direct product, metabelian, nilpotent (class 4), monomial, 2-elementary
Aliases: C7×C2.D16, D8⋊1C28, C56.94D4, C14.13D16, C14.9SD32, C28.30SD16, (C7×D8)⋊7C4, (C2×C16)⋊3C14, (C2×C112)⋊7C2, C8.7(C2×C28), C2.D8⋊1C14, C8.14(C7×D4), C2.1(C7×D16), C56.63(C2×C4), (C14×D8).7C2, (C2×D8).1C14, (C2×C14).49D8, C4.1(C7×SD16), C2.1(C7×SD32), C22.8(C7×D8), (C2×C28).405D4, C28.69(C22⋊C4), (C2×C56).416C22, C14.37(D4⋊C4), (C7×C2.D8)⋊10C2, (C2×C4).59(C7×D4), C4.1(C7×C22⋊C4), (C2×C8).71(C2×C14), C2.6(C7×D4⋊C4), SmallGroup(448,161)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C2.D16
G = < a,b,c,d | a7=b2=c16=1, d2=b, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=bc-1 >
Subgroups: 178 in 66 conjugacy classes, 34 normal (30 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, C14, C14, C16, C4⋊C4, C2×C8, D8, D8, C2×D4, C28, C28, C2×C14, C2×C14, C2.D8, C2×C16, C2×D8, C56, C2×C28, C2×C28, C7×D4, C22×C14, C2.D16, C112, C7×C4⋊C4, C2×C56, C7×D8, C7×D8, D4×C14, C7×C2.D8, C2×C112, C14×D8, C7×C2.D16
Quotients: C1, C2, C4, C22, C7, C2×C4, D4, C14, C22⋊C4, D8, SD16, C28, C2×C14, D4⋊C4, D16, SD32, C2×C28, C7×D4, C2.D16, C7×C22⋊C4, C7×D8, C7×SD16, C7×D4⋊C4, C7×D16, C7×SD32, C7×C2.D16
►On 224 points
Generators in S224
(1 155 95 62 33 98 205)(2 156 96 63 34 99 206)(3 157 81 64 35 100 207)(4 158 82 49 36 101 208)(5 159 83 50 37 102 193)(6 160 84 51 38 103 194)(7 145 85 52 39 104 195)(8 146 86 53 40 105 196)(9 147 87 54 41 106 197)(10 148 88 55 42 107 198)(11 149 89 56 43 108 199)(12 150 90 57 44 109 200)(13 151 91 58 45 110 201)(14 152 92 59 46 111 202)(15 153 93 60 47 112 203)(16 154 94 61 48 97 204)(17 182 119 76 141 172 218)(18 183 120 77 142 173 219)(19 184 121 78 143 174 220)(20 185 122 79 144 175 221)(21 186 123 80 129 176 222)(22 187 124 65 130 161 223)(23 188 125 66 131 162 224)(24 189 126 67 132 163 209)(25 190 127 68 133 164 210)(26 191 128 69 134 165 211)(27 192 113 70 135 166 212)(28 177 114 71 136 167 213)(29 178 115 72 137 168 214)(30 179 116 73 138 169 215)(31 180 117 74 139 170 216)(32 181 118 75 140 171 217)
(1 134)(2 135)(3 136)(4 137)(5 138)(6 139)(7 140)(8 141)(9 142)(10 143)(11 144)(12 129)(13 130)(14 131)(15 132)(16 133)(17 53)(18 54)(19 55)(20 56)(21 57)(22 58)(23 59)(24 60)(25 61)(26 62)(27 63)(28 64)(29 49)(30 50)(31 51)(32 52)(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)(65 201)(66 202)(67 203)(68 204)(69 205)(70 206)(71 207)(72 208)(73 193)(74 194)(75 195)(76 196)(77 197)(78 198)(79 199)(80 200)(81 213)(82 214)(83 215)(84 216)(85 217)(86 218)(87 219)(88 220)(89 221)(90 222)(91 223)(92 224)(93 209)(94 210)(95 211)(96 212)(97 127)(98 128)(99 113)(100 114)(101 115)(102 116)(103 117)(104 118)(105 119)(106 120)(107 121)(108 122)(109 123)(110 124)(111 125)(112 126)(145 171)(146 172)(147 173)(148 174)(149 175)(150 176)(151 161)(152 162)(153 163)(154 164)(155 165)(156 166)(157 167)(158 168)(159 169)(160 170)
(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)
(1 133 134 16)(2 15 135 132)(3 131 136 14)(4 13 137 130)(5 129 138 12)(6 11 139 144)(7 143 140 10)(8 9 141 142)(17 18 53 54)(19 32 55 52)(20 51 56 31)(21 30 57 50)(22 49 58 29)(23 28 59 64)(24 63 60 27)(25 26 61 62)(33 190 191 48)(34 47 192 189)(35 188 177 46)(36 45 178 187)(37 186 179 44)(38 43 180 185)(39 184 181 42)(40 41 182 183)(65 208 201 72)(66 71 202 207)(67 206 203 70)(68 69 204 205)(73 200 193 80)(74 79 194 199)(75 198 195 78)(76 77 196 197)(81 224 213 92)(82 91 214 223)(83 222 215 90)(84 89 216 221)(85 220 217 88)(86 87 218 219)(93 212 209 96)(94 95 210 211)(97 98 127 128)(99 112 113 126)(100 125 114 111)(101 110 115 124)(102 123 116 109)(103 108 117 122)(104 121 118 107)(105 106 119 120)(145 174 171 148)(146 147 172 173)(149 170 175 160)(150 159 176 169)(151 168 161 158)(152 157 162 167)(153 166 163 156)(154 155 164 165)
