metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊C8.4C2, Q8⋊C4⋊7D7, C56⋊1C4⋊11C2, (C2×C8).19D14, C4⋊C4.153D14, Q8⋊Dic7⋊9C2, (C2×Q8).20D14, C14.71(C4○D8), C4.57(C4○D28), (C2×C56).19C22, D14⋊3Q8.4C2, C4.Dic14⋊12C2, (C22×D7).20D4, C22.204(D4×D7), C28.163(C4○D4), C4.88(D4⋊2D7), (C2×C28).254C23, (C2×Dic7).156D4, C7⋊2(C23.20D4), C4⋊Dic7.98C22, (Q8×C14).37C22, C2.10(Q8.D14), C2.18(SD16⋊D7), C14.36(C8.C22), C2.18(D14.D4), C14.26(C22.D4), C4⋊C4⋊7D7.2C2, (C7×Q8⋊C4)⋊7C2, (C2×C7⋊C8).44C22, (C2×C4×D7).26C22, (C2×C14).267(C2×D4), (C7×C4⋊C4).55C22, (C2×C4).361(C22×D7), SmallGroup(448,348)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊C8.C2
G = < a,b,c,d | a14=b2=c8=1, d2=a7c4, bab=a-1, ac=ca, ad=da, cbc-1=a7b, dbd-1=bc4, dcd-1=a7c-1 >
Subgroups: 468 in 96 conjugacy classes, 37 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C22⋊C8, Q8⋊C4, Q8⋊C4, C4.Q8, C2.D8, C42⋊C2, C22⋊Q8, C7⋊C8, C56, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C23.20D4, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×C4×D7, Q8×C14, C4.Dic14, C56⋊1C4, D14⋊C8, Q8⋊Dic7, C7×Q8⋊C4, C4⋊C4⋊7D7, D14⋊3Q8, D14⋊C8.C2
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C22.D4, C4○D8, C8.C22, C22×D7, C23.20D4, C4○D28, D4×D7, D4⋊2D7, D14.D4, SD16⋊D7, Q8.D14, D14⋊C8.C2
►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 40)(2 39)(3 38)(4 37)(5 36)(6 35)(7 34)(8 33)(9 32)(10 31)(11 30)(12 29)(13 42)(14 41)(15 27)(16 26)(17 25)(18 24)(19 23)(20 22)(43 223)(44 222)(45 221)(46 220)(47 219)(48 218)(49 217)(50 216)(51 215)(52 214)(53 213)(54 212)(55 211)(56 224)(57 156)(58 155)(59 168)(60 167)(61 166)(62 165)(63 164)(64 163)(65 162)(66 161)(67 160)(68 159)(69 158)(70 157)(71 74)(72 73)(75 84)(76 83)(77 82)(78 81)(79 80)(85 88)(86 87)(89 98)(90 97)(91 96)(92 95)(93 94)(99 101)(102 112)(103 111)(104 110)(105 109)(106 108)(113 119)(114 118)(115 117)(120 126)(121 125)(122 124)(127 137)(128 136)(129 135)(130 134)(131 133)(138 140)(141 142)(143 154)(144 153)(145 152)(146 151)(147 150)(148 149)(169 191)(170 190)(171 189)(172 188)(173 187)(174 186)(175 185)(176 184)(177 183)(178 196)(179 195)(180 194)(181 193)(182 192)(197 204)(198 203)(199 202)(200 201)(205 210)(206 209)(207 208)
(1 215 156 191 41 45 58 177)(2 216 157 192 42 46 59 178)(3 217 158 193 29 47 60 179)(4 218 159 194 30 48 61 180)(5 219 160 195 31 49 62 181)(6 220 161 196 32 50 63 182)(7 221 162 183 33 51 64 169)(8 222 163 184 34 52 65 170)(9 223 164 185 35 53 66 171)(10 224 165 186 36 54 67 172)(11 211 166 187 37 55 68 173)(12 212 167 188 38 56 69 174)(13 213 168 189 39 43 70 175)(14 214 155 190 40 44 57 176)(15 77 101 198 133 153 124 91)(16 78 102 199 134 154 125 92)(17 79 103 200 135 141 126 93)(18 80 104 201 136 142 113 94)(19 81 105 202 137 143 114 95)(20 82 106 203 138 144 115 96)(21 83 107 204 139 145 116 97)(22 84 108 205 140 146 117 98)(23 71 109 206 127 147 118 85)(24 72 110 207 128 148 119 86)(25 73 111 208 129 149 120 87)(26 74 112 209 130 150 121 88)(27 75 99 210 131 151 122 89)(28 76 100 197 132 152 123 90)
