direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×D15⋊C8, D30⋊2C8, C5⋊C8⋊9D6, C10⋊1(S3×C8), C30⋊2(C2×C8), C6⋊1(D5⋊C8), D15⋊2(C2×C8), C15⋊3(C22×C8), C15⋊C8⋊8C22, D30.13(C2×C4), D30.C2.4C4, (C2×Dic3).9F5, C22.21(S3×F5), C6.25(C22×F5), C30.25(C22×C4), Dic5.29(C4×S3), (C10×Dic3).8C4, Dic3.15(C2×F5), (C22×D15).5C4, (C2×Dic5).149D6, D30.C2.16C22, Dic5.37(C22×S3), (C3×Dic5).35C23, (C6×Dic5).146C22, C5⋊2(S3×C2×C8), (C6×C5⋊C8)⋊5C2, (C2×C5⋊C8)⋊6S3, C3⋊2(C2×D5⋊C8), C2.5(C2×S3×F5), (C3×C5⋊C8)⋊8C22, C10.25(S3×C2×C4), (C2×C15⋊C8)⋊5C2, (C2×C6).23(C2×F5), (C2×C10).20(C4×S3), (C2×C30).20(C2×C4), (C2×D30.C2).11C2, (C3×Dic5).27(C2×C4), (C5×Dic3).14(C2×C4), SmallGroup(480,1006)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — C2×D15⋊C8 |
Subgroups: 692 in 152 conjugacy classes, 62 normal (26 characteristic)
C1, C2, C2 [×2], C2 [×4], C3, C4 [×4], C22, C22 [×6], C5, S3 [×4], C6, C6 [×2], C8 [×4], C2×C4 [×6], C23, D5 [×4], C10, C10 [×2], Dic3 [×2], C12 [×2], D6 [×6], C2×C6, C15, C2×C8 [×6], C22×C4, Dic5 [×2], C20 [×2], D10 [×6], C2×C10, C3⋊C8 [×2], C24 [×2], C4×S3 [×4], C2×Dic3, C2×C12, C22×S3, D15 [×4], C30, C30 [×2], C22×C8, C5⋊C8 [×2], C5⋊C8 [×2], C4×D5 [×4], C2×Dic5, C2×C20, C22×D5, S3×C8 [×4], C2×C3⋊C8, C2×C24, S3×C2×C4, C5×Dic3 [×2], C3×Dic5 [×2], D30 [×6], C2×C30, D5⋊C8 [×4], C2×C5⋊C8, C2×C5⋊C8, C2×C4×D5, S3×C2×C8, C3×C5⋊C8 [×2], C15⋊C8 [×2], D30.C2 [×4], C6×Dic5, C10×Dic3, C22×D15, C2×D5⋊C8, D15⋊C8 [×4], C6×C5⋊C8, C2×C15⋊C8, C2×D30.C2, C2×D15⋊C8
Quotients:
C1, C2 [×7], C4 [×4], C22 [×7], S3, C8 [×4], C2×C4 [×6], C23, D6 [×3], C2×C8 [×6], C22×C4, F5, C4×S3 [×2], C22×S3, C22×C8, C2×F5 [×3], S3×C8 [×2], S3×C2×C4, D5⋊C8 [×2], C22×F5, S3×C2×C8, S3×F5, C2×D5⋊C8, D15⋊C8 [×2], C2×S3×F5, C2×D15⋊C8
Generators and relations
G = < a,b,c,d | a2=b15=c2=d8=1, ab=ba, ac=ca, ad=da, cbc=b-1, dbd-1=b13, dcd-1=b12c >
►On 240 points
Generators in S240
(1 66)(2 67)(3 68)(4 69)(5 70)(6 71)(7 72)(8 73)(9 74)(10 75)(11 61)(12 62)(13 63)(14 64)(15 65)(16 90)(17 76)(18 77)(19 78)(20 79)(21 80)(22 81)(23 82)(24 83)(25 84)(26 85)(27 86)(28 87)(29 88)(30 89)(31 102)(32 103)(33 104)(34 105)(35 91)(36 92)(37 93)(38 94)(39 95)(40 96)(41 97)(42 98)(43 99)(44 100)(45 101)(46 106)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 113)(54 114)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(121 185)(122 186)(123 187)(124 188)(125 189)(126 190)(127 191)(128 192)(129 193)(130 194)(131 195)(132 181)(133 182)(134 183)(135 184)(136 208)(137 209)(138 210)(139 196)(140 197)(141 198)(142 199)(143 200)(144 201)(145 202)(146 203)(147 204)(148 205)(149 206)(150 207)(151 216)(152 217)(153 218)(154 219)(155 220)(156 221)(157 222)(158 223)(159 224)(160 225)(161 211)(162 212)(163 213)(164 214)(165 215)(166 231)(167 232)(168 233)(169 234)(170 235)(171 236)(172 237)(173 238)(174 239)(175 240)(176 226)(177 227)(178 228)(179 229)(180 230)
