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## G = SD32⋊D7order 448 = 26·7

### 2nd semidirect product of SD32 and D7 acting via D7/C7=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C56 — SD32⋊D7
 Chief series C1 — C7 — C14 — C28 — C56 — C8×D7 — D7×Q16 — SD32⋊D7
 Lower central C7 — C14 — C28 — C56 — SD32⋊D7
 Upper central C1 — C2 — C4 — C8 — SD32

Generators and relations for SD32⋊D7
G = < a,b,c,d | a16=b2=c7=d2=1, bab=a7, ac=ca, dad=a9, bc=cb, dbd=a8b, dcd=c-1 >

Subgroups: 480 in 82 conjugacy classes, 31 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C7, C8, C8, C2×C4, D4, Q8, D7, C14, C14, C16, C16, C2×C8, D8, SD16, Q16, Q16, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, M5(2), SD32, SD32, Q32, C2×Q16, C4○D8, C7⋊C8, C56, Dic14, C4×D7, C4×D7, C2×Dic7, C7⋊D4, C7×D4, C7×Q8, Q32⋊C2, C7⋊C16, C112, C8×D7, Dic28, D4.D7, C7⋊Q16, C7×D8, C7×Q16, D42D7, Q8×D7, C16⋊D7, Dic56, D8.D7, C7⋊Q32, C7×SD32, D83D7, D7×Q16, SD32⋊D7
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, D14, C2×D8, C22×D7, Q32⋊C2, D4×D7, D7×D8, SD32⋊D7

Smallest permutation representation of SD32⋊D7
On 224 points
Generators in S224
(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)
(1 181)(2 188)(3 179)(4 186)(5 177)(6 184)(7 191)(8 182)(9 189)(10 180)(11 187)(12 178)(13 185)(14 192)(15 183)(16 190)(17 196)(18 203)(19 194)(20 201)(21 208)(22 199)(23 206)(24 197)(25 204)(26 195)(27 202)(28 193)(29 200)(30 207)(31 198)(32 205)(33 120)(34 127)(35 118)(36 125)(37 116)(38 123)(39 114)(40 121)(41 128)(42 119)(43 126)(44 117)(45 124)(46 115)(47 122)(48 113)(49 216)(50 223)(51 214)(52 221)(53 212)(54 219)(55 210)(56 217)(57 224)(58 215)(59 222)(60 213)(61 220)(62 211)(63 218)(64 209)(65 130)(66 137)(67 144)(68 135)(69 142)(70 133)(71 140)(72 131)(73 138)(74 129)(75 136)(76 143)(77 134)(78 141)(79 132)(80 139)(81 102)(82 109)(83 100)(84 107)(85 98)(86 105)(87 112)(88 103)(89 110)(90 101)(91 108)(92 99)(93 106)(94 97)(95 104)(96 111)(145 175)(146 166)(147 173)(148 164)(149 171)(150 162)(151 169)(152 176)(153 167)(154 174)(155 165)(156 172)(157 163)(158 170)(159 161)(160 168)
(1 94 156 39 21 137 221)(2 95 157 40 22 138 222)(3 96 158 41 23 139 223)(4 81 159 42 24 140 224)(5 82 160 43 25 141 209)(6 83 145 44 26 142 210)(7 84 146 45 27 143 211)(8 85 147 46 28 144 212)(9 86 148 47 29 129 213)(10 87 149 48 30 130 214)(11 88 150 33 31 131 215)(12 89 151 34 32 132 216)(13 90 152 35 17 133 217)(14 91 153 36 18 134 218)(15 92 154 37 19 135 219)(16 93 155 38 20 136 220)(49 178 110 169 127 205 79)(50 179 111 170 128 206 80)(51 180 112 171 113 207 65)(52 181 97 172 114 208 66)(53 182 98 173 115 193 67)(54 183 99 174 116 194 68)(55 184 100 175 117 195 69)(56 185 101 176 118 196 70)(57 186 102 161 119 197 71)(58 187 103 162 120 198 72)(59 188 104 163 121 199 73)(60 189 105 164 122 200 74)(61 190 106 165 123 201 75)(62 191 107 166 124 202 76)(63 192 108 167 125 203 77)(64 177 109 168 126 204 78)
(1 221)(2 214)(3 223)(4 216)(5 209)(6 218)(7 211)(8 220)(9 213)(10 222)(11 215)(12 224)(13 217)(14 210)(15 219)(16 212)(17 152)(18 145)(19 154)(20 147)(21 156)(22 149)(23 158)(24 151)(25 160)(26 153)(27 146)(28 155)(29 148)(30 157)(31 150)(32 159)(34 42)(36 44)(38 46)(40 48)(49 178)(50 187)(51 180)(52 189)(53 182)(54 191)(55 184)(56 177)(57 186)(58 179)(59 188)(60 181)(61 190)(62 183)(63 192)(64 185)(65 112)(66 105)(67 98)(68 107)(69 100)(70 109)(71 102)(72 111)(73 104)(74 97)(75 106)(76 99)(77 108)(78 101)(79 110)(80 103)(81 132)(82 141)(83 134)(84 143)(85 136)(86 129)(87 138)(88 131)(89 140)(90 133)(91 142)(92 135)(93 144)(94 137)(95 130)(96 139)(114 122)(116 124)(118 126)(120 128)(161 197)(162 206)(163 199)(164 208)(165 201)(166 194)(167 203)(168 196)(169 205)(170 198)(171 207)(172 200)(173 193)(174 202)(175 195)(176 204)

