direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C8○D4, C56.80C23, C28.93C24, C4○D4.4C28, D4.8(C2×C28), Q8.9(C2×C28), (C2×C56)⋊54C22, (C22×C56)⋊27C2, (C22×C8)⋊13C14, (C2×D4).12C28, (D4×C14).24C4, (Q8×C14).20C4, (C2×Q8).10C28, C8.17(C22×C14), C4.22(C22×C28), C2.11(C23×C28), C4.17(C23×C14), C14.63(C23×C4), C23.20(C2×C28), (C2×M4(2))⋊17C14, M4(2)⋊11(C2×C14), (C14×M4(2))⋊35C2, (C2×C28).969C23, C28.167(C22×C4), C22.4(C22×C28), (C7×M4(2))⋊40C22, (C22×C28).600C22, (C2×C8)⋊16(C2×C14), (C7×C4○D4).8C4, (C2×C4).53(C2×C28), (C7×D4).30(C2×C4), (C7×Q8).33(C2×C4), (C2×C28).274(C2×C4), (C2×C4○D4).14C14, (C14×C4○D4).28C2, C4○D4.14(C2×C14), (C22×C14).86(C2×C4), (C2×C14).35(C22×C4), (C7×C4○D4).59C22, (C2×C4).139(C22×C14), (C22×C4).127(C2×C14), SmallGroup(448,1350)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×C8○D4
G = < a,b,c,d | a14=b8=d2=1, c2=b4, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=b4c >
Subgroups: 290 in 266 conjugacy classes, 242 normal (20 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C2×C8, C2×C8, M4(2), C22×C4, C2×D4, C2×Q8, C4○D4, C28, C28, C2×C14, C2×C14, C2×C14, C22×C8, C2×M4(2), C8○D4, C2×C4○D4, C56, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C2×C8○D4, C2×C56, C2×C56, C7×M4(2), C22×C28, D4×C14, Q8×C14, C7×C4○D4, C22×C56, C14×M4(2), C7×C8○D4, C14×C4○D4, C14×C8○D4
Quotients: C1, C2, C4, C22, C7, C2×C4, C23, C14, C22×C4, C24, C28, C2×C14, C8○D4, C23×C4, C2×C28, C22×C14, C2×C8○D4, C22×C28, C23×C14, C7×C8○D4, C23×C28, C14×C8○D4
►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)
(1 108 196 51 166 86 74 131)(2 109 183 52 167 87 75 132)(3 110 184 53 168 88 76 133)(4 111 185 54 155 89 77 134)(5 112 186 55 156 90 78 135)(6 99 187 56 157 91 79 136)(7 100 188 43 158 92 80 137)(8 101 189 44 159 93 81 138)(9 102 190 45 160 94 82 139)(10 103 191 46 161 95 83 140)(11 104 192 47 162 96 84 127)(12 105 193 48 163 97 71 128)(13 106 194 49 164 98 72 129)(14 107 195 50 165 85 73 130)(15 34 180 124 63 141 216 203)(16 35 181 125 64 142 217 204)(17 36 182 126 65 143 218 205)(18 37 169 113 66 144 219 206)(19 38 170 114 67 145 220 207)(20 39 171 115 68 146 221 208)(21 40 172 116 69 147 222 209)(22 41 173 117 70 148 223 210)(23 42 174 118 57 149 224 197)(24 29 175 119 58 150 211 198)(25 30 176 120 59 151 212 199)(26 31 177 121 60 152 213 200)(27 32 178 122 61 153 214 201)(28 33 179 123 62 154 215 202)
(1 60 166 26)(2 61 167 27)(3 62 168 28)(4 63 155 15)(5 64 156 16)(6 65 157 17)(7 66 158 18)(8 67 159 19)(9 68 160 20)(10 69 161 21)(11 70 162 22)(12 57 163 23)(13 58 164 24)(14 59 165 25)(29 106 150 98)(30 107 151 85)(31 108 152 86)(32 109 153 87)(33 110 154 88)(34 111 141 89)(35 112 142 90)(36 99 143 91)(37 100 144 92)(38 101 145 93)(39 102 146 94)(40 103 147 95)(41 104 148 96)(42 105 149 97)(43 206 137 113)(44 207 138 114)(45 208 139 115)(46 209 140 116)(47 210 127 117)(48 197 128 118)(49 198 129 119)(50 199 130 120)(51 200 131 121)(52 201 132 122)(53 202 133 123)(54 203 134 124)(55 204 135 125)(56 205 136 126)(71 174 193 224)(72 175 194 211)(73 176 195 212)(74 177 196 213)(75 178 183 214)(76 179 184 215)(77 180 185 216)(78 181 186 217)(79 182 187 218)(80 169 188 219)(81 170 189 220)(82 171 190 221)(83 172 191 222)(84 173 192 223)
(1 159)(2 160)(3 161)(4 162)(5 163)(6 164)(7 165)(8 166)(9 167)(10 168)(11 155)(12 156)(13 157)(14 158)(15 22)(16 23)(17 24)(18 25)(19 26)(20 27)(21 28)(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(43 130)(44 131)(45 132)(46 133)(47 134)(48 135)(49 136)(50 137)(51 138)(52 139)(53 140)(54 127)(55 128)(56 129)(57 64)(58 65)(59 66)(60 67)(61 68)(62 69)(63 70)(71 186)(72 187)(73 188)(74 189)(75 190)(76 191)(77 192)(78 193)(79 194)(80 195)(81 196)(82 183)(83 184)(84 185)(85 100)(86 101)(87 102)(88 103)(89 104)(90 105)(91 106)(92 107)(93 108)(94 109)(95 110)(96 111)(97 112)(98 99)(113 120)(114 121)(115 122)(116 123)(117 124)(118 125)(119 126)(141 148)(142 149)(143 150)(144 151)(145 152)(146 153)(147 154)(169 176)(170 177)(171 178)(172 179)(173 180)(174 181)(175 182)(197 204)(198 205)(199 206)(200 207)(201 208)(202 209)(203 210)(211 218)(212 219)(213 220)(214 221)(215 222)(216 223)(217 224)
