metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C8.2D30, D4.4D30, C40.27D6, Q8.6D30, SD16⋊2D15, Dic60⋊9C2, D30.32D4, C24.27D10, C60.69C23, C120.16C22, Dic15.37D4, Dic30.23C22, (Q8×D15)⋊9C2, C40⋊S3⋊2C2, (C3×SD16)⋊2D5, (C5×SD16)⋊2S3, (C5×D4).16D6, C15⋊7Q16⋊9C2, C2.20(D4×D15), C6.113(D4×D5), C5⋊5(D4.D6), (C5×Q8).30D6, D4.D15⋊12C2, (C15×SD16)⋊2C2, (C3×D4).16D10, C30.320(C2×D4), C10.115(S3×D4), C3⋊5(SD16⋊D5), (C3×Q8).13D10, C4.6(C22×D15), D4⋊2D15.2C2, C15⋊28(C8.C22), C20.107(C22×S3), C15⋊3C8.19C22, (C4×D15).26C22, (D4×C15).23C22, C12.107(C22×D5), (Q8×C15).22C22, SmallGroup(480,880)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for SD16⋊D15
G = < a,b,c,d | a8=b2=c15=d2=1, bab=a3, ac=ca, dad=a5, bc=cb, dbd=a4b, dcd=c-1 >
Subgroups: 708 in 120 conjugacy classes, 41 normal (all characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, S3, C6, C6, C8, C8, C2×C4, D4, D4, Q8, Q8, D5, C10, C10, Dic3, C12, C12, D6, C2×C6, C15, M4(2), SD16, SD16, Q16, C2×Q8, C4○D4, Dic5, C20, C20, D10, C2×C10, C3⋊C8, C24, Dic6, C4×S3, C2×Dic3, C3⋊D4, C3×D4, C3×Q8, D15, C30, C30, C8.C22, C5⋊2C8, C40, Dic10, C4×D5, C2×Dic5, C5⋊D4, C5×D4, C5×Q8, C8⋊S3, Dic12, D4.S3, C3⋊Q16, C3×SD16, D4⋊2S3, S3×Q8, Dic15, Dic15, C60, C60, D30, C2×C30, C8⋊D5, Dic20, D4.D5, C5⋊Q16, C5×SD16, D4⋊2D5, Q8×D5, D4.D6, C15⋊3C8, C120, Dic30, Dic30, C4×D15, C4×D15, C2×Dic15, C15⋊7D4, D4×C15, Q8×C15, SD16⋊D5, C40⋊S3, Dic60, D4.D15, C15⋊7Q16, C15×SD16, D4⋊2D15, Q8×D15, SD16⋊D15
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, D10, C22×S3, D15, C8.C22, C22×D5, S3×D4, D30, D4×D5, D4.D6, C22×D15, SD16⋊D5, D4×D15, SD16⋊D15
►On 240 points
Generators in S240
(1 227 50 208 17 215 32 182)(2 228 51 209 18 216 33 183)(3 229 52 210 19 217 34 184)(4 230 53 196 20 218 35 185)(5 231 54 197 21 219 36 186)(6 232 55 198 22 220 37 187)(7 233 56 199 23 221 38 188)(8 234 57 200 24 222 39 189)(9 235 58 201 25 223 40 190)(10 236 59 202 26 224 41 191)(11 237 60 203 27 225 42 192)(12 238 46 204 28 211 43 193)(13 239 47 205 29 212 44 194)(14 240 48 206 30 213 45 195)(15 226 49 207 16 214 31 181)(61 151 98 136 76 177 110 121)(62 152 99 137 77 178 111 122)(63 153 100 138 78 179 112 123)(64 154 101 139 79 180 113 124)(65 155 102 140 80 166 114 125)(66 156 103 141 81 167 115 126)(67 157 104 142 82 168 116 127)(68 158 105 143 83 169 117 128)(69 159 91 144 84 170 118 129)(70 160 92 145 85 171 119 130)(71 161 93 146 86 172 120 131)(72 162 94 147 87 173 106 132)(73 163 95 148 88 174 107 133)(74 164 96 149 89 175 108 134)(75 165 97 150 90 176 109 135)