(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 27)(2 26)(3 25)(4 24)(5 23)(6 22)(7 21)(8 20)(9 19)(10 18)(11 17)(12 16)(13 30)(14 29)(15 28)(31 48)(32 47)(33 46)(34 60)(35 59)(36 58)(37 57)(38 56)(39 55)(40 54)(41 53)(42 52)(43 51)(44 50)(45 49)(61 76)(62 90)(63 89)(64 88)(65 87)(66 86)(67 85)(68 84)(69 83)(70 82)(71 81)(72 80)(73 79)(74 78)(75 77)(91 119)(92 118)(93 117)(94 116)(95 115)(96 114)(97 113)(98 112)(99 111)(100 110)(101 109)(102 108)(103 107)(104 106)(105 120)(121 147)(122 146)(123 145)(124 144)(125 143)(126 142)(127 141)(128 140)(129 139)(130 138)(131 137)(132 136)(133 150)(134 149)(135 148)(151 175)(152 174)(153 173)(154 172)(155 171)(156 170)(157 169)(158 168)(159 167)(160 166)(161 180)(162 179)(163 178)(164 177)(165 176)(181 208)(182 207)(183 206)(184 205)(185 204)(186 203)(187 202)(188 201)(189 200)(190 199)(191 198)(192 197)(193 196)(194 210)(195 209)(211 230)(212 229)(213 228)(214 227)(215 226)(216 240)(217 239)(218 238)(219 237)(220 236)(221 235)(222 234)(223 233)(224 232)(225 231)
(1 166 50 150 28 161 45 134)(2 173 54 148 29 153 34 132)(3 180 58 146 30 160 38 130)(4 172 47 144 16 152 42 128)(5 179 51 142 17 159 31 126)(6 171 55 140 18 151 35 124)(7 178 59 138 19 158 39 122)(8 170 48 136 20 165 43 135)(9 177 52 149 21 157 32 133)(10 169 56 147 22 164 36 131)(11 176 60 145 23 156 40 129)(12 168 49 143 24 163 44 127)(13 175 53 141 25 155 33 125)(14 167 57 139 26 162 37 123)(15 174 46 137 27 154 41 121)(61 226 120 202 82 221 96 193)(62 233 109 200 83 213 100 191)(63 240 113 198 84 220 104 189)(64 232 117 196 85 212 93 187)(65 239 106 209 86 219 97 185)(66 231 110 207 87 211 101 183)(67 238 114 205 88 218 105 181)(68 230 118 203 89 225 94 194)(69 237 107 201 90 217 98 192)(70 229 111 199 76 224 102 190)(71 236 115 197 77 216 91 188)(72 228 119 210 78 223 95 186)(73 235 108 208 79 215 99 184)(74 227 112 206 80 222 103 182)(75 234 116 204 81 214 92 195)
G:=sub<Sym(240)| (1,66)(2,67)(3,68)(4,69)(5,70)(6,71)(7,72)(8,73)(9,74)(10,75)(11,61)(12,62)(13,63)(14,64)(15,65)(16,90)(17,76)(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,85)(27,86)(28,87)(29,88)(30,89)(31,102)(32,103)(33,104)(34,105)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,97)(42,98)(43,99)(44,100)(45,101)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(121,185)(122,186)(123,187)(124,188)(125,189)(126,190)(127,191)(128,192)(129,193)(130,194)(131,195)(132,181)(133,182)(134,183)(135,184)(136,208)(137,209)(138,210)(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)(146,203)(147,204)(148,205)(149,206)(150,207)(151,216)(152,217)(153,218)(154,219)(155,220)(156,221)(157,222)(158,223)(159,224)(160,225)(161,211)(162,212)(163,213)(164,214)(165,215)(166,231)(167,232)(168,233)(169,234)(170,235)(171,236)(172,237)(173,238)(174,239)(175,240)(176,226)(177,227)(178,228)(179,229)(180,230), (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), (1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,30)(14,29)(15,28)(31,48)(32,47)(33,46)(34,60)(35,59)(36,58)(37,57)(38,56)(39,55)(40,54)(41,53)(42,52)(43,51)(44,50)(45,49)(61,76)(62,90)(63,89)(64,88)(65,87)(66,86)(67,85)(68,84)(69,83)(70,82)(71,81)(72,80)(73,79)(74,78)(75,77)(91,119)(92,118)(93,117)(94,116)(95,115)(96,114)(97,113)(98,112)(99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(105,120)(121,147)(122,146)(123,145)(124,144)(125,143)(126,142)(127,141)(128,140)(129,139)(130,138)(131,137)(132,136)(133,150)(134,149)(135,148)(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,180)(162,179)(163,