metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.22D14, Q8⋊C4⋊1D7, (C8×Dic7)⋊22C2, (C2×C8).207D14, Q8⋊Dic7⋊2C2, (C2×Q8).14D14, C4.Dic14⋊5C2, C2.D56.8C2, C14.D8.3C2, C28.18(C4○D4), C14.68(C4○D8), C4.31(C4○D28), (C2×Dic7).92D4, C22.194(D4×D7), C2.7(Q8.D14), C4.57(D4⋊2D7), (C2×C56).195C22, (C2×C28).240C23, C28.23D4.4C2, (C2×D28).59C22, C4⋊Dic7.88C22, (Q8×C14).23C22, C14.29(C4.4D4), C2.16(SD16⋊3D7), C7⋊3(C42.78C22), (C4×Dic7).227C22, C2.19(Dic7.D4), (C7×Q8⋊C4)⋊17C2, (C2×C14).253(C2×D4), (C7×C4⋊C4).41C22, (C2×C7⋊C8).217C22, (C2×C4).347(C22×D7), SmallGroup(448,334)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C8).207D14
G = < a,b,c,d | a2=b8=1, c14=a, d2=ab4, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=ab3, dcd-1=ab4c13 >
Subgroups: 532 in 96 conjugacy classes, 37 normal (all characteristic)
C1, C2 [×3], C2, C4 [×2], C4 [×5], C22, C22 [×3], C7, C8 [×2], C2×C4, C2×C4 [×5], D4 [×2], Q8 [×2], C23, D7, C14 [×3], C42, C22⋊C4 [×2], C4⋊C4, C4⋊C4 [×3], C2×C8, C2×C8, C2×D4, C2×Q8, Dic7 [×3], C28 [×2], C28 [×2], D14 [×3], C2×C14, C4×C8, D4⋊C4 [×2], Q8⋊C4, Q8⋊C4, C4.4D4, C42.C2, C7⋊C8, C56, D28 [×2], C2×Dic7 [×2], C2×Dic7, C2×C28, C2×C28 [×2], C7×Q8 [×2], C22×D7, C42.78C22, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4 [×2], C7×C4⋊C4, C2×C56, C2×D28, Q8×C14, C14.D8, C8×Dic7, C2.D56, Q8⋊Dic7, C7×Q8⋊C4, C4.Dic14, C28.23D4, (C2×C8).207D14
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, D7, C2×D4, C4○D4 [×2], D14 [×3], C4.4D4, C4○D8 [×2], C22×D7, C42.78C22, C4○D28, D4×D7, D4⋊2D7, Dic7.D4, SD16⋊3D7, Q8.D14, (C2×C8).207D14
►On 224 points
Generators in S224
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(113 127)(114 128)(115 129)(116 130)(117 131)(118 132)(119 133)(120 134)(121 135)(122 136)(123 137)(124 138)(125 139)(126 140)(141 155)(142 156)(143 157)(144 158)(145 159)(146 160)(147 161)(148 162)(149 163)(150 164)(151 165)(152 166)(153 167)(154 168)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)(175 189)(176 190)(177 191)(178 192)(179 193)(180 194)(181 195)(182 196)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)
(1 139 178 54 78 199 154 93)(2 41 155 126 79 108 179 214)(3 113 180 56 80 201 156 95)(4 43 157 128 81 110 181 216)(5 115 182 30 82 203 158 97)(6 45 159 130 83 112 183 218)(7 117 184 32 84 205 160 99)(8 47 161 132 57 86 185 220)(9 119 186 34 58 207 162 101)(10 49 163 134 59 88 187 222)(11 121 188 36 60 209 164 103)(12 51 165 136 61 90 189 224)(13 123 190 38 62 211 166 105)(14 53 167 138 63 92 191 198)(15 125 192 40 64 213 168 107)(16 55 141 140 65 94 193 200)(17 127 194 42 66 215 142 109)(18 29 143 114 67 96 195 202)(19 129 196 44 68 217 144 111)(20 31 145 116 69 98 169 204)(21 131 170 46 70 219 146 85)(22 33 147 118 71 100 171 206)(23 133 172 48 72 221 148 87)(24 35 149 120 73 102 173 208)(25 135 174 50 74 223 150 89)(26 37 151 122 75 104 175 210)(27 137 176 52 76 197 152 91)(28 39 153 124 77 106 177 212)