(1 69)(2 70)(3 71)(4 72)(5 73)(6 74)(7 75)(8 61)(9 62)(10 63)(11 64)(12 65)(13 66)(14 67)(15 68)(16 83)(17 84)(18 85)(19 86)(20 87)(21 88)(22 89)(23 90)(24 76)(25 77)(26 78)(27 79)(28 80)(29 81)(30 82)(31 105)(32 91)(33 92)(34 93)(35 94)(36 95)(37 96)(38 97)(39 98)(40 99)(41 100)(42 101)(43 102)(44 103)(45 104)(46 114)(47 115)(48 116)(49 117)(50 118)(51 119)(52 120)(53 106)(54 107)(55 108)(56 109)(57 110)(58 111)(59 112)(60 113)(121 222)(122 223)(123 224)(124 225)(125 211)(126 212)(127 213)(128 214)(129 215)(130 216)(131 217)(132 218)(133 219)(134 220)(135 221)(136 234)(137 235)(138 236)(139 237)(140 238)(141 239)(142 240)(143 226)(144 227)(145 228)(146 229)(147 230)(148 231)(149 232)(150 233)(151 200)(152 201)(153 202)(154 203)(155 204)(156 205)(157 206)(158 207)(159 208)(160 209)(161 210)(162 196)(163 197)(164 198)(165 199)(166 193)(167 194)(168 195)(169 181)(170 182)(171 183)(172 184)(173 185)(174 186)(175 187)(176 188)(177 189)(178 190)(179 191)(180 192)
(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 15)(2 14)(3 13)(4 12)(5 11)(6 10)(7 9)(16 17)(18 30)(19 29)(20 28)(21 27)(22 26)(23 25)(31 32)(33 45)(34 44)(35 43)(36 42)(37 41)(38 40)(46 53)(47 52)(48 51)(49 50)(54 60)(55 59)(56 58)(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)(91 117)(92 116)(93 115)(94 114)(95 113)(96 112)(97 111)(98 110)(99 109)(100 108)(101 107)(102 106)(103 120)(104 119)(105 118)(122 135)(123 134)(124 133)(125 132)(126 131)(127 130)(128 129)(137 150)(138 149)(139 148)(140 147)(141 146)(142 145)(143 144)(152 165)(153 164)(154 163)(155 162)(156 161)(157 160)(158 159)(166 173)(167 172)(168 171)(169 170)(174 180)(175 179)(176 178)(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)
G:=sub<Sym(240)| (1,227,50,208,17,215,32,182)(2,228,51,209,18,216,33,183)(3,229,52,210,19,217,34,184)(4,230,53,196,20,218,35,185)(5,231,54,197,21,219,36,186)(6,232,55,198,22,220,37,187)(7,233,56,199,23,221,38,188)(8,234,57,200,24,222,39,189)(9,235,58,201,25,223,40,190)(10,236,59,202,26,224,41,191)(11,237,60,203,27,225,42,192)(12,238,46,204,28,211,43,193)(13,239,47,205,29,212,44,194)(14,240,48,206,30,213,45,195)(15,226,49,207,16,214,31,181)(61,151,98,136,76,177,110,121)(62,152,99,137,77,178,111,122)(63,153,100,138,78,179,112,123)(64,154,101,139,79,180,113,124)(65,155,102,140,80,166,114,125)(66,156,103,141,81,167,115,126)(67,157,104,142,82,168,116,127)(68,158,105,143,83,169,117,128)(69,159,91,144,84,170,118,129)(70,160,92,145,85,171,119,130)(71,161,93,146,86,172,120,131)(72,162,94,147,87,173,106,132)(73,163,95,148,88,174,107,133)(74,164,96,149,89,175,108,134)(75,165,97,150,90,176,109,135), (1,69)(2,70)(3,71)(4,72)(5,73)(6,74)(7,75)(8,61)(9,62)(10,63)(11,64)(12,65)(13,66)(14,67)(15,68)(16,83)(17,84)(18,85)(19,86)(20,87)(21,88)(22,89)(23,90)(24,76)(25,77)(26,78)(27,79)(28,80)(29,81)(30,82)(31,105)(32,91)(33,92)(34,93)(35,94)(36,95)(37,96)(38,97)(39,98)(40,99)(41,100)(42,101)(43,102)(44,103)(45,104)(46,114)(47,115)(48,116)(49,117)(50,118)(51,119)(52,120)(53,106)(54,107)(55,108)(56,109)(57,110)(58,111)(59,112)(60,113)(121,222)(122,223)(123,224)(124,225)(125,211)(126,212)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,234)(137,235)(138,236)(139,237)(140,238)(141,239)(142,240