(1 201 34 87)(2 202 35 88)(3 203 36 89)(4 204 37 90)(5 205 38 91)(6 206 39 92)(7 207 40 93)(8 208 41 94)(9 209 42 95)(10 210 29 96)(11 197 30 97)(12 198 31 98)(13 199 32 85)(14 200 33 86)(15 174 140 195)(16 175 127 196)(17 176 128 183)(18 177 129 184)(19 178 130 185)(20 179 131 186)(21 180 132 187)(22 181 133 188)(23 182 134 189)(24 169 135 190)(25 170 136 191)(26 171 137 192)(27 172 138 193)(28 173 139 194)(43 118 220 102)(44 119 221 103)(45 120 222 104)(46 121 223 105)(47 122 224 106)(48 123 211 107)(49 124 212 108)(50 125 213 109)(51 126 214 110)(52 113 215 111)(53 114 216 112)(54 115 217 99)(55 116 218 100)(56 117 219 101)(57 141 162 72)(58 142 163 73)(59 143 164 74)(60 144 165 75)(61 145 166 76)(62 146 167 77)(63 147 168 78)(64 148 155 79)(65 149 156 80)(66 150 157 81)(67 151 158 82)(68 152 159 83)(69 153 160 84)(70 154 161 71)
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), (1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,42)(14,41)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)(43,223)(44,222)(45,221)(46,220)(47,219)(48,218)(49,217)(50,216)(51,215)(52,214)(53,213)(54,212)(55,211)(56,224)(57,156)(58,155)(59,168)(60,167)(61,166)(62,165)(63,164)(64,163)(65,162)(66,161)(67,160)(68,159)(69,158)(70,157)(71,74)(72,73)(75,84)(76,83)(77,82)(78,81)(79,80)(85,88)(86,87)(89,98)(90,97)(91,96)(92,95)(93,94)(99,101)(102,112)(103,111)(104,110)(105,109)(106,108)(113,119)(114,118)(115,117)(120,126)(121,125)(122,124)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,142)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(169,191)(170,190)(171,189)(172,188)(173,187)(174,186)(175,185)(176,184)(177,183)(178,196)(179,195)(180,194)(181,193)(182,192)(197,204)(198,203)(199,202)(200,201)(205,210)(206,209)(207,208), (1,215,156,191,41,45,58,177)(2,216,157,192,42,46,59,178)(3,217,158,193,29,47,60,179)(4,218,159,194,30,48,61,180)(5,219,160,195,31,49,62,181)(6,220,161,196,32,50,63,182)(7,221,162,183,33,51,64,169)(8,222,163,184,34,52,65,170)(9,223,164,185,35,53,66,171)(10,224,165,186,36,54,67,172)(11,211,166,187,37,55,68,173)(12,212,167,188,38,56,69,174)(13,213,168,189,39,43,70,175)(14,214,155,190,40,44,57,176)(15,77,101,198,133,153,124,91)(16,78,102,199,134,154,125,92)(17,79,103,200,135,141,126,93)(18,80,104,201,136,142,113,94)(19,81,105,202,137,143,114,95)(20,82,106,203,138,144,115,96)(21,83,107,204,139,145,116,97)(22,84,108,205,140,146,117,98)(23,71,109,206,127,147,118,85)(24,72,110,207,128,148,119,86)(25,73,111,208,129,149,120,87)(26,74,112,209,130,150,121,88)(27,75,99,210,131,151,122,89)(28,76,100,197,132,152,123,90), (1,201,34,87)(2,202,35,88)(3,203,36,89)(4,204,37,90)(5,205,38,91)(6,206,39,92)(7,207,40,93)(8,208,41,94)(9,209,42,95)(10,210,29,96)(11,197,30,97)(12,198,31,98)(13,199,32,85)(14,200,33,86)(15,174,140,195)(16,175,127,196)(17,176,128,183)(18,177,129,184)(19,178,130,185)(20,179,131,186)(21,180,132,187)(22,181,133,188)(23,182,134,189)(24,169,135,190)(25,170,136,191)(26,171,137,192)(27,172,138,193)(28,173,139,194)(43,118,220,102)(44,119,221,103)(45,120,222,104)(46,121,223,105)(47,122,224,106)(48,123,211,107)(49,124,212,108)(50,125,213,109)(51,126,214,110)(52,113,215,111)(53,114,216,112)(54,115,217,99)(55,116,218,100)(56,117,219,101)(57,141,162,72)(58,142,163,73)(59,143,164,74)(60,144,165,75)(61,145,166,76)(62,146,167,77)(63,147,168,78)(64,148,155,79)(65,149,156,80)(66,150,157,81)(67,151,158,82)(68,152,159,83)(69,153,160,84)(70,154,161,71)>;