178)(164,177)(165,176)(181,208)(182,207)(183,206)(184,205)(185,204)(186,203)(187,202)(188,201)(189,200)(190,199)(191,198)(192,197)(193,196)(194,210)(195,209)(211,230)(212,229)(213,228)(214,227)(215,226)(216,240)(217,239)(218,238)(219,237)(220,236)(221,235)(222,234)(223,233)(224,232)(225,231), (1,166,50,150,28,161,45,134)(2,173,54,148,29,153,34,132)(3,180,58,146,30,160,38,130)(4,172,47,144,16,152,42,128)(5,179,51,142,17,159,31,126)(6,171,55,140,18,151,35,124)(7,178,59,138,19,158,39,122)(8,170,48,136,20,165,43,135)(9,177,52,149,21,157,32,133)(10,169,56,147,22,164,36,131)(11,176,60,145,23,156,40,129)(12,168,49,143,24,163,44,127)(13,175,53,141,25,155,33,125)(14,167,57,139,26,162,37,123)(15,174,46,137,27,154,41,121)(61,226,120,202,82,221,96,193)(62,233,109,200,83,213,100,191)(63,240,113,198,84,220,104,189)(64,232,117,196,85,212,93,187)(65,239,106,209,86,219,97,185)(66,231,110,207,87,211,101,183)(67,238,114,205,88,218,105,181)(68,230,118,203,89,225,94,194)(69,237,107,201,90,217,98,192)(70,229,111,199,76,224,102,190)(71,236,115,197,77,216,91,188)(72,228,119,210,78,223,95,186)(73,235,108,208,79,215,99,184)(74,227,112,206,80,222,103,182)(75,234,116,204,81,214,92,195)>;
G:=Group( (1,66)(2,67)(3,68)(4,69)(5,70)(6,71)(7,72)(8,73)(9,74)(10,75)(11,61)(12,62)(13,63)(14,64)(15,65)(16,90)(17,76)(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,85)(27,86)(28,87)(29,88)(30,89)(31,102)(32,103)(33,104)(34,105)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,97)(42,98)(43,99)(44,100)(45,101)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(121,185)(122,186)(123,187)(124,188)(125,189)(126,190)(127,191)(128,192)(129,193)(130,194)(131,195)(132,181)(133,182)(134,183)(135,184)(136,208)(137,209)(138,210)(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)(146,203)(147,204)(148,205)(149,206)(150,207)(151,216)(152,217)(153,218)(154,219)(155,220)(156,221)(157,222)(158,223)(159,224)(160,225)(161,211)(162,212)(163,213)(164,214)(165,215)(166,231)(167,232)(168,233)(169,234)(170,235)(171,236)(172,237)(173,238)(174,239)(175,240)(176,226)(177,227)(178,228)(179,229)(180,230), (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), (1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,30)(14,29)(15,28)(31,48)(32,47)(33,46)(34,60)(35,59)(36,58)(37,57)(38,56)(39,55)(40,54)(41,53)(42,52)(43,51)(44,50)(45,49)(61,76)(62,90)(63,89)(64,88)(65,87)(66,86)(67,85)(68,84)(69,83)(70,82)(71,81)(72,80)(73,79)(74,78)(75,77)(91,119)(92,118)(93,117)(94,116)(95,115)(96,114)(97,113)(98,112)(99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(105,120)(121,147)(122,146)(123,145)(124,144)(125,143)(126,142)(127,141)(128,140)(129,139)(130,138)(131,137)(132,136)(133,150)(134,149)(135,148)(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,180)(162,179)(163,178)(164,177)(165,176)(181,208)(182,207)(183,206)(184,205)(185,204)(186,203)(187,202)(188,201)(189,200)(190,199)(191,198)(192,197)(193,196)(194,210)(195,209)(211,230)(212,229)(213,228)(214,227)(215,226)(216,240)(217,239)(218,238)(219,237)(220,236)(221,235)(222,234)(223,233)(224,232)(225,231), (1,166,50,150,28,161,45,134)(2,173,54,148,29,153,34,132)(3,180,58,146,30,160,38,130)(4,172,47,144,16,152,42,128