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

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

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

49 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 7A 7B 7C 8A 8B 8C 14A 14B 14C 14D 14E 14F 16A 16B 16C 16D 28A 28B 28C 28D 28E 28F 56A ··· 56F 112A ··· 112L order 1 2 2 2 4 4 4 4 4 7 7 7 8 8 8 14 14 14 14 14 14 16 16 16 16 28 28 28 28 28 28 56 ··· 56 112 ··· 112 size 1 1 8 14 2 8 14 56 56 2 2 2 2 2 28 2 2 2 16 16 16 4 4 28 28 4 4 4 16 16 16 4 ··· 4 4 ··· 4

49 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 4 type + + + + + + + + + + + + + + + + - + + - image C1 C2 C2 C2 C2 C2 C2 C2 D4 D4 D7 D8 D8 D14 D14 D14 Q32⋊C2 D4×D7 D7×D8 SD32⋊D7 kernel SD32⋊D7 C16⋊D7 Dic56 D8.D7 C7⋊Q32 C7×SD32 D8⋊3D7 D7×Q16 C7⋊C8 C4×D7 SD32 Dic7 D14 C16 D8 Q16 C7 C4 C2 C1 # reps 1 1 1 1 1 1 1 1 1 1 3 2 2 3 3 3 2 3 6 12

Matrix representation of SD32⋊D7 in GL8(𝔽113)

 7 0 54 34 0 0 0 0 0 7 79 0 0 0 0 0 0 48 106 0 0 0 0 0 65 70 0 106 0 0 0 0 0 0 0 0 22 95 15 87 0 0 0 0 18 85 69 104 0 0 0 0 8 36 7 3 0 0 0 0 74 76 95 112
,
 10 0 3 27 0 0 0 0 0 10 86 0 0 0 0 0 0 79 103 0 0 0 0 0 34 54 0 103 0 0 0 0 0 0 0 0 69 1 36 0 0 0 0 0 3 4 0 112 0 0 0 0 78 89 44 22 0 0 0 0 106 18 108 109
,
 9 1 0 0 0 0 0 0 112 0 0 0 0 0 0 0 0 0 88 1 0 0 0 0 0 0 53 34 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
,
 80 33 0 0 0 0 0 0 104 33 0 0 0 0 0 0 0 0 34 9 0 0 0 0 0 0 60 79 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 15 69 112 0 0 0 0 0 6 8 0 112

G:=sub<GL(8,GF(113))| [7,0,0,65,0,0,0,0,0,7,48,70,0,0,0,0,54,79,106,0,0,0,0,0,34,0,0,106,0,0,0,0,0,0,0,0,22,18,8,74,0,0,0,0,95,85,36,76,0,0,0,0,15,69,7,95,0,0,0,0,87,104,3,112],[10,0,0,34,0,0,0,0,0,10,79,54,0,0,0,0,3,86,103,0,0,0,0,0,27,0,0,103,0,0,0,0,0,0,0,0,69,3,78,106,0,0,0,0,1,4,89,18,0,0,0,0,36,0,44,108,0,0,0,0,0,112,22,109],[9,112,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,88,53,0,0,0,0,0,0,1,34,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[80,104,0,0,0,0,0,0,33,33,0,0,0,0,0,0,0,0,34,60,0,0,0,0,0,0,9,79,0,0,0,0,0,0,0,0,1,0,15,6,0,0,0,0,0,1,69,8,0,0,0,0,0,0,112,0,0,0,0,0,0,0,0,112] >;

SD32⋊D7 in GAP, Magma, Sage, TeX

{\rm SD}_{32}\rtimes D_7
% in TeX

G:=Group("SD32:D7");
// GroupNames label

G:=SmallGroup(448,449);
// by ID

G=gap.SmallGroup(448,449);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,135,346,185,192,851,438,102,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^16=b^2=c^7=d^2=1,b*a*b=a^7,a*c=c*a,d*a*d=a^9,b*c=c*b,d*b*d=a^8*b,d*c*d=c^-1>;
// generators/relations

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