(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 99 64 46)(2 31 65 112)(3 97 66 44)(4 29 67 110)(5 95 68 42)(6 55 69 108)(7 93 70 40)(8 53 71 106)(9 91 72 38)(10 51 73 104)(11 89 74 36)(12 49 75 102)(13 87 76 34)(14 47 77 100)(15 85 78 32)(16 45 79 98)(17 111 80 30)(18 43 81 96)(19 109 82 56)(20 41 83 94)(21 107 84 54)(22 39 57 92)(23 105 58 52)(24 37 59 90)(25 103 60 50)(26 35 61 88)(27 101 62 48)(28 33 63 86)(113 196 215 158)(114 143 216 181)(115 194 217 156)(116 141 218 179)(117 192 219 154)(118 167 220 177)(119 190 221 152)(120 165 222 175)(121 188 223 150)(122 163 224 173)(123 186 197 148)(124 161 198 171)(125 184 199 146)(126 159 200 169)(127 182 201 144)(128 157 202 195)(129 180 203 142)(130 155 204 193)(131 178 205 168)(132 153 206 191)(133 176 207 166)(134 151 208 189)(135 174 209 164)(136 149 210 187)(137 172 211 162)(138 147 212 185)(139 170 213 160)(140 145 214 183)
G:=sub<Sym(224)| (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (1,139,178,54,78,199,154,93)(2,41,155,126,79,108,179,214)(3,113,180,56,80,201,156,95)(4,43,157,128,81,110,181,216)(5,115,182,30,82,203,158,97)(6,45,159,130,83,112,183,218)(7,117,184,32,84,205,160,99)(8,47,161,132,57,86,185,220)(9,119,186,34,58,207,162,101)(10,49,163,134,59,88,187,222)(11,121,188,36,60,209,164,103)(12,51,165,136,61,90,189,224)(13,123,190,38,62,211,166,105)(14,53,167,138,63,92,191,198)(15,125,192,40,64,213,168,107)(16,55,141,140,65,94,193,200)(17,127,194,42,66,215,142,109)(18,29,143,114,67,96,195,202)(19,129,196,44,68,217,144,111)(20,31,145,116,69,98,169,204)(21,131,170,46,70,219,146,85)(22,33,147,118,71,100,171,206)(23,133,172,48,72,221,148,87)(24,35,149,120,73,102,173,208)(25,135,174,50,74,223,150,89)(26,37,151,122,75,104,175,210)(27,137,176,52,76,197,152,91)(28,39,153,124,77,106,177,212), (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), (1,99,64,46)(2,31,65,112)(3,97,66,44)(4,29,67,110)(5,95,68,42)(6,55,69,108)(7,93,70,40)(8,53,71,106)(9,91,72,38)(10,51,73,104)(11,89,74,36)(12,49,75,102)(13,87,76,34)(14,47,77,100)(15,85,78,32)(16,45,79,98)(17,111,80,30)(18,43,81,96)(19,109,82,56)(20,41,83,94)(21,107,84,54)(22,39,57,92)(23,105,58,52)(24,37,59,90)(25,103,60,50)(26,35,61,88)(27,101,62,48)(28,33,63,86)(113,196,215,158)(114,143,216,181)(115,194,217,156)(116,141,218,179)(117,192,219,154)(118,167,220,177)(119,190,221,152)(120,165,222,175)(121,188,223,150)(122,163,224,173)(123,186,197,148)(124,161,198,171)(125,184,199,146)(126,159,200,169)(127,182,201,144)(128,157,202,195)(129,180,203,142)(130,155,204,193)(131,178,205,168)(132,153,206,191)(133,176,207,166)(134,151,208,189)(135,174,209,164)(136,149,210,187)(137,172,211,162)(138,147,212,185)(139,170,213,160)(140,145,214,183)>;
