direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C7⋊SD32, Q16⋊6D14, C14⋊3SD32, C56.24D4, C28.23D8, C56.26C23, D56.9C22, C7⋊4(C2×SD32), C7⋊C16⋊9C22, (C2×Q16)⋊1D7, (C14×Q16)⋊4C2, C14.65(C2×D8), (C2×C14).44D8, C4.10(D4⋊D7), (C2×D56).10C2, (C2×C8).239D14, C28.181(C2×D4), (C2×C28).182D4, C8.16(C7⋊D4), (C7×Q16)⋊6C22, C8.32(C22×D7), (C2×C56).91C22, C22.23(D4⋊D7), (C2×C7⋊C16)⋊8C2, C2.20(C2×D4⋊D7), C4.11(C2×C7⋊D4), (C2×C4).144(C7⋊D4), SmallGroup(448,712)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C7⋊SD32
G = < a,b,c,d | a2=b7=c16=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c7 >
Subgroups: 612 in 90 conjugacy classes, 39 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C16, C2×C8, D8, Q16, Q16, C2×D4, C2×Q8, C28, C28, D14, C2×C14, C2×C16, SD32, C2×D8, C2×Q16, C56, D28, C2×C28, C2×C28, C7×Q8, C22×D7, C2×SD32, C7⋊C16, D56, D56, C2×C56, C7×Q16, C7×Q16, C2×D28, Q8×C14, C2×C7⋊C16, C7⋊SD32, C2×D56, C14×Q16, C2×C7⋊SD32
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, D14, SD32, C2×D8, C7⋊D4, C22×D7, C2×SD32, D4⋊D7, C2×C7⋊D4, C7⋊SD32, C2×D4⋊D7, C2×C7⋊SD32
►On 224 points
Generators in S224
(1 89)(2 90)(3 91)(4 92)(5 93)(6 94)(7 95)(8 96)(9 81)(10 82)(11 83)(12 84)(13 85)(14 86)(15 87)(16 88)(17 215)(18 216)(19 217)(20 218)(21 219)(22 220)(23 221)(24 222)(25 223)(26 224)(27 209)(28 210)(29 211)(30 212)(31 213)(32 214)(33 191)(34 192)(35 177)(36 178)(37 179)(38 180)(39 181)(40 182)(41 183)(42 184)(43 185)(44 186)(45 187)(46 188)(47 189)(48 190)(49 132)(50 133)(51 134)(52 135)(53 136)(54 137)(55 138)(56 139)(57 140)(58 141)(59 142)(60 143)(61 144)(62 129)(63 130)(64 131)(65 98)(66 99)(67 100)(68 101)(69 102)(70 103)(71 104)(72 105)(73 106)(74 107)(75 108)(76 109)(77 110)(78 111)(79 112)(80 97)(113 204)(114 205)(115 206)(116 207)(117 208)(118 193)(119 194)(120 195)(121 196)(122 197)(123 198)(124 199)(125 200)(126 201)(127 202)(128 203)(145 175)(146 176)(147 161)(148 162)(149 163)(150 164)(151 165)(152 166)(153 167)(154 168)(155 169)(156 170)(157 171)(158 172)(159 173)(160 174)
(1 129 163 110 17 185 121)(2 122 186 18 111 164 130)(3 131 165 112 19 187 123)(4 124 188 20 97 166 132)(5 133 167 98 21 189 125)(6 126 190 22 99 168 134)(7 135 169 100 23 191 127)(8 128 192 24 101 170 136)(9 137 171 102 25 177 113)(10 114 178 26 103 172 138)(11 139 173 104 27 179 115)(12 116 180 28 105 174 140)(13 141 175 106 29 181 117)(14 118 182 30 107 176 142)(15 143 161 108 31 183 119)(16 120 184 32 109 162 144)(33 202 95 52 155 67 221)(34 222 68 156 53 96 203)(35 204 81 54 157 69 223)(36 224 70 158 55 82 205)(37 206 83 56 159 71 209)(38 210 72 160 57 84 207)(39 208 85 58 145 73 211)(40 212 74 146 59 86 193)(41 194 87 60 147 75 213)(42 214 76 148 61 88 195)(43 196 89 62 149 77 215)(44 216 78 150 63 90 197)(45 198 91 64 151 79 217)(46 218 80 152 49 92 199)(47 200 93 50 153 65 219)(48 220 66 154 51 94 201)
(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)
(2 8)(3 15)(4 6)(5 13)(7 11)(10 16)(12 14)(17 110)(18 101)(19 108)(20 99)(21 106)(22 97)(23 104)(24 111)(25 102)(26 109)(27 100)(28 107)(29 98)(30 105)(31 112)(32 103)(33 159)(34 150)(35 157)(36 148)(37 155)(38 146)(39 153)(40 160)(41 151)(42 158)(43 149)(44 156)(45 147)(46 154)(47 145)(48 152)(49 201)(50 208)(51 199)(52 206)(53 197)(54 204)(55 195)(56 202)(57 193)(58 200)(59 207)(60 198)(61 205)(62 196)(63 203)(64 194)(65 211)(66 218)(67 209)(68 216)(69 223)(70 214)(71 221)(72 212)(73 219)(74 210)(75 217)(76 224)(77 215)(78 222)(79 213)(80 220)(82 88)(83 95)(84 86)(85 93)(87 91)(90 96)(92 94)(113 137)(114 144)(115 135)(116 142)(117 133)(118 140)(119 131)(120 138)(121 129)(122 136)(123 143)(124 134)(125 141)(126 132)(127 139)(128 130)(161 187)(162 178)(163 185)(164 192)(165 183)(166 190)(167 181)(168 188)(169 179)(170 186)(171 177)(172 184)(173 191)(174 182)(175 189)(176 180)
