metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: SD32⋊2D7, D14.8D8, D8.4D14, C16.2D14, Dic56⋊6C2, Q16.1D14, C56.18C23, C112.9C22, Dic7.10D8, Dic28.3C22, C7⋊C8.4D4, C4.6(D4×D7), D8.D7⋊4C2, D8⋊3D7.C2, (D7×Q16)⋊4C2, (C4×D7).9D4, C7⋊Q32⋊1C2, C2.21(D7×D8), C16⋊D7⋊2C2, (C7×SD32)⋊2C2, C14.37(C2×D8), C28.12(C2×D4), C7⋊2(Q32⋊C2), C7⋊C16.1C22, (C8×D7).5C22, (C7×D8).4C22, C8.24(C22×D7), (C7×Q16).2C22, SmallGroup(448,449)
Series: Derived ►Chief ►Lower central ►Upper central
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, D4⋊2D7, Q8×D7, C16⋊D7, Dic56, D8.D7, C7⋊Q32, C7×SD32, D8⋊3D7, 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
►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