Copied to
clipboard

## G = SD16⋊D15order 480 = 25·3·5

### 2nd semidirect product of SD16 and D15 acting via D15/C15=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — SD16⋊D15
 Chief series C1 — C5 — C15 — C30 — C60 — C4×D15 — Q8×D15 — SD16⋊D15
 Lower central C15 — C30 — C60 — SD16⋊D15
 Upper central C1 — C2 — C4 — SD16

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 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3, C6, C6, C8, C8, C2×C4 [×3], D4, D4, Q8, Q8 [×3], D5, C10, C10, Dic3 [×3], C12, C12, D6, C2×C6, C15, M4(2), SD16, SD16, Q16 [×2], C2×Q8, C4○D4, Dic5 [×3], C20, C20, D10, C2×C10, C3⋊C8, C24, Dic6 [×3], C4×S3 [×2], C2×Dic3, C3⋊D4, C3×D4, C3×Q8, D15, C30, C30, C8.C22, C52C8, C40, Dic10 [×3], C4×D5 [×2], C2×Dic5, C5⋊D4, C5×D4, C5×Q8, C8⋊S3, Dic12, D4.S3, C3⋊Q16, C3×SD16, D42S3, S3×Q8, Dic15, Dic15 [×2], C60, C60, D30, C2×C30, C8⋊D5, Dic20, D4.D5, C5⋊Q16, C5×SD16, D42D5, Q8×D5, D4.D6, C153C8, C120, Dic30 [×2], Dic30, C4×D15, C4×D15, C2×Dic15, C157D4, D4×C15, Q8×C15, SD16⋊D5, C40⋊S3, Dic60, D4.D15, C157Q16, C15×SD16, D42D15, Q8×D15, SD16⋊D15
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, D15, C8.C22, C22×D5, S3×D4, D30 [×3], D4×D5, D4.D6, C22×D15, SD16⋊D5, D4×D15, SD16⋊D15

Smallest permutation representation of SD16⋊D15
On 240 points
Generators in S240
(1 238 54 197 24 211 31 189)(2 239 55 198 25 212 32 190)(3 240 56 199 26 213 33 191)(4 226 57 200 27 214 34 192)(5 227 58 201 28 215 35 193)(6 228 59 202 29 216 36 194)(7 229 60 203 30 217 37 195)(8 230 46 204 16 218 38 181)(9 231 47 205 17 219 39 182)(10 232 48 206 18 220 40 183)(11 233 49 207 19 221 41 184)(12 234 50 208 20 222 42 185)(13 235 51 209 21 223 43 186)(14 236 52 210 22 224 44 187)(15 237 53 196 23 225 45 188)(61 155 98 147 83 169 109 124)(62 156 99 148 84 170 110 125)(63 157 100 149 85 171 111 126)(64 158 101 150 86 172 112 127)(65 159 102 136 87 173 113 128)(66 160 103 137 88 174 114 129)(67 161 104 138 89 175 115 130)(68 162 105 139 90 176 116 131)(69 163 91 140 76 177 117 132)(70 164 92 141 77 178 118 133)(71 165 93 142 78 179 119 134)(72 151 94 143 79 180 120 135)(73 152 95 144 80 166 106 121)(74 153 96 145 81 167 107 122)(75 154 97 146 82 168 108 123)
(1 73)(2 74)(3 75)(4 61)(5 62)(6 63)(7 64)(8 65)(9 66)(10 67)(11 68)(12 69)(13 70)(14 71)(15 72)(16 87)(17 88)(18 89)(19 90)(20 76)(21 77)(22 78)(23 79)(24 80)(25 81)(26 82)(27 83)(28 84)(29 85)(30 86)(31 95)(32 96)(33 97)(34 98)(35 99)(36 100)(37 101)(38 102)(39 103)(40 104)(41 105)(42 91)(43 92)(44 93)(45 94)(46 113)(47 114)(48 115)(49 116)(50 117)(51 118)(52 119)(53 120)(54 106)(55 107)(56 108)(57 109)(58 110)(59 111)(60 112)(121 211)(122 212)(123 213)(124 214)(125 215)(126 216)(127 217)(128 218)(129 219)(130 220)(131 221)(132 222)(133 223)(134 224)(135 225)(136 230)(137 231)(138 232)(139 233)(140 234)(141 235)(142 236)(143 237)(144 238)(145 239)(146 240)(147 226)(148 227)(149 228)(150 229)(151 196)(152 197)(153 198)(154 199)(155 200)(156 201)(157 202)(158 203)(159 204)(160 205)(161 206)(162 207)(163 208)(164 209)(165 210)(166 189)(167 190)(168 191)(169 192)(170 193)(171 194)(172 195)(173 181)(174 182)(175 183)(176 184)(177 185)(178 186)(179 187)(180 188)
(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)(17 30)(18 29)(19 28)(20 27)(21 26)(22 25)(23 24)(31 45)(32 44)(33 43)(34 42)(35 41)(36 40)(37 39)(47 60)(48 59)(49 58)(50 57)(51 56)(52 55)(53 54)(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)(91 109)(92 108)(93 107)(94 106)(95 120)(96 119)(97 118)(98 117)(99 116)(100 115)(101 114)(102 113)(103 112)(104 111)(105 110)(121 135)(122 134)(123 133)(124 132)(125 131)(126 130)(127 129)(137 150)(138 149)(139 148)(140 147)(141 146)(142 145)(143 144)(151 152)(153 165)(154 164)(155 163)(156 162)(157 161)(158 160)(166 180)(167 179)(168 178)(169 177)(170 176)(171 175)(172 174)(181 204)(182 203)(183 202)(184 201)(185 200)(186 199)(187 198)(188 197)(189 196)(190 210)(191 209)(192 208)(193 207)(194 206)(195 205)(211 237)(212 236)(213 235)(214 234)(215 233)(216 232)(217 231)(218 230)(219 229)(220 228)(221 227)(222 226)(223 240)(224 239)(225 238)

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

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

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

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

׿
×
𝔽