G:=sub<Sym(224)| (1,155,95,62,33,98,205)(2,156,96,63,34,99,206)(3,157,81,64,35,100,207)(4,158,82,49,36,101,208)(5,159,83,50,37,102,193)(6,160,84,51,38,103,194)(7,145,85,52,39,104,195)(8,146,86,53,40,105,196)(9,147,87,54,41,106,197)(10,148,88,55,42,107,198)(11,149,89,56,43,108,199)(12,150,90,57,44,109,200)(13,151,91,58,45,110,201)(14,152,92,59,46,111,202)(15,153,93,60,47,112,203)(16,154,94,61,48,97,204)(17,182,119,76,141,172,218)(18,183,120,77,142,173,219)(19,184,121,78,143,174,220)(20,185,122,79,144,175,221)(21,186,123,80,129,176,222)(22,187,124,65,130,161,223)(23,188,125,66,131,162,224)(24,189,126,67,132,163,209)(25,190,127,68,133,164,210)(26,191,128,69,134,165,211)(27,192,113,70,135,166,212)(28,177,114,71,136,167,213)(29,178,115,72,137,168,214)(30,179,116,73,138,169,215)(31,180,117,74,139,170,216)(32,181,118,75,140,171,217), (1,134)(2,135)(3,136)(4,137)(5,138)(6,139)(7,140)(8,141)(9,142)(10,143)(11,144)(12,129)(13,130)(14,131)(15,132)(16,133)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,49)(30,50)(31,51)(32,52)(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)(65,201)(66,202)(67,203)(68,204)(69,205)(70,206)(71,207)(72,208)(73,193)(74,194)(75,195)(76,196)(77,197)(78,198)(79,199)(80,200)(81,213)(82,214)(83,215)(84,216)(85,217)(86,218)(87,219)(88,220)(89,221)(90,222)(91,223)(92,224)(93,209)(94,210)(95,211)(96,212)(97,127)(98,128)(99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(105,119)(106,120)(107,121)(108,122)(109,123)(110,124)(111,125)(112,126)(145,171)(146,172)(147,173)(148,174)(149,175)(150,176)(151,161)(152,162)(153,163)(154,164)(155,165)(156,166)(157,167)(158,168)(159,169)(160,170), (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), (1,133,134,16)(2,15,135,132)(3,131,136,14)(4,13,137,130)(5,129,138,12)(6,11,139,144)(7,143,140,10)(8,9,141,142)(17,18,53,54)(19,32,55,52)(20,51,56,31)(21,30,57,50)(22,49,58,29)(23,28,59,64)(24,63,60,27)(25,26,61,62)(33,190,191,48)(34,47,192,189)(35,188,177,46)(36,45,178,187)(37,186,179,44)(38,43,180,185)(39,184,181,42)(40,41,182,183)(65,208,201,72)(66,71,202,207)(67,206,203,70)(68,69,204,205)(73,200,193,80)(74,79,194,199)(75,198,195,78)(76,77,196,197)(81,224,213,92)(82,91,214,223)(83,222,215,90)(84,89,216,221)(85,220,217,88)(86,87,218,219)(93,212,209,96)(94,95,210,211)(97,98,127,128)(99,112,113,126)(100,125,114,111)(101,110,115,124)(102,123,116,109)(103,108,117,122)(104,121,118,107)(105,106,119,120)(145,174,171,148)(146,147,172,173)(149,170,175,160)(150,159,176,169)(151,168,161,158)(152,157,162,167)(153,166,163,156)(154,155,164,165)>;
G:=Group( (1,155,95,62,33,98,205)(2,156,96,63,34,99,206)(3,157,81,64,35,100,207)(4,158,82,49,36,101,208)(5,159,83,50,37,102,193)(6,160,84,51,38,103,194)(7,145,85,52,39,104,195)(8,146,86,53,40,105,196)(9,147,87,54,41,106,197)(10,148,88,55,42,107,198)(11,149,89,56,43,108,199)(12,150,90,57,44,109,200)(13,151,91,58,45,110,201)(14,152,92,59,46,111,202)(15,153,93,60,47,112,203)(16,154,94,61,48,97,204)(17,182,119,76,141,172,218)(18,183,120,77,142,173,219)(19,184,121,78,143,174,220)(20,185,122,79,144,175,221)(21,186,123,80,129,176,222)(22,187,124,65,130,161,223)(23,188,125,66,131,162,224)(24,189,126