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, C2, C3, C4, C22, C22, C22, C5, C6, C6, C6, C2×C4, C23, C23, C23, C10, C10, C10, Dic3, C2×C6, C2×C6, C2×C6, C15, C22⋊C4, C22×C4, C24, Dic5, C2×C10, C2×C10, C2×C10, C2×Dic3, C22×C6, C22×C6, C22×C6, C30, C30, C30, C2×C22⋊C4, C2×Dic5, C22×C10, C22×C10, C22×C10, C6.D4, C22×Dic3, C23×C6, Dic15, C2×C30, C2×C30, C2×C30, C23.D5, C22×Dic5, C23×C10, C2×C6.D4, C2×Dic15, C2×Dic15, C22×C30, C22×C30, C22×C30, C2×C23.D5, C30.38D4, C22×Dic15, C23×C30, C2×C30.38D4
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, D5, Dic3, D6, C22⋊C4, C22×C4, C2×D4, Dic5, D10, C2×Dic3, C3⋊D4, C22×S3, D15, C2×C22⋊C4, C2×Dic5, C5⋊D4, C22×D5, C6.D4, C22×Dic3, C2×C3⋊D4, Dic15, D30, C23.D5, C22×Dic5, C2×C5⋊D4, C2×C6.D4, C2×Dic15, C15⋊7D4, C22×D15, C2×C23.D5, C30.38D4, C22×Dic15, C2×C15⋊7D4, C2×C30.38D4
►On 240 points
Generators in S240
(1 55)(2 56)(3 57)(4 58)(5 59)(6 60)(7 31)(8 32)(9 33)(10 34)(11 35)(12 36)(13 37)(14 38)(15 39)(16 40)(17 41)(18 42)(19 43)(20 44)(21 45)(22 46)(23 47)(24 48)(25 49)(26 50)(27 51)(28 52)(29 53)(30 54)(61 117)(62 118)(63 119)(64 120)(65 91)(66 92)(67 93)(68 94)(69 95)(70 96)(71 97)(72 98)(73 99)(74 100)(75 101)(76 102)(77 103)(78 104)(79 105)(80 106)(81 107)(82 108)(83 109)(84 110)(85 111)(86 112)(87 113)(88 114)(89 115)(90 116)(121 172)(122 173)(123 174)(124 175)(125 176)(126 177)(127 178)(128 179)(129 180)(130 151)(131 152)(132 153)(133 154)(134 155)(135 156)(136 157)(137 158)(138 159)(139 160)(140 161)(141 162)(142 163)(143 164)(144 165)(145 166)(146 167)(147 168)(148 169)(149 170)(150 171)(181 225)(182 226)(183 227)(184 228)(185 229)(186 230)(187 231)(188 232)(189 233)(190 234)(191 235)(192 236)(193 237)(194 238)(195 239)(196 240)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)
(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)
(1 223 123 88)(2 222 124 87)(3 221 125 86)(4 220 126 85)(5 219 127 84)(6 218 128 83)(7 217 129 82)(8 216 130 81)(9 215 131 80)(10 214 132 79)(11 213 133 78)(12 212 134 77)(13 211 135 76)(14 240 136 75)(15 239 137 74)(16 238 138 73)(17 237 139 72)(18 236 140 71)(19 235 141 70)(20 234 142 69)(21 233 143 68)(22 232 144 67)(23 231 145 66)(24 230 146 65)(25 229 147 64)(26 228 148 63)(27 227 149 62)(28 226 150 61)(29 225 121 90)(30 224 122 89)(31 203 180 108)(32 202 151 107)(33 201 152 106)(34 200 153 105)(35 199 154 104)(36 198 155 103)(37 197 156 102)(38 196 157 101)(39 195 158 100)(40 194 159 99)(41 193 160 98)(42 192 161 97)(43 191 162 96)(44 190 163 95)(45 189 164 94)(46 188 165 93)(47 187 166 92)(48 186 167 91)(49 185 168 120)(50 184 169 119)(51 183 170 118)(52 182 171 117)(53 181 172 116)(54 210 173 115)(55 209 174 114)(56 208 175 113)(57 207 176 112)(58 206 177 111)(59 205 178 110)(60 204 179 109)