G:=Group( (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (1,139,178,54,78,199,154,93)(2,41,155,126,79,108,179,214)(3,113,180,56,80,201,156,95)(4,43,157,128,81,110,181,216)(5,115,182,30,82,203,158,97)(6,45,159,130,83,112,183,218)(7,117,184,32,84,205,160,99)(8,47,161,132,57,86,185,220)(9,119,186,34,58,207,162,101)(10,49,163,134,59,88,187,222)(11,121,188,36,60,209,164,103)(12,51,165,136,61,90,189,224)(13,123,190,38,62,211,166,105)(14,53,167,138,63,92,191,198)(15,125,192,40,64,213,168,107)(16,55,141,140,65,94,193,200)(17,127,194,42,66,215,142,109)(18,29,143,114,67,96,195,202)(19,129,196,44,68,217,144,111)(20,31,145,116,69,98,169,204)(21,131,170,46,70,219,146,85)(22,33,147,118,71,100,171,206)(23,133,172,48,72,221,148,87)(24,35,149,120,73,102,173,208)(25,135,174,50,74,223,150,89)(26,37,151,122,75,104,175,210)(27,137,176,52,76,197,152,91)(28,39,153,124,77,106,177,212), (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), (1,99,64,46)(2,31,65,112)(3,97,66,44)(4,29,67,110)(5,95,68,42)(6,55,69,108)(7,93,70,40)(8,53,71,106)(9,91,72,38)(10,51,73,104)(11,89,74,36)(12,49,75,102)(13,87,76,34)(14,47,77,100)(15,85,78,32)(16,45,79,98)(17,111,80,30)(18,43,81,96)(19,109,82,56)(20,41,83,94)(21,107,84,54)(22,39,57,92)(23,105,58,52)(24,37,59,90)(25,103,60,50)(26,35,61,88)(27,101,62,48)(28,33,63,86)(113,196,215,158)(114,143,216,181)(115,194,217,156)(116,141,218,179)(117,192,219,154)(118,167,220,177)(119,190,221,152)(120,165,222,175)(121,188,223,150)(122,163,224,173)(123,186,197,148)(124,161,198,171)(125,184,199,146)(126,159,200,169)(127,182,201,144)(128,157,202,195)(129,180,203,142)(130,155,204,193)(131,178,205,168)(132,153,206,191)(133,176,207,166)(134,151,208,189)(135,174,209,164)(136,149,210,187)(137,172,211,162)(138,147,212,185)(139,170,213,160)(140,145,214,183) );
G=PermutationGroup([(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(113,127),(114,128),(115,129),(116,130),(117,131),(118,132),(119,133),(120,134),(121,135),(122,136),(123,137),(124,138),(125,139),(126,140),(141,155),(142,156),(143,157),(144,158),(145,159),(146,160),(147,161),(148,162),(149,163),(150,164),(151,165),(152,166),(153,167),(154,168),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188),(175,189),(176,190),(177,191),(178,192),(179,193),(180,194),(181,195),(182,196),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224)], [(1,139,178,54,78,199,154,93),(2,41,155,126,79,108,179,214),(3,113,180,56,80,201,156,95),(4,43,157,128,81,110,181,216),(5,115,182,30,82,203,158,97),(6,45,159,130,83,112,183,218),(7,117,184,32,84,205,160,99),(8,47,161,132,57,86,185,220),(9,119,186,34,58,207,162,101),(10,49,163,134,59,88,187,222),(11,121,188,36,60,209,164,103),(12,51,165,136,61,90,189,224),(13,123,190,38,62,211,166,105),(14,53,167,138,63,92,191,198),(15,125,192,40,64,213,168,107),(16,55,141,140,65,94,193,200),(17,127,194,42,66,215,142,109),(18,29,143,114,67,96,195,202),(19,129,196,44,68,217,144,111),(20,31,145,116,69,98,169,204),(21,131,170,46,70,219,146,85),(22,33,147,118,71,100,171,206),(23,133,172,48,72,221,148,87),(24,35,149,120,73,102,173,208),(25,135,174,50,74,223,150,89),(26,37,151,122,75,104,175,210),(27,137,176,52