,67,132,163,209)(25,190,127,68,133,164,210)(26,191,128,69,134,165,211)(27,192,113,70,135,166,212)(28,177,114,71,136,167,213)(29,178,115,72,137,168,214)(30,179,116,73,138,169,215)(31,180,117,74,139,170,216)(32,181,118,75,140,171,217), (1,134)(2,135)(3,136)(4,137)(5,138)(6,139)(7,140)(8,141)(9,142)(10,143)(11,144)(12,129)(13,130)(14,131)(15,132)(16,133)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,49)(30,50)(31,51)(32,52)(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)(65,201)(66,202)(67,203)(68,204)(69,205)(70,206)(71,207)(72,208)(73,193)(74,194)(75,195)(76,196)(77,197)(78,198)(79,199)(80,200)(81,213)(82,214)(83,215)(84,216)(85,217)(86,218)(87,219)(88,220)(89,221)(90,222)(91,223)(92,224)(93,209)(94,210)(95,211)(96,212)(97,127)(98,128)(99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(105,119)(106,120)(107,121)(108,122)(109,123)(110,124)(111,125)(112,126)(145,171)(146,172)(147,173)(148,174)(149,175)(150,176)(151,161)(152,162)(153,163)(154,164)(155,165)(156,166)(157,167)(158,168)(159,169)(160,170), (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), (1,133,134,16)(2,15,135,132)(3,131,136,14)(4,13,137,130)(5,129,138,12)(6,11,139,144)(7,143,140,10)(8,9,141,142)(17,18,53,54)(19,32,55,52)(20,51,56,31)(21,30,57,50)(22,49,58,29)(23,28,59,64)(24,63,60,27)(25,26,61,62)(33,190,191,48)(34,47,192,189)(35,188,177,46)(36,45,178,187)(37,186,179,44)(38,43,180,185)(39,184,181,42)(40,41,182,183)(65,208,201,72)(66,71,202,207)(67,206,203,70)(68,69,204,205)(73,200,193,80)(74,79,194,199)(75,198,195,78)(76,77,196,197)(81,224,213,92)(82,91,214,223)(83,222,215,90)(84,89,216,221)(85,220,217,88)(86,87,218,219)(93,212,209,96)(94,95,210,211)(97,98,127,128)(99,112,113,126)(100,125,114,111)(101,110,115,124)(102,123,116,109)(103,108,117,122)(104,121,118,107)(105,106,119,120)(145,174,171,148)(146,147,172,173)(149,170,175,160)(150,159,176,169)(151,168,161,158)(152,157,162,167)(153,166,163,156)(154,155,164,165) );
G=PermutationGroup([[(1,155,95,62,33,98,205),(2,156,96,63,34,99,206),(3,157,81,64,35,100,207),(4,158,82,49,36,101,208),(5,159,83,50,37,102,193),(6,160,84,51,38,103,194),(7,145,85,52,39,104,195),(8,146,86,53,40,105,196),(9,147,87,54,41,106,197),(10,148,88,55,42,107,198),(11,149,89,56,43,108,199),(12,150,90,57,44,109,200),(13,151,91,58,45,110,201),(14,152,92,59,46,111,202),(15,153,93,60,47,112,203),(16,154,94,61,48,97,204),(17,182,119,76,141,172,218),(18,183,120,77,142,173,219),(19,184,121,78,143,174,220),(20,185,122,79,144,175,221),(21,186,123,80,129,176,222),(22,187,124,65,130,161,223),(23,188,125,66,131,162,224),(24,189,126,67,132,163,209),(25,190,127,68,133,164,210),(26,191,128,69,134,165,211),(27,192,113,70,135,166,212),(28,177,114,71,136,167,213),(29,178,115,72,137,168,214),(30,179,116,73,138,169,215),(31,180,117,74,139,170,216),(32,181,118,75,140,171,217)], [(1,134),(2,135),(3,136),(4,137),(5,138),(6,139),(7,140),(8,141),(9,142),(10,143),(11,144),(12,129),(13,130),(14,131),(15,132),(16,133),(17,53),(18,54),(19,55),(20,56),(21,57),(22,58),(23,59),(24,60),(25,61),(26,62),(27,63),(28,64),(29,49),(30,50),(31,51),(32,52),(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),(65,201),(66,202),(67,203),(68,204),(69,205),(70,206),(71,207),(72,208),(73,193),(74,194),(75,195),(76,196),(77,197),(78,198),(79,199),(80,200),(81,213),(82,214),(83,215),(84,216),(85,217),(86,218),(87,219),(88,220),(89,221),(90,222),(91,223),(92,224),(93,209),(94,210),(95,211),(96,212),(97,127),(98,128),(99,113),(100,114