(1 194 16 209)(2 193 17 208)(3 192 18 207)(4 191 19 206)(5 190 20 205)(6 189 21 204)(7 188 22 203)(8 187 23 202)(9 186 24 201)(10 185 25 200)(11 184 26 199)(12 183 27 198)(13 182 28 197)(14 181 29 196)(15 210 30 195)(31 232 46 217)(32 231 47 216)(33 230 48 215)(34 229 49 214)(35 228 50 213)(36 227 51 212)(37 226 52 211)(38 225 53 240)(39 224 54 239)(40 223 55 238)(41 222 56 237)(42 221 57 236)(43 220 58 235)(44 219 59 234)(45 218 60 233)(61 171 76 156)(62 170 77 155)(63 169 78 154)(64 168 79 153)(65 167 80 152)(66 166 81 151)(67 165 82 180)(68 164 83 179)(69 163 84 178)(70 162 85 177)(71 161 86 176)(72 160 87 175)(73 159 88 174)(74 158 89 173)(75 157 90 172)(91 146 106 131)(92 145 107 130)(93 144 108 129)(94 143 109 128)(95 142 110 127)(96 141 111 126)(97 140 112 125)(98 139 113 124)(99 138 114 123)(100 137 115 122)(101 136 116 121)(102 135 117 150)(103 134 118 149)(104 133 119 148)(105 132 120 147)
G:=sub<Sym(240)| (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,49)(26,50)(27,51)(28,52)(29,53)(30,54)(61,117)(62,118)(63,119)(64,120)(65,91)(66,92)(67,93)(68,94)(69,95)(70,96)(71,97)(72,98)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(85,111)(86,112)(87,113)(88,114)(89,115)(90,116)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)(127,178)(128,179)(129,180)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,161)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170)(150,171)(181,225)(182,226)(183,227)(184,228)(185,229)(186,230)(187,231)(188,232)(189,233)(190,234)(191,235)(192,236)(193,237)(194,238)(195,239)(196,240)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (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), (1,223,123,88)(2,222,124,87)(3,221,125,86)(4,220,126,85)(5,219,127,84)(6,218,128,83)(7,217,129,82)(8,216,130,81)(9,215,131,80)(10,214,132,79)(11,213,133,78)(12,212,134,77)(13,211,135,76)(14,240,136,75)(15,239,137,74)(16,238,138,73)(17,237,139,72)(18,236,140,71)(19,235,141,70)(20,234,142,69)(21,233,143,68)(22,232,144,67)(23,231,145,66)(24,230,146,65)(25,229,147,64)(26,228,148,63)(27,227,149,62)(28,226,150,61)(29,225,121,90)(30,224,122,89)(31,203,180,108)(32,202,151,107)(33,201,152,106)(34,200,153,105)(35,199,154,104)(36,198,155,103)(37,197,156,102)(38,196,157,101)(39,195,158,100)(40,194,159,99)(41,193,160,98)(42,192,161,97)(43,191,162,96)(44,190,163,95)(45,189,164,94)(46,188,165,93)(47,187,166,92)(48,186,167,91)(49,185,168,120)(50,184,169,119)(51,183,170,118)(52,182,171,117)(53,181,172,116)(54,210,173,115)(55,209,174,114)(56,208,175,113)(57,207,176,112)(58,206,177,111)(59,205,178,110)(60,204,179,109), (1,194,16,209)(2,193,17,208)(3,192,18,207)(4,191,19,206)(5,190,20,205)(6,189,21,204)(7,188,22,203)(8,187,23,202)(9,186,24,201)(10,185,25,200)(11,184,26,199)(12,183,27,198)(13,182,28,197)(14,181,29,196)(15,210,30,195)(31,232,46,217)(32,231,47,216)(33,230,48,215)(34,229,49,214)(35,228,50,213)(36,227,51,212)(37,226,52,211)(38,225,53,240)(39,224,54,239)(40,223,55,238)(41,222,56,237)(42,221,57,236)(43,220,58,235)(44,219,59,234)(45,218,60,233)(61,171,76,156)(62,170,77,155)(63,169,78,154)(64,168,79,153)(65,167,80,152)(66,166,81,151)(67,165,82,180)(68,164,83,179)(69,163,84,178)(70,162,85,177)(71,161,86,176)(72,160,87,175)(73,159,88,174)(74,158,89,173)(75,157,90,172)(91,146,106,131)(92,145,107,130)(93,144,108,129)(94,143,109,128)(95,142,110,127)(96,141,111,126)(97,140,112,125)(98,139,113,124)(99,138,114,123)(100,137,115,122)(101,136,116,121)(102,135,117,150)(103,134,118,149)(104,133,119,148)(105,132,120,147)>;