)(143,226)(144,227)(145,228)(146,229)(147,230)(148,231)(149,232)(150,233)(151,200)(152,201)(153,202)(154,203)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)(161,210)(162,196)(163,197)(164,198)(165,199)(166,193)(167,194)(168,195)(169,181)(170,182)(171,183)(172,184)(173,185)(174,186)(175,187)(176,188)(177,189)(178,190)(179,191)(180,192), (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), (1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(16,17)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25)(31,32)(33,45)(34,44)(35,43)(36,42)(37,41)(38,40)(46,53)(47,52)(48,51)(49,50)(54,60)(55,59)(56,58)(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)(91,117)(92,116)(93,115)(94,114)(95,113)(96,112)(97,111)(98,110)(99,109)(100,108)(101,107)(102,106)(103,120)(104,119)(105,118)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)(152,165)(153,164)(154,163)(155,162)(156,161)(157,160)(158,159)(166,173)(167,172)(168,171)(169,170)(174,180)(175,179)(176,178)(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)>;
G:=Group( (1,227,50,208,17,215,32,182)(2,228,51,209,18,216,33,183)(3,229,52,210,19,217,34,184)(4,230,53,196,20,218,35,185)(5,231,54,197,21,219,36,186)(6,232,55,198,22,220,37,187)(7,233,56,199,23,221,38,188)(8,234,57,200,24,222,39,189)(9,235,58,201,25,223,40,190)(10,236,59,202,26,224,41,191)(11,237,60,203,27,225,42,192)(12,238,46,204,28,211,43,193)(13,239,47,205,29,212,44,194)(14,240,48,206,30,213,45,195)(15,226,49,207,16,214,31,181)(61,151,98,136,76,177,110,121)(62,152,99,137,77,178,111,122)(63,153,100,138,78,179,112,123)(64,154,101,139,79,180,113,124)(65,155,102,140,80,166,114,125)(66,156,103,141,81,167,115,126)(67,157,104,142,82,168,116,127)(68,158,105,143,83,169,117,128)(69,159,91,144,84,170,118,129)(70,160,92,145,85,171,119,130)(71,161,93,146,86,172,120,131)(72,162,94,147,87,173,106,132)(73,163,95,148,88,174,107,133)(74,164,96,149,89,175,108,134)(75,165,97,150,90,176,109,135), (1,69)(2,70)(3,71)(4,72)(5,73)(6,74)(7,75)(8,61)(9,62)(10,63)(11,64)(12,65)(13,66)(14,67)(15,68)(16,83)(17,84)(18,85)(19,86)(20,87)(21,88)(22,89)(23,90)(24,76)(25,77)(26,78)(27,79)(28,80)(29,81)(30,82)(31,105)(32,91)(33,92)(34,93)(35,94)(36,95)(37,96)(38,97)(39,98)(40,99)(41,100)(42,101)(43,102)(44,103)(45,104)(46,114)(47,115)(48,116)(49,117)(50,118)(51,119)(52,120)(53,106)(54,107)(55,108)(56,109)(57,110)(58,111)(59,112)(60,113)(121,222)(122,223)(123,224)(124,225)(125,211)(126,212)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,234)(137,235)(138,236)(139,237)(140,238)(141,239)(142,240)(143,226)(144,227)(145,228)(146,229)(147,230)(148,231)(149,232)(150,233)(151,200)(152,201)(153,202)(154,203)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)(161,210)(162,196)(163,197)(164,198)(165,199)(166,193)(167,194)(168,195)(169,181)(170,182)(171,183)(172,184)(173,185)(174,186)(175,187)(176,188)(177,189)(178,190)(179,