G:=sub<Sym(224)| (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,81)(10,82)(11,83)(12,84)(13,85)(14,86)(15,87)(16,88)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,209)(28,210)(29,211)(30,212)(31,213)(32,214)(33,191)(34,192)(35,177)(36,178)(37,179)(38,180)(39,181)(40,182)(41,183)(42,184)(43,185)(44,186)(45,187)(46,188)(47,189)(48,190)(49,132)(50,133)(51,134)(52,135)(53,136)(54,137)(55,138)(56,139)(57,140)(58,141)(59,142)(60,143)(61,144)(62,129)(63,130)(64,131)(65,98)(66,99)(67,100)(68,101)(69,102)(70,103)(71,104)(72,105)(73,106)(74,107)(75,108)(76,109)(77,110)(78,111)(79,112)(80,97)(113,204)(114,205)(115,206)(116,207)(117,208)(118,193)(119,194)(120,195)(121,196)(122,197)(123,198)(124,199)(125,200)(126,201)(127,202)(128,203)(145,175)(146,176)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(155,169)(156,170)(157,171)(158,172)(159,173)(160,174), (1,129,163,110,17,185,121)(2,122,186,18,111,164,130)(3,131,165,112,19,187,123)(4,124,188,20,97,166,132)(5,133,167,98,21,189,125)(6,126,190,22,99,168,134)(7,135,169,100,23,191,127)(8,128,192,24,101,170,136)(9,137,171,102,25,177,113)(10,114,178,26,103,172,138)(11,139,173,104,27,179,115)(12,116,180,28,105,174,140)(13,141,175,106,29,181,117)(14,118,182,30,107,176,142)(15,143,161,108,31,183,119)(16,120,184,32,109,162,144)(33,202,95,52,155,67,221)(34,222,68,156,53,96,203)(35,204,81,54,157,69,223)(36,224,70,158,55,82,205)(37,206,83,56,159,71,209)(38,210,72,160,57,84,207)(39,208,85,58,145,73,211)(40,212,74,146,59,86,193)(41,194,87,60,147,75,213)(42,214,76,148,61,88,195)(43,196,89,62,149,77,215)(44,216,78,150,63,90,197)(45,198,91,64,151,79,217)(46,218,80,152,49,92,199)(47,200,93,50,153,65,219)(48,220,66,154,51,94,201), (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), (2,8)(3,15)(4,6)(5,13)(7,11)(10,16)(12,14)(17,110)(18,101)(19,108)(20,99)(21,106)(22,97)(23,104)(24,111)(25,102)(26,109)(27,100)(28,107)(29,98)(30,105)(31,112)(32,103)(33,159)(34,150)(35,157)(36,148)(37,155)(38,146)(39,153)(40,160)(41,151)(42,158)(43,149)(44,156)(45,147)(46,154)(47,145)(48,152)(49,201)(50,208)(51,199)(52,206)(53,197)(54,204)(55,195)(56,202)(57,193)(58,200)(59,207)(60,198)(61,205)(62,196)(63,203)(64,194)(65,211)(66,218)(67,209)(68,216)(69,223)(70,214)(71,221)(72,212)(73,219)(74,210)(75,217)(76,224)(77,215)(78,222)(79,213)(80,220)(82,88)(83,95)(84,86)(85,93)(87,91)(90,96)(92,94)(113,137)(114,144)(115,135)(116,142)(117,133)(118,140)(119,131)(120,138)(121,129)(122,136)(123,143)(124,134)(125,141)(126,132)(127,139)(128,130)(161,187)(162,178)(163,185)(164,192)(165,183)(166,190)(167,181)(168,188)(169,179)(170,186)(171,177)(172,184)(173,191)(174,182)(175,189)(176,180)>;