),(101,115),(102,116),(103,117),(104,118),(105,119),(106,120),(107,121),(108,122),(109,123),(110,124),(111,125),(112,126),(145,171),(146,172),(147,173),(148,174),(149,175),(150,176),(151,161),(152,162),(153,163),(154,164),(155,165),(156,166),(157,167),(158,168),(159,169),(160,170)], [(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)], [(1,133,134,16),(2,15,135,132),(3,131,136,14),(4,13,137,130),(5,129,138,12),(6,11,139,144),(7,143,140,10),(8,9,141,142),(17,18,53,54),(19,32,55,52),(20,51,56,31),(21,30,57,50),(22,49,58,29),(23,28,59,64),(24,63,60,27),(25,26,61,62),(33,190,191,48),(34,47,192,189),(35,188,177,46),(36,45,178,187),(37,186,179,44),(38,43,180,185),(39,184,181,42),(40,41,182,183),(65,208,201,72),(66,71,202,207),(67,206,203,70),(68,69,204,205),(73,200,193,80),(74,79,194,199),(75,198,195,78),(76,77,196,197),(81,224,213,92),(82,91,214,223),(83,222,215,90),(84,89,216,221),(85,220,217,88),(86,87,218,219),(93,212,209,96),(94,95,210,211),(97,98,127,128),(99,112,113,126),(100,125,114,111),(101,110,115,124),(102,123,116,109),(103,108,117,122),(104,121,118,107),(105,106,119,120),(145,174,171,148),(146,147,172,173),(149,170,175,160),(150,159,176,169),(151,168,161,158),(152,157,162,167),(153,166,163,156),(154,155,164,165)]])
154 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 14A | ··· | 14R | 14S | ··· | 14AD | 16A | ··· | 16H | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X | 112A | ··· | 112AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 16 | ··· | 16 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 | 112 | ··· | 112 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 2 | 2 | 8 | 8 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 8 | ··· | 8 | 2 | ··· | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 2 | ··· | 2 | 2 | ··· | 2 |
154 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | ||||||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C7 | C14 | C14 | C14 | C28 | D4 | D4 | SD16 | D8 | D16 | SD32 | C7×D4 | C7×D4 | C7×SD16 | C7×D8 | C7×D16 | C7×SD32 |
| kernel | C7×C2.D16 | C7×C2.D8 | C2×C112 | C14×D8 | C7×D8 | C2.D16 | C2.D8 | C2×C16 | C2×D8 | D8 | C56 | C2×C28 | C28 | C2×C14 | C14 | C14 | C8 | C2×C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 6 | 6 | 6 | 6 | 24 | 1 | 1 | 2 | 2 | 4 | 4 | 6 | 6 | 12 | 12 | 24 | 24 |
Matrix representation of C7×C2.D16 ►in GL5(𝔽113)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 106 | 0 | 0 | 0 |
| 0 | 0 | 106 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 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 |
| 98 | 0 | 0 | 0 | 0 |
| 0 | 70 | 23 | 0 | 0 |
| 0 | 8 | 43 | 0 | 0 |
| 0 | 0 | 0 | 4 | 18 |
| 0 | 0 | 0 | 95 | 4 |
| 15 | 0 | 0 | 0 | 0 |
| 0 | 43 | 5 | 0 | 0 |
| 0 | 105 | 70 | 0 | 0 |
| 0 | 0 | 0 | 4 | 18 |
| 0 | 0 | 0 | 18 | 109 |
G:=sub<GL(5,GF(113))| [1,0,0,0,0,0,106,0,0,0,0,0,106,0,0,0,0,0,1,0,0,0,0,0,1],[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],[98,0,0,0,0,0,70,8,0,0,0,23,43,0,0,0,0,0,4,95,0,0,0,18,4],[15,0,0,0,0,0,43,105,0,0,0,5,70,0,0,0,0,0,4,18,0,0,0,18,109] >;
C7×C2.D16 in GAP, Magma, Sage, TeX
C_7\times C_2.D_{16} % in TeX
G:=Group("C7xC2.D16"); // GroupNames label
G:=SmallGroup(448,161);
// by ID
G=gap.SmallGroup(448,161);
# by ID
G:=PCGroup([7,-2,-2,-7,-2,-2,-2,-2,392,421,3923,1970,360,14117,7068,124]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^2=c^16=1,d^2=b,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=b*c^-1>;
// generators/relations