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), (1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,42)(14,41)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)(43,223)(44,222)(45,221)(46,220)(47,219)(48,218)(49,217)(50,216)(51,215)(52,214)(53,213)(54,212)(55,211)(56,224)(57,156)(58,155)(59,168)(60,167)(61,166)(62,165)(63,164)(64,163)(65,162)(66,161)(67,160)(68,159)(69,158)(70,157)(71,74)(72,73)(75,84)(76,83)(77,82)(78,81)(79,80)(85,88)(86,87)(89,98)(90,97)(91,96)(92,95)(93,94)(99,101)(102,112)(103,111)(104,110)(105,109)(106,108)(113,119)(114,118)(115,117)(120,126)(121,125)(122,124)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,142)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(169,191)(170,190)(171,189)(172,188)(173,187)(174,186)(175,185)(176,184)(177,183)(178,196)(179,195)(180,194)(181,193)(182,192)(197,204)(198,203)(199,202)(200,201)(205,210)(206,209)(207,208), (1,215,156,191,41,45,58,177)(2,216,157,192,42,46,59,178)(3,217,158,193,29,47,60,179)(4,218,159,194,30,48,61,180)(5,219,160,195,31,49,62,181)(6,220,161,196,32,50,63,182)(7,221,162,183,33,51,64,169)(8,222,163,184,34,52,65,170)(9,223,164,185,35,53,66,171)(10,224,165,186,36,54,67,172)(11,211,166,187,37,55,68,173)(12,212,167,188,38,56,69,174)(13,213,168,189,39,43,70,175)(14,214,155,190,40,44,57,176)(15,77,101,198,133,153,124,91)(16,78,102,199,134,154,125,92)(17,79,103,200,135,141,126,93)(18,80,104,201,136,142,113,94)(19,81,105,202,137,143,114,95)(20,82,106,203,138,144,115,96)(21,83,107,204,139,145,116,97)(22,84,108,205,140,146,117,98)(23,71,109,206,127,147,118,85)(24,72,110,207,128,148,119,86)(25,73,111,208,129,149,120,87)(26,74,112,209,130,150,121,88)(27,75,99,210,131,151,122,89)(28,76,100,197,132,152,123,90), (1,201,34,87)(2,202,35,88)(3,203,36,89)(4,204,37,90)(5,205,38,91)(6,206,39,92)(7,207,40,93)(8,208,41,94)(9,209,42,95)(10,210,29,96)(11,197,30,97)(12,198,31,98)(13,199,32,85)(14,200,33,86)(15,174,140,195)(16,175,127,196)(17,176,128,183)(18,177,129,184)(19,178,130,185)(20,179,131,186)(21,180,132,187)(22,181,133,188)(23,182,134,189)(24,169,135,190)(25,170,136,191)(26,171,137,192)(27,172,138,193)(28,173,139,194)(43,118,220,102)(44,119,221,103)(45,120,222,104)(46,121,223,105)(47,122,224,106)(48,123,211,107)(49,124,212,108)(50,125,213,109)(51,126,214,110)(52,113,215,111)(53,114,216,112)(54,115,217,99)(55,116,218,100)(56,117,219,101)(57,141,162,72)(58,142,163,73)(59,143,164,74)(60,144,165,75)(61,145,166,76)(62,146,167,77)(63,147,168,78)(64,148,155,79)(65,149,156,80)(66,150,157,81)(67,151,158,82)(68,152,159,83)(69,153,160,84)(70,154,161,71) );
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)], [(1,40),(2,39),(3,38),(4,37),(5,36),(6,35),(7,34),(8,33),(9,32),(10,31),(11,30),(12,29),(13,42),(14,41),(15,27),(16,26),(17,25),(18,24),(19,23),(20,22),(43,223),(44,222),(45,221),(46,220),(47,219),(48,218),(49,217),(50,216),(51,215),(52,214),(53,213),(54,212),(55,211),(56,224),(57,156),(58,155),(59,168),(60,167),(61,166),(62,165),(63,164),(64,163),(65,162),(66,161),(67,160),(68,159),(69,158),(70,157),(71,74),(72,73),(75,84),(76,83),(77,82),(78,81),(79,80),(85,88),(86,87),(89,98),(90,97),(91,96),(92,95),(93,94),(99,101),(102,112),(103,111),(104,110),(105,109),(106,108),(113,119),(114,118),(115,117),(120,126),(121,125),(122,124),(127,137),(128,136),(129,135),(130,134),(131,133),(138,140),(141,142),(143,154),(144,153),(145,152),(146,151),(147,150),(148,149),(169,191),(170,190),(171,189),(172,188),(