191)(180,192), (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), (1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(16,17)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25)(31,32)(33,45)(34,44)(35,43)(36,42)(37,41)(38,40)(46,53)(47,52)(48,51)(49,50)(54,60)(55,59)(56,58)(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)(91,117)(92,116)(93,115)(94,114)(95,113)(96,112)(97,111)(98,110)(99,109)(100,108)(101,107)(102,106)(103,120)(104,119)(105,118)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)(152,165)(153,164)(154,163)(155,162)(156,161)(157,160)(158,159)(166,173)(167,172)(168,171)(169,170)(174,180)(175,179)(176,178)(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) );
G=PermutationGroup([[(1,227,50,208,17,215,32,182),(2,228,51,209,18,216,33,183),(3,229,52,210,19,217,34,184),(4,230,53,196,20,218,35,185),(5,231,54,197,21,219,36,186),(6,232,55,198,22,220,37,187),(7,233,56,199,23,221,38,188),(8,234,57,200,24,222,39,189),(9,235,58,201,25,223,40,190),(10,236,59,202,26,224,41,191),(11,237,60,203,27,225,42,192),(12,238,46,204,28,211,43,193),(13,239,47,205,29,212,44,194),(14,240,48,206,30,213,45,195),(15,226,49,207,16,214,31,181),(61,151,98,136,76,177,110,121),(62,152,99,137,77,178,111,122),(63,153,100,138,78,179,112,123),(64,154,101,139,79,180,113,124),(65,155,102,140,80,166,114,125),(66,156,103,141,81,167,115,126),(67,157,104,142,82,168,116,127),(68,158,105,143,83,169,117,128),(69,159,91,144,84,170,118,129),(70,160,92,145,85,171,119,130),(71,161,93,146,86,172,120,131),(72,162,94,147,87,173,106,132),(73,163,95,148,88,174,107,133),(74,164,96,149,89,175,108,134),(75,165,97,150,90,176,109,135)], [(1,69),(2,70),(3,71),(4,72),(5,73),(6,74),(7,75),(8,61),(9,62),(10,63),(11,64),(12,65),(13,66),(14,67),(15,68),(16,83),(17,84),(18,85),(19,86),(20,87),(21,88),(22,89),(23,90),(24,76),(25,77),(26,78),(27,79),(28,80),(29,81),(30,82),(31,105),(32,91),(33,92),(34,93),(35,94),(36,95),(37,96),(38,97),(39,98),(40,99),(41,100),(42,101),(43,102),(44,103),(45,104),(46,114),(47,115),(48,116),(49,117),(50,118),(51,119),(52,120),(53,106),(54,107),(55,108),(56,109),(57,110),(58,111),(59,112),(60,113),(121,222),(122,223),(123,224),(124,225),(125,211),(126,212),(127,213),(128,214),(129,215),(130,216),(131,217),(132,218),(133,219),(134,220),(135,221),(136,234),(137,235),(138,236),(139,237),(140,238),(141,239),(142,240),(143,226),(144,227),(145,228),(146,229),(147,230),(148,231),(149,232),(150,233),(151,200),(152,201),(153,202),(154,203),(155,204),(156,205),(157,206),(158,207),(159,208),(160,209),(161,210),(162,196),(163,197),(164,198),(165,199),(166,193),(167,194),(168,195),(169,181),(170,182),(171,183),(172,184),(173,185),(174,186),(175,187),(176,188),(177,189),(178,190),(179,191),(180,192)], [(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)], [(1,15),(2,14),(3,13),(4,12),(5,11),(6,10),(7,9),(16,17),(18,30