G:=Group( (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,49)(26,50)(27,51)(28,52)(29,53)(30,54)(61,117)(62,118)(63,119)(64,120)(65,91)(66,92)(67,93)(68,94)(69,95)(70,96)(71,97)(72,98)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(85,111)(86,112)(87,113)(88,114)(89,115)(90,116)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)(127,178)(128,179)(129,180)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,161)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170)(150,171)(181,225)(182,226)(183,227)(184,228)(185,229)(186,230)(187,231)(188,232)(189,233)(190,234)(191,235)(192,236)(193,237)(194,238)(195,239)(196,240)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (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), (1,223,123,88)(2,222,124,87)(3,221,125,86)(4,220,126,85)(5,219,127,84)(6,218,128,83)(7,217,129,82)(8,216,130,81)(9,215,131,80)(10,214,132,79)(11,213,133,78)(12,212,134,77)(13,211,135,76)(14,240,136,75)(15,239,137,74)(16,238,138,73)(17,237,139,72)(18,236,140,71)(19,235,141,70)(20,234,142,69)(21,233,143,68)(22,232,144,67)(23,231,145,66)(24,230,146,65)(25,229,147,64)(26,228,148,63)(27,227,149,62)(28,226,150,61)(29,225,121,90)(30,224,122,89)(31,203,180,108)(32,202,151,107)(33,201,152,106)(34,200,153,105)(35,199,154,104)(36,198,155,103)(37,197,156,102)(38,196,157,101)(39,195,158,100)(40,194,159,99)(41,193,160,98)(42,192,161,97)(43,191,162,96)(44,190,163,95)(45,189,164,94)(46,188,165,93)(47,187,166,92)(48,186,167,91)(49,185,168,120)(50,184,169,119)(51,183,170,118)(52,182,171,117)(53,181,172,116)(54,210,173,115)(55,209,174,114)(56,208,175,113)(57,207,176,112)(58,206,177,111)(59,205,178,110)(60,204,179,109), (1,194,16,209)(2,193,17,208)(3,192,18,207)(4,191,19,206)(5,190,20,205)(6,189,21,204)(7,188,22,203)(8,187,23,202)(9,186,24,201)(10,185,25,200)(11,184,26,199)(12,183,27,198)(13,182,28,197)(14,181,29,196)(15,210,30,195)(31,232,46,217)(32,231,47,216)(33,230,48,215)(34,229,49,214)(35,228,50,213)(36,227,51,212)(37,226,52,211)(38,225,53,240)(39,224,54,239)(40,223,55,238)(41,222,56,237)(42,221,57,236)(43,220,58,235)(44,219,59,234)(45,218,60,233)(61,171,76,156)(62,170,77,155)(63,169,78,154)(64,168,79,153)(65,167,80,152)(66,166,81,151)(67,165,82,180)(68,164,83,179)(69,163,84,178)(70,162,85,177)(71,161,86,176)(72,160,87,175)(73,159,88,174)(74,158,89,173)(75,157,90,172)(91,146,106,131)(92,145,107,130)(93,144,108,129)(94,143,109,128)(95,142,110,127)(96,141,111,126)(97,140,112,125)(98,139,113,124)(99,138,114,123)(100,137,115,122)(101,136,116,121)(102,135,117,150)(103,134,118,149)(104,133,119,148)(105,132,120,147) );