173,187),(174,186),(175,185),(176,184),(177,183),(178,196),(179,195),(180,194),(181,193),(182,192),(197,204),(198,203),(199,202),(200,201),(205,210),(206,209),(207,208)], [(1,215,156,191,41,45,58,177),(2,216,157,192,42,46,59,178),(3,217,158,193,29,47,60,179),(4,218,159,194,30,48,61,180),(5,219,160,195,31,49,62,181),(6,220,161,196,32,50,63,182),(7,221,162,183,33,51,64,169),(8,222,163,184,34,52,65,170),(9,223,164,185,35,53,66,171),(10,224,165,186,36,54,67,172),(11,211,166,187,37,55,68,173),(12,212,167,188,38,56,69,174),(13,213,168,189,39,43,70,175),(14,214,155,190,40,44,57,176),(15,77,101,198,133,153,124,91),(16,78,102,199,134,154,125,92),(17,79,103,200,135,141,126,93),(18,80,104,201,136,142,113,94),(19,81,105,202,137,143,114,95),(20,82,106,203,138,144,115,96),(21,83,107,204,139,145,116,97),(22,84,108,205,140,146,117,98),(23,71,109,206,127,147,118,85),(24,72,110,207,128,148,119,86),(25,73,111,208,129,149,120,87),(26,74,112,209,130,150,121,88),(27,75,99,210,131,151,122,89),(28,76,100,197,132,152,123,90)], [(1,201,34,87),(2,202,35,88),(3,203,36,89),(4,204,37,90),(5,205,38,91),(6,206,39,92),(7,207,40,93),(8,208,41,94),(9,209,42,95),(10,210,29,96),(11,197,30,97),(12,198,31,98),(13,199,32,85),(14,200,33,86),(15,174,140,195),(16,175,127,196),(17,176,128,183),(18,177,129,184),(19,178,130,185),(20,179,131,186),(21,180,132,187),(22,181,133,188),(23,182,134,189),(24,169,135,190),(25,170,136,191),(26,171,137,192),(27,172,138,193),(28,173,139,194),(43,118,220,102),(44,119,221,103),(45,120,222,104),(46,121,223,105),(47,122,224,106),(48,123,211,107),(49,124,212,108),(50,125,213,109),(51,126,214,110),(52,113,215,111),(53,114,216,112),(54,115,217,99),(55,116,218,100),(56,117,219,101),(57,141,162,72),(58,142,163,73),(59,143,164,74),(60,144,165,75),(61,145,166,76),(62,146,167,77),(63,147,168,78),(64,148,155,79),(65,149,156,80),(66,150,157,81),(67,151,158,82),(68,152,159,83),(69,153,160,84),(70,154,161,71)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C4○D8 | C4○D28 | C8.C22 | D4⋊2D7 | D4×D7 | SD16⋊D7 | Q8.D14 |
| kernel | D14⋊C8.C2 | C4.Dic14 | C56⋊1C4 | D14⋊C8 | Q8⋊Dic7 | C7×Q8⋊C4 | C4⋊C4⋊7D7 | D14⋊3Q8 | C2×Dic7 | C22×D7 | Q8⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×Q8 | C14 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 3 | 3 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D14⋊C8.C2 ►in GL4(𝔽113) generated by
| 9 | 33 | 0 | 0 |
| 80 | 80 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 9 | 33 | 0 | 0 |
| 1 | 104 | 0 | 0 |
| 0 | 0 | 112 | 93 |
| 0 | 0 | 0 | 1 |
| 58 | 75 | 0 | 0 |
| 38 | 55 | 0 | 0 |
| 0 | 0 | 69 | 79 |
| 0 | 0 | 0 | 95 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 84 | 111 |
| 0 | 0 | 82 | 29 |
G:=sub<GL(4,GF(113))| [9,80,0,0,33,80,0,0,0,0,1,0,0,0,0,1],[9,1,0,0,33,104,0,0,0,0,112,0,0,0,93,1],[58,38,0,0,75,55,0,0,0,0,69,0,0,0,79,95],[98,0,0,0,0,98,0,0,0,0,84,82,0,0,111,29] >;
D14⋊C8.C2 in GAP, Magma, Sage, TeX
D_{14}\rtimes C_8.C_2 % in TeX
G:=Group("D14:C8.C2"); // GroupNames label
G:=SmallGroup(448,348);
// by ID
G=gap.SmallGroup(448,348);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,64,254,219,184,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=a^7*c^4,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^7*b,d*b*d^-1=b*c^4,d*c*d^-1=a^7*c^-1>;
// generators/relations