)(5,179,51,142,17,159,31,126)(6,171,55,140,18,151,35,124)(7,178,59,138,19,158,39,122)(8,170,48,136,20,165,43,135)(9,177,52,149,21,157,32,133)(10,169,56,147,22,164,36,131)(11,176,60,145,23,156,40,129)(12,168,49,143,24,163,44,127)(13,175,53,141,25,155,33,125)(14,167,57,139,26,162,37,123)(15,174,46,137,27,154,41,121)(61,226,120,202,82,221,96,193)(62,233,109,200,83,213,100,191)(63,240,113,198,84,220,104,189)(64,232,117,196,85,212,93,187)(65,239,106,209,86,219,97,185)(66,231,110,207,87,211,101,183)(67,238,114,205,88,218,105,181)(68,230,118,203,89,225,94,194)(69,237,107,201,90,217,98,192)(70,229,111,199,76,224,102,190)(71,236,115,197,77,216,91,188)(72,228,119,210,78,223,95,186)(73,235,108,208,79,215,99,184)(74,227,112,206,80,222,103,182)(75,234,116,204,81,214,92,195) );
G=PermutationGroup([(1,66),(2,67),(3,68),(4,69),(5,70),(6,71),(7,72),(8,73),(9,74),(10,75),(11,61),(12,62),(13,63),(14,64),(15,65),(16,90),(17,76),(18,77),(19,78),(20,79),(21,80),(22,81),(23,82),(24,83),(25,84),(26,85),(27,86),(28,87),(29,88),(30,89),(31,102),(32,103),(33,104),(34,105),(35,91),(36,92),(37,93),(38,94),(39,95),(40,96),(41,97),(42,98),(43,99),(44,100),(45,101),(46,106),(47,107),(48,108),(49,109),(50,110),(51,111),(52,112),(53,113),(54,114),(55,115),(56,116),(57,117),(58,118),(59,119),(60,120),(121,185),(122,186),(123,187),(124,188),(125,189),(126,190),(127,191),(128,192),(129,193),(130,194),(131,195),(132,181),(133,182),(134,183),(135,184),(136,208),(137,209),(138,210),(139,196),(140,197),(141,198),(142,199),(143,200),(144,201),(145,202),(146,203),(147,204),(148,205),(149,206),(150,207),(151,216),(152,217),(153,218),(154,219),(155,220),(156,221),(157,222),(158,223),(159,224),(160,225),(161,211),(162,212),(163,213),(164,214),(165,215),(166,231),(167,232),(168,233),(169,234),(170,235),(171,236),(172,237),(173,238),(174,239),(175,240),(176,226),(177,227),(178,228),(179,229),(180,230)], [(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)], [(1,27),(2,26),(3,25),(4,24),(5,23),(6,22),(7,21),(8,20),(9,19),(10,18),(11,17),(12,16),(13,30),(14,29),(15,28),(31,48),(32,47),(33,46),(34,60),(35,59),(36,58),(37,57),(38,56),(39,55),(40,54),(41,53),(42,52),(43,51),(44,50),(45,49),(61,76),(62,90),(63,89),(64,88),(65,87),(66,86),(67,85),(68,84),(69,83),(70,82),(71,81),(72,80),(73,79),(74,78),(75,77),(91,119),(92,118),(93,117),(94,116),(95,115),(96,114),(97,113),(98,112),(99,111),(100,110),(101,109),(102,108),(103,107),(104,106),(105,120),(121,147),(122,146),(123,145),(124,144),(125,143),(126,142),(127,141),(128,140),(129,139),(130,138),(131,137),(132,136),(133,150),(134,149),(135,148),(151,175),(152,174),(153,173),(154,172),(155,171),(156,170),(157,169),(158,168),(159,167),(160,166),(161,180),(162,179),(163,178),(164,177),(165,176),(181,208),(182,207),(183,206),(184,205),(185,204),(186,203),(187,202),(188,201),(189,200),(190,199),(191,198),(192,197),(193,196),(194,210),(195,209),(211,230),(212,229),(213,228),(214,227),(215,226),(216,240),(217,239),(218,238),(219,237),(220,236),(221,235),(222,234),(223,233),(224,232),(225,231)], [(1,166,50,150,28,161,45,134),(2,173,54,148,29,153,34,132),(3,180,58,146,30,160,38,130),(4,172,47,144,16,152,42,128),(5,179,51,142