G=PermutationGroup([[(1,55),(2,56),(3,57),(4,58),(5,59),(6,60),(7,31),(8,32),(9,33),(10,34),(11,35),(12,36),(13,37),(14,38),(15,39),(16,40),(17,41),(18,42),(19,43),(20,44),(21,45),(22,46),(23,47),(24,48),(25,49),(26,50),(27,51),(28,52),(29,53),(30,54),(61,117),(62,118),(63,119),(64,120),(65,91),(66,92),(67,93),(68,94),(69,95),(70,96),(71,97),(72,98),(73,99),(74,100),(75,101),(76,102),(77,103),(78,104),(79,105),(80,106),(81,107),(82,108),(83,109),(84,110),(85,111),(86,112),(87,113),(88,114),(89,115),(90,116),(121,172),(122,173),(123,174),(124,175),(125,176),(126,177),(127,178),(128,179),(129,180),(130,151),(131,152),(132,153),(133,154),(134,155),(135,156),(136,157),(137,158),(138,159),(139,160),(140,161),(141,162),(142,163),(143,164),(144,165),(145,166),(146,167),(147,168),(148,169),(149,170),(150,171),(181,225),(182,226),(183,227),(184,228),(185,229),(186,230),(187,231),(188,232),(189,233),(190,234),(191,235),(192,236),(193,237),(194,238),(195,239),(196,240),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224)], [(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)], [(1,223,123,88),(2,222,124,87),(3,221,125,86),(4,220,126,85),(5,219,127,84),(6,218,128,83),(7,217,129,82),(8,216,130,81),(9,215,131,80),(10,214,132,79),(11,213,133,78),(12,212,134,77),(13,211,135,76),(14,240,136,75),(15,239,137,74),(16,238,138,73),(17,237,139,72),(18,236,140,71),(19,235,141,70),(20,234,142,69),(21,233,143,68),(22,232,144,67),(23,231,145,66),(24,230,146,65),(25,229,147,64),(26,228,148,63),(27,227,149,62),(28,226,150,61),(29,225,121,90),(30,224,122,89),(31,203,180,108),(32,202,151,107),(33,201,152,106),(34,200,153,105),(35,199,154,104),(36,198,155,103),(37,197,156,102),(38,196,157,101),(39,195,158,100),(40,194,159,99),(41,193,160,98),(42,192,161,97),(43,191,162,96),(44,190,163,95),(45,189,164,94),(46,188,165,93),(47,187,166,92),(48,186,167,91),(49,185,168,120),(50,184,169,119),(51,183,170,118),(52,182,171,117),(53,181,172,116),(54,210,173,115),(55,209,174,114),(56,208,175,113),(57,207,176,112),(58,206,177,111),(59,205,178,110),(60,204,179,109)], [(1,194,16,209),(2,193,17,208),(3,192,18,207),(4,191,19,206),(5,190,20,205),(6,189,21,204),(7,188,22,203),(8,187,23,202),(9,186,24,201),(10,185,25,200),(11,184,26,199),(12,183,27,198),(13,182,28,197),(14,181,29,196),(15,210,30,195),(31,232,46,217),(32,231,47,216),(33,230,48,215),(34,229,49,214),(35,228,50,213),(36,227,51,212),(37,226,52,211),(38,225,53,240),(39,224,54,239),(40,223,55,238),(41,222,56,237),(42,221,57,236),(43,220,58,235),(44,219,59,234),(45,218,60,233),(61,171,76,156),(62,170,77,155),(63,169,78,154),(64,168,79,153),(65,167,80,152),(66,166,81,151),(67,165,82,180),(68,164,83,179),(69,163,84,178),(70,162,85,177),(71,161,86,176),(72,160,87,175),(73,159,88,174),(74,158,89,173),(75,157,90,172),(91,146,106,131),(92,145,107,130),(93,144,108,129),(94,143,109,128),(95,142,110,127),(96,141,111,126),(97,140,112,125),(98,139,113,124),(99,138,114,123),(100,137,115,122),(101,136,116,121),(102,135,117,150),(103,134,118,149),(104,133,119,148),(105,132,120,147)]])
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