),(19,29),(20,28),(21,27),(22,26),(23,25),(31,32),(33,45),(34,44),(35,43),(36,42),(37,41),(38,40),(46,53),(47,52),(48,51),(49,50),(54,60),(55,59),(56,58),(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),(91,117),(92,116),(93,115),(94,114),(95,113),(96,112),(97,111),(98,110),(99,109),(100,108),(101,107),(102,106),(103,120),(104,119),(105,118),(122,135),(123,134),(124,133),(125,132),(126,131),(127,130),(128,129),(137,150),(138,149),(139,148),(140,147),(141,146),(142,145),(143,144),(152,165),(153,164),(154,163),(155,162),(156,161),(157,160),(158,159),(166,173),(167,172),(168,171),(169,170),(174,180),(175,179),(176,178),(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)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 5A | 5B | 6A | 6B | 8A | 8B | 10A | 10B | 10C | 10D | 12A | 12B | 15A | 15B | 15C | 15D | 20A | 20B | 20C | 20D | 24A | 24B | 30A | 30B | 30C | 30D | 30E | 30F | 30G | 30H | 40A | 40B | 40C | 40D | 60A | 60B | 60C | 60D | 60E | 60F | 60G | 60H | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | 20 | 20 | 20 | 24 | 24 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 40 | 40 | 40 | 40 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 4 | 30 | 2 | 2 | 4 | 30 | 60 | 60 | 2 | 2 | 2 | 8 | 4 | 60 | 2 | 2 | 8 | 8 | 4 | 8 | 2 | 2 | 2 | 2 | 4 | 4 | 8 | 8 | 4 | 4 | 2 | 2 | 2 | 2 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | D4 | D5 | D6 | D6 | D6 | D10 | D10 | D10 | D15 | D30 | D30 | D30 | C8.C22 | S3×D4 | D4×D5 | D4.D6 | SD16⋊D5 | D4×D15 | SD16⋊D15 |
| kernel | SD16⋊D15 | C40⋊S3 | Dic60 | D4.D15 | C15⋊7Q16 | C15×SD16 | D4⋊2D15 | Q8×D15 | C5×SD16 | Dic15 | D30 | C3×SD16 | C40 | C5×D4 | C5×Q8 | C24 | C3×D4 | C3×Q8 | SD16 | C8 | D4 | Q8 | C15 | C10 | C6 | C5 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 1 | 1 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of SD16⋊D15 ►in GL4(𝔽241) generated by
| 0 | 0 | 62 | 58 |
| 0 | 0 | 183 | 179 |
| 210 | 212 | 62 | 58 |
| 29 | 31 | 183 | 179 |
| 128 | 42 | 117 | 125 |
| 199 | 113 | 116 | 124 |
| 66 | 225 | 113 | 199 |
| 16 | 175 | 42 | 128 |
| 64 | 225 | 0 | 0 |
| 16 | 173 | 0 | 0 |
| 0 | 0 | 64 | 225 |
| 0 | 0 | 16 | 173 |
| 64 | 225 | 0 | 0 |
| 30 | 177 | 0 | 0 |
| 0 | 0 | 64 | 225 |
| 0 | 0 | 30 | 177 |
G:=sub<GL(4,GF(241))| [0,0,210,29,0,0,212,31,62,183,62,183,58,179,58,179],[128,199,66,16,42,113,225,175,117,116,113,42,125,124,199,128],[64,16,0,0,225,173,0,0,0,0,64,16,0,0,225,173],[64,30,0,0,225,177,0,0,0,0,64,30,0,0,225,177] >;
SD16⋊D15 in GAP, Magma, Sage, TeX
{\rm SD}_{16}\rtimes D_{15} % in TeX
G:=Group("SD16:D15"); // GroupNames label
G:=SmallGroup(480,880);
// by ID
G=gap.SmallGroup(480,880);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,422,135,346,185,80,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^2=c^15=d^2=1,b*a*b=a^3,a*c=c*a,d*a*d=a^5,b*c=c*b,d*b*d=a^4*b,d*c*d=c^-1>;
// generators/relations