,17,159,31,126),(6,171,55,140,18,151,35,124),(7,178,59,138,19,158,39,122),(8,170,48,136,20,165,43,135),(9,177,52,149,21,157,32,133),(10,169,56,147,22,164,36,131),(11,176,60,145,23,156,40,129),(12,168,49,143,24,163,44,127),(13,175,53,141,25,155,33,125),(14,167,57,139,26,162,37,123),(15,174,46,137,27,154,41,121),(61,226,120,202,82,221,96,193),(62,233,109,200,83,213,100,191),(63,240,113,198,84,220,104,189),(64,232,117,196,85,212,93,187),(65,239,106,209,86,219,97,185),(66,231,110,207,87,211,101,183),(67,238,114,205,88,218,105,181),(68,230,118,203,89,225,94,194),(69,237,107,201,90,217,98,192),(70,229,111,199,76,224,102,190),(71,236,115,197,77,216,91,188),(72,228,119,210,78,223,95,186),(73,235,108,208,79,215,99,184),(74,227,112,206,80,222,103,182),(75,234,116,204,81,214,92,195)])
Matrix representation ►G ⊆ GL6(𝔽241)
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 1 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 1 | 0 |
| 0 | 0 | 0 | 240 | 0 | 1 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 1 | 240 | 0 | 0 |
| 1 | 240 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 240 |
| 0 | 0 | 0 | 1 | 240 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 149 | 92 | 93 | 0 |
| 0 | 0 | 1 | 92 | 0 | 149 |
| 0 | 0 | 149 | 0 | 92 | 1 |
| 0 | 0 | 0 | 93 | 92 | 149 |
G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[0,1,0,0,0,0,240,240,0,0,0,0,0,0,0,0,0,1,0,0,240,240,240,240,0,0,1,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,240,240,0,0,0,0,0,0,240,0,0,0,0,0,1,1,1,1,0,0,0,0,0,240,0,0,0,0,240,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,149,1,149,0,0,0,92,92,0,93,0,0,93,0,92,92,0,0,0,149,1,149] >;
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 6A | 6B | 6C | 8A | ··· | 8H | 8I | ··· | 8P | 10A | 10B | 10C | 12A | 12B | 12C | 12D | 15 | 20A | 20B | 20C | 20D | 24A | ··· | 24H | 30A | 30B | 30C |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 6 | 6 | 6 | 8 | ··· | 8 | 8 | ··· | 8 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 20 | 20 | 20 | 20 | 24 | ··· | 24 | 30 | 30 | 30 |
| size | 1 | 1 | 1 | 1 | 15 | 15 | 15 | 15 | 2 | 3 | 3 | 3 | 3 | 5 | 5 | 5 | 5 | 4 | 2 | 2 | 2 | 5 | ··· | 5 | 15 | ··· | 15 | 4 | 4 | 4 | 10 | 10 | 10 | 10 | 8 | 12 | 12 | 12 | 12 | 10 | ··· | 10 | 8 | 8 | 8 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | S3 | D6 | D6 | C4×S3 | C4×S3 | S3×C8 | F5 | C2×F5 | C2×F5 | D5⋊C8 | S3×F5 | D15⋊C8 | C2×S3×F5 |
| kernel | C2×D15⋊C8 | D15⋊C8 | C6×C5⋊C8 | C2×C15⋊C8 | C2×D30.C2 | D30.C2 | C10×Dic3 | C22×D15 | D30 | C2×C5⋊C8 | C5⋊C8 | C2×Dic5 | Dic5 | C2×C10 | C10 | C2×Dic3 | Dic3 | C2×C6 | C6 | C22 | C2 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 2 | 2 | 16 | 1 | 2 | 1 | 2 | 2 | 8 | 1 | 2 | 1 | 4 | 1 | 2 | 1 |
In GAP, Magma, Sage, TeX
C_2\times D_{15}\rtimes C_8 % in TeX
G:=Group("C2xD15:C8"); // GroupNames label
G:=SmallGroup(480,1006);
// by ID
G=gap.SmallGroup(480,1006);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,120,80,1356,9414,2379]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^15=c^2=d^8=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,d*b*d^-1=b^13,d*c*d^-1=b^12*c>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