G:=Group( (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,81)(10,82)(11,83)(12,84)(13,85)(14,86)(15,87)(16,88)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,209)(28,210)(29,211)(30,212)(31,213)(32,214)(33,191)(34,192)(35,177)(36,178)(37,179)(38,180)(39,181)(40,182)(41,183)(42,184)(43,185)(44,186)(45,187)(46,188)(47,189)(48,190)(49,132)(50,133)(51,134)(52,135)(53,136)(54,137)(55,138)(56,139)(57,140)(58,141)(59,142)(60,143)(61,144)(62,129)(63,130)(64,131)(65,98)(66,99)(67,100)(68,101)(69,102)(70,103)(71,104)(72,105)(73,106)(74,107)(75,108)(76,109)(77,110)(78,111)(79,112)(80,97)(113,204)(114,205)(115,206)(116,207)(117,208)(118,193)(119,194)(120,195)(121,196)(122,197)(123,198)(124,199)(125,200)(126,201)(127,202)(128,203)(145,175)(146,176)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(155,169)(156,170)(157,171)(158,172)(159,173)(160,174), (1,129,163,110,17,185,121)(2,122,186,18,111,164,130)(3,131,165,112,19,187,123)(4,124,188,20,97,166,132)(5,133,167,98,21,189,125)(6,126,190,22,99,168,134)(7,135,169,100,23,191,127)(8,128,192,24,101,170,136)(9,137,171,102,25,177,113)(10,114,178,26,103,172,138)(11,139,173,104,27,179,115)(12,116,180,28,105,174,140)(13,141,175,106,29,181,117)(14,118,182,30,107,176,142)(15,143,161,108,31,183,119)(16,120,184,32,109,162,144)(33,202,95,52,155,67,221)(34,222,68,156,53,96,203)(35,204,81,54,157,69,223)(36,224,70,158,55,82,205)(37,206,83,56,159,71,209)(38,210,72,160,57,84,207)(39,208,85,58,145,73,211)(40,212,74,146,59,86,193)(41,194,87,60,147,75,213)(42,214,76,148,61,88,195)(43,196,89,62,149,77,215)(44,216,78,150,63,90,197)(45,198,91,64,151,79,217)(46,218,80,152,49,92,199)(47,200,93,50,153,65,219)(48,220,66,154,51,94,201), (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), (2,8)(3,15)(4,6)(5,13)(7,11)(10,16)(12,14)(17,110)(18,101)(19,108)(20,99)(21,106)(22,97)(23,104)(24,111)(25,102)(26,109)(27,100)(28,107)(29,98)(30,105)(31,112)(32,103)(33,159)(34,150)(35,157)(36,148)(37,155)(38,146)(39,153)(40,160)(41,151)(42,158)(43,149)(44,156)(45,147)(46,154)(47,145)(48,152)(49,201)(50,208)(51,199)(52,206)(53,197)(54,204)(55,195)(56,202)(57,193)(58,200)(59,207)(60,198)(61,205)(62,196)(63,203)(64,194)(65,211)(66,218)(67,209)(68,216)(69,223)(70,214)(71,221)(72,212)(73,219)(74,210)(75,217)(76,224)(77,215)(78,222)(79,213)(80,220)(82,88)(83,95)(84,86)(85,93)(87,91)(90,96)(92,94)(113,137)(114,144)(115,135)(116,142)(117,133)(118,140)(119,131)(120,138)(121,129)(122,136)(123,143)(124,134)(125,141)(126,132)(127,139)(128,130)(161,187)(162,178)(163,185)(164,192)(165,183)(166,190)(167,181)(168,188)(169,179)(170,186)(171,177)(172,184)(173,191)(174,182)(175,189)(176,180) );
G=PermutationGroup([[(1,89),(2,90),(3,91),(4,92),(5,93),(6,94),(7,95),(8,96),(9,81),(10,82),(11,83),(12,84),(13,85),(14,86),(15,87),(16,88),(17,215),(18,216),(19,217),(20,218),(21,219),(22,220),(23,221),(24,222),(25,223),(26,224),(27,209),(28,210),(29,211),(30,212),(31,213),(32,214),(33,191),(34,192),(35,177),(36,178),(37,179),(38,180),(39,181),(40,182),(41,183),(42,184),(43,185),(44,186),(45,187),(46,188),(47,189),(48,190),(49,132),(50,133),(51,134),(52,135),(53,136),(54,137),(55,138),(56,139),(57,140),(58,141),(59,142),(60,143),(61,144),(62,129),(63,130),(64,131),(65,98),(66,99),(67,100),(68,101),(69,102),(70,103),(71,104),(72,105),(73,106),(74,107),(75,108),(76,109),(77,110),(78,111),(79,112),(80,97),(113,204),(114,205),(115,206),(116,207),(117,208),(118,193),(119,194),(120,195),(121,196),(122,197),(123,198),(124,199),(125,200),(126,201),(127,202),(128,203),(145,175),(146,176),(147,161),(148,162),(149,163),(150,164),(151,165),(152,166),(153,167),(154,168),(155,169),(156,170),(157,171),(158,172),(159,173),(160,174)], [(1,129,163,110,17,185,121),(2,122,186,18,111,164,130),(3,131,165,112,19,187,123),(4,124,188,20,97,166,132),(5,133,167,98,21,189,125),(6,126,190,22,99,168,134),(7,135,169,100,23,191,127),(8,128,192,24,101