,76,197,152,91),(28,39,153,124,77,106,177,212)], [(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)], [(1,99,64,46),(2,31,65,112),(3,97,66,44),(4,29,67,110),(5,95,68,42),(6,55,69,108),(7,93,70,40),(8,53,71,106),(9,91,72,38),(10,51,73,104),(11,89,74,36),(12,49,75,102),(13,87,76,34),(14,47,77,100),(15,85,78,32),(16,45,79,98),(17,111,80,30),(18,43,81,96),(19,109,82,56),(20,41,83,94),(21,107,84,54),(22,39,57,92),(23,105,58,52),(24,37,59,90),(25,103,60,50),(26,35,61,88),(27,101,62,48),(28,33,63,86),(113,196,215,158),(114,143,216,181),(115,194,217,156),(116,141,218,179),(117,192,219,154),(118,167,220,177),(119,190,221,152),(120,165,222,175),(121,188,223,150),(122,163,224,173),(123,186,197,148),(124,161,198,171),(125,184,199,146),(126,159,200,169),(127,182,201,144),(128,157,202,195),(129,180,203,142),(130,155,204,193),(131,178,205,168),(132,153,206,191),(133,176,207,166),(134,151,208,189),(135,174,209,164),(136,149,210,187),(137,172,211,162),(138,147,212,185),(139,170,213,160),(140,145,214,183)])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 56 | 2 | 2 | 8 | 8 | 14 | 14 | 14 | 14 | 56 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
64 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 | D7 | C4○D4 | D14 | D14 | D14 | C4○D8 | C4○D28 | D4⋊2D7 | D4×D7 | SD16⋊3D7 | Q8.D14 |
| kernel | (C2×C8).207D14 | C14.D8 | C8×Dic7 | C2.D56 | Q8⋊Dic7 | C7×Q8⋊C4 | C4.Dic14 | C28.23D4 | C2×Dic7 | Q8⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×Q8 | C14 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 3 | 3 | 3 | 8 | 12 | 3 | 3 | 6 | 6 |
Matrix representation of (C2×C8).207D14 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 51 | 0 | 0 |
| 0 | 0 | 51 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 31 | 82 |
| 0 | 0 | 0 | 0 | 31 | 31 |
| 34 | 10 | 0 | 0 | 0 | 0 |
| 79 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 0 | 0 | 0 |
| 0 | 0 | 62 | 98 | 0 | 0 |
| 0 | 0 | 0 | 0 | 100 | 13 |
| 0 | 0 | 0 | 0 | 13 | 13 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 26 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 51 | 0 | 0 |
| 0 | 0 | 0 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 82 | 31 |
| 0 | 0 | 0 | 0 | 31 | 31 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,98,51,0,0,0,0,51,15,0,0,0,0,0,0,31,31,0,0,0,0,82,31],[34,79,0,0,0,0,10,0,0,0,0,0,0,0,15,62,0,0,0,0,0,98,0,0,0,0,0,0,100,13,0,0,0,0,13,13],[112,26,0,0,0,0,0,1,0,0,0,0,0,0,98,0,0,0,0,0,51,15,0,0,0,0,0,0,82,31,0,0,0,0,31,31] >;
(C2×C8).207D14 in GAP, Magma, Sage, TeX
(C_2\times C_8)._{207}D_{14} % in TeX
G:=Group("(C2xC8).207D14"); // GroupNames label
G:=SmallGroup(448,334);
// by ID
G=gap.SmallGroup(448,334);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,701,120,1094,135,184,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^8=1,c^14=a,d^2=a*b^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=a*b^3,d*c*d^-1=a*b^4*c^13>;
// generators/relations