], [(1,128,95,176),(2,127,96,175),(3,126,97,174),(4,125,98,173),(5,124,99,172),(6,123,100,171),(7,122,101,170),(8,121,102,169),(9,150,103,168),(10,149,104,167),(11,148,105,166),(12,147,106,165),(13,146,107,164),(14,145,108,163),(15,144,109,162),(16,143,110,161),(17,142,111,160),(18,141,112,159),(19,140,113,158),(20,139,114,157),(21,138,115,156),(22,137,116,155),(23,136,117,154),(24,135,118,153),(25,134,119,152),(26,133,120,151),(27,132,91,180),(28,131,92,179),(29,130,93,178),(30,129,94,177),(31,70,196,235),(32,69,197,234),(33,68,198,233),(34,67,199,232),(35,66,200,231),(36,65,201,230),(37,64,202,229),(38,63,203,228),(39,62,204,227),(40,61,205,226),(41,90,206,225),(42,89,207,224),(43,88,208,223),(44,87,209,222),(45,86,210,221),(46,85,181,220),(47,84,182,219),(48,83,183,218),(49,82,184,217),(50,81,185,216),(51,80,186,215),(52,79,187,214),(53,78,188,213),(54,77,189,212),(55,76,190,211),(56,75,191,240),(57,74,192,239),(58,73,193,238),(59,72,194,237),(60,71,195,236)], [(1,234,16,219),(2,233,17,218),(3,232,18,217),(4,231,19,216),(5,230,20,215),(6,229,21,214),(7,228,22,213),(8,227,23,212),(9,226,24,211),(10,225,25,240),(11,224,26,239),(12,223,27,238),(13,222,28,237),(14,221,29,236),(15,220,30,235),(31,177,46,162),(32,176,47,161),(33,175,48,160),(34,174,49,159),(35,173,50,158),(36,172,51,157),(37,171,52,156),(38,170,53,155),(39,169,54,154),(40,168,55,153),(41,167,56,152),(42,166,57,151),(43,165,58,180),(44,164,59,179),(45,163,60,178),(61,118,76,103),(62,117,77,102),(63,116,78,101),(64,115,79,100),(65,114,80,99),(66,113,81,98),(67,112,82,97),(68,111,83,96),(69,110,84,95),(70,109,85,94),(71,108,86,93),(72,107,87,92),(73,106,88,91),(74,105,89,120),(75,104,90,119),(121,189,136,204),(122,188,137,203),(123,187,138,202),(124,186,139,201),(125,185,140,200),(126,184,141,199),(127,183,142,198),(128,182,143,197),(129,181,144,196),(130,210,145,195),(131,209,146,194),(132,208,147,193),(133,207,148,192),(134,206,149,191),(135,205,150,190)])
132 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 3 | 4A | ··· | 4H | 5A | 5B | 6A | ··· | 6O | 10A | ··· | 10AD | 15A | 15B | 15C | 15D | 30A | ··· | 30BH |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 3 | 4 | ··· | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 15 | 15 | 15 | 15 | 30 | ··· | 30 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 30 | ··· | 30 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 |
132 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | - | + | - | + | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C4 | S3 | D4 | D5 | Dic3 | D6 | Dic5 | D10 | C3⋊D4 | D15 | C5⋊D4 | Dic15 | D30 | C15⋊7D4 |
| kernel | C2×C30.38D4 | C30.38D4 | C22×Dic15 | C23×C30 | C22×C30 | C23×C10 | C2×C30 | C23×C6 | C22×C10 | C22×C10 | C22×C6 | C22×C6 | C2×C10 | C24 | C2×C6 | C23 | C23 | C22 |
| # reps | 1 | 4 | 2 | 1 | 8 | 1 | 4 | 2 | 4 | 3 | 8 | 6 | 8 | 4 | 16 | 16 | 12 | 32 |
Matrix representation of C2×C30.38D4 ►in GL6(𝔽61)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 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 |
| 20 | 0 | 0 | 0 | 0 | 0 |
| 59 | 58 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 60 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 0 |
| 0 | 0 | 0 | 0 | 22 | 48 |
| 28 | 17 | 0 | 0 | 0 | 0 |
| 22 | 33 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 22 | 0 | 0 |
| 0 | 0 | 47 | 59 | 0 | 0 |
| 0 | 0 | 0 | 0 | 56 | 20 |
| 0 | 0 | 0 | 0 | 11 | 5 |
| 33 | 44 | 0 | 0 | 0 | 0 |
| 3 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 59 | 39 | 0 | 0 |
| 0 | 0 | 14 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 56 | 20 |
| 0 | 0 | 0 | 0 | 17 | 5 |
G:=sub<GL(6,GF(61))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[20,59,0,0,0,0,0,58,0,0,0,0,0,0,43,1,0,0,0,0,60,0,0,0,0,0,0,0,14,22,0,0,0,0,0,48],[28,22,0,0,0,0,17,33,0,0,0,0,0,0,2,47,0,0,0,0,22,59,0,0,0,0,0,0,56,11,0,0,0,0,20,5],[33,3,0,0,0,0,44,28,0,0,0,0,0,0,59,14,0,0,0,0,39,2,0,0,0,0,0,0,56,17,0,0,0,0,20,5] >;
C2×C30.38D4 in GAP, Magma, Sage, TeX
C_2\times C_{30}._{38}D_4 % in TeX
G:=Group("C2xC30.38D4"); // GroupNames label
G:=SmallGroup(480,917);
// by ID
G=gap.SmallGroup(480,917);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,422,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^30=c^4=1,d^2=b^15,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^15*c^-1>;
// generators/relations