,170,136),(9,137,171,102,25,177,113),(10,114,178,26,103,172,138),(11,139,173,104,27,179,115),(12,116,180,28,105,174,140),(13,141,175,106,29,181,117),(14,118,182,30,107,176,142),(15,143,161,108,31,183,119),(16,120,184,32,109,162,144),(33,202,95,52,155,67,221),(34,222,68,156,53,96,203),(35,204,81,54,157,69,223),(36,224,70,158,55,82,205),(37,206,83,56,159,71,209),(38,210,72,160,57,84,207),(39,208,85,58,145,73,211),(40,212,74,146,59,86,193),(41,194,87,60,147,75,213),(42,214,76,148,61,88,195),(43,196,89,62,149,77,215),(44,216,78,150,63,90,197),(45,198,91,64,151,79,217),(46,218,80,152,49,92,199),(47,200,93,50,153,65,219),(48,220,66,154,51,94,201)], [(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)], [(2,8),(3,15),(4,6),(5,13),(7,11),(10,16),(12,14),(17,110),(18,101),(19,108),(20,99),(21,106),(22,97),(23,104),(24,111),(25,102),(26,109),(27,100),(28,107),(29,98),(30,105),(31,112),(32,103),(33,159),(34,150),(35,157),(36,148),(37,155),(38,146),(39,153),(40,160),(41,151),(42,158),(43,149),(44,156),(45,147),(46,154),(47,145),(48,152),(49,201),(50,208),(51,199),(52,206),(53,197),(54,204),(55,195),(56,202),(57,193),(58,200),(59,207),(60,198),(61,205),(62,196),(63,203),(64,194),(65,211),(66,218),(67,209),(68,216),(69,223),(70,214),(71,221),(72,212),(73,219),(74,210),(75,217),(76,224),(77,215),(78,222),(79,213),(80,220),(82,88),(83,95),(84,86),(85,93),(87,91),(90,96),(92,94),(113,137),(114,144),(115,135),(116,142),(117,133),(118,140),(119,131),(120,138),(121,129),(122,136),(123,143),(124,134),(125,141),(126,132),(127,139),(128,130),(161,187),(162,178),(163,185),(164,192),(165,183),(166,190),(167,181),(168,188),(169,179),(170,186),(171,177),(172,184),(173,191),(174,182),(175,189),(176,180)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 16A | ··· | 16H | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 16 | ··· | 16 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 56 | 56 | 2 | 2 | 8 | 8 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 14 | ··· | 14 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | D8 | D8 | D14 | D14 | SD32 | C7⋊D4 | C7⋊D4 | D4⋊D7 | D4⋊D7 | C7⋊SD32 |
| kernel | C2×C7⋊SD32 | C2×C7⋊C16 | C7⋊SD32 | C2×D56 | C14×Q16 | C56 | C2×C28 | C2×Q16 | C28 | C2×C14 | C2×C8 | Q16 | C14 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 3 | 2 | 2 | 3 | 6 | 8 | 6 | 6 | 3 | 3 | 12 |
Matrix representation of C2×C7⋊SD32 ►in GL5(𝔽113)
| 112 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 9 | 112 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 112 | 0 | 0 | 0 | 0 |
| 0 | 79 | 108 | 0 | 0 |
| 0 | 28 | 34 | 0 | 0 |
| 0 | 0 | 0 | 9 | 81 |
| 0 | 0 | 0 | 112 | 16 |
| 112 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 9 | 112 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 81 | 112 |
G:=sub<GL(5,GF(113))| [112,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,9,1,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,1],[112,0,0,0,0,0,79,28,0,0,0,108,34,0,0,0,0,0,9,112,0,0,0,81,16],[112,0,0,0,0,0,1,9,0,0,0,0,112,0,0,0,0,0,1,81,0,0,0,0,112] >;
C2×C7⋊SD32 in GAP, Magma, Sage, TeX
C_2\times C_7\rtimes {\rm SD}_{32} % in TeX
G:=Group("C2xC7:SD32"); // GroupNames label
G:=SmallGroup(448,712);
// by ID
G=gap.SmallGroup(448,712);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,254,184,675,185,192,1684,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^7=c^16=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^7>;
// generators/relations