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), (1,108,196,51,166,86,74,131)(2,109,183,52,167,87,75,132)(3,110,184,53,168,88,76,133)(4,111,185,54,155,89,77,134)(5,112,186,55,156,90,78,135)(6,99,187,56,157,91,79,136)(7,100,188,43,158,92,80,137)(8,101,189,44,159,93,81,138)(9,102,190,45,160,94,82,139)(10,103,191,46,161,95,83,140)(11,104,192,47,162,96,84,127)(12,105,193,48,163,97,71,128)(13,106,194,49,164,98,72,129)(14,107,195,50,165,85,73,130)(15,34,180,124,63,141,216,203)(16,35,181,125,64,142,217,204)(17,36,182,126,65,143,218,205)(18,37,169,113,66,144,219,206)(19,38,170,114,67,145,220,207)(20,39,171,115,68,146,221,208)(21,40,172,116,69,147,222,209)(22,41,173,117,70,148,223,210)(23,42,174,118,57,149,224,197)(24,29,175,119,58,150,211,198)(25,30,176,120,59,151,212,199)(26,31,177,121,60,152,213,200)(27,32,178,122,61,153,214,201)(28,33,179,123,62,154,215,202), (1,60,166,26)(2,61,167,27)(3,62,168,28)(4,63,155,15)(5,64,156,16)(6,65,157,17)(7,66,158,18)(8,67,159,19)(9,68,160,20)(10,69,161,21)(11,70,162,22)(12,57,163,23)(13,58,164,24)(14,59,165,25)(29,106,150,98)(30,107,151,85)(31,108,152,86)(32,109,153,87)(33,110,154,88)(34,111,141,89)(35,112,142,90)(36,99,143,91)(37,100,144,92)(38,101,145,93)(39,102,146,94)(40,103,147,95)(41,104,148,96)(42,105,149,97)(43,206,137,113)(44,207,138,114)(45,208,139,115)(46,209,140,116)(47,210,127,117)(48,197,128,118)(49,198,129,119)(50,199,130,120)(51,200,131,121)(52,201,132,122)(53,202,133,123)(54,203,134,124)(55,204,135,125)(56,205,136,126)(71,174,193,224)(72,175,194,211)(73,176,195,212)(74,177,196,213)(75,178,183,214)(76,179,184,215)(77,180,185,216)(78,181,186,217)(79,182,187,218)(80,169,188,219)(81,170,189,220)(82,171,190,221)(83,172,191,222)(84,173,192,223), (1,159)(2,160)(3,161)(4,162)(5,163)(6,164)(7,165)(8,166)(9,167)(10,168)(11,155)(12,156)(13,157)(14,158)(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,130)(44,131)(45,132)(46,133)(47,134)(48,135)(49,136)(50,137)(51,138)(52,139)(53,140)(54,127)(55,128)(56,129)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,186)(72,187)(73,188)(74,189)(75,190)(76,191)(77,192)(78,193)(79,194)(80,195)(81,196)(82,183)(83,184)(84,185)(85,100)(86,101)(87,102)(88,103)(89,104)(90,105)(91,106)(92,107)(93,108)(94,109)(95,110)(96,111)(97,112)(98,99)(113,120)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(141,148)(142,149)(143,150)(144,151)(145,152)(146,153)(147,154)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)(197,204)(198,205)(199,206)(200,207)(201,208)(202,209)(203,210)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224)>;
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), (1,108,196,51,166,86,74,131)(2,109,183,52,167,87,75,132)(3,110,184,53,168,88,76,133)(4,111,185,54,155,89,77,134)(5,112,186,55,156,90,78,135)(6,99,187,56,157,91,79,136)(7,100,188,43,158,92,80,137)(8,101,189,44,159,93,81,138)(9,102,190,45,160,94,82,139)(10,103,191,46,161,95,83,140)(11,104,192,47,162,96,84,127)(12,105,193,48,163,97,71,128)(13,106,194,49,164,98,72,129)(14,107,195,50,165,85,73,130)(15,34,180,124,63,141,216,203)(16,35,181,125,64,142,217,204)(17,36,182,126,65,143,218,205)(18,37,169,113,66,144,219,206)(19,38,170,114,67,145,220,207)(20,39,171,115,68,146,221,208)(21,40,172,116,69,147,222,209)(22,41,173,117,70,148,223,210)(23,42,174,118,57,149,224,197)(24,29,175,119,58,150,211,198)(25,30,176,120,59,151,212,199)(26,31,177,121,60,152,213,200)(27,32,178,122,61,153,214,201)(28,33,179,123,62,154,215,202), (1,60,166,26)(2,61,167,27)(3,62,168,28)(4,63,155,15)(5,64,156,16)(6,65,157,17)(7,66,158,18)(8,67,159,19)(9,68,160,20)(10,69,161,21)(11,70,162,22)(12,57,163,23)(13,58,164,24)(14,59,165,25)(29,106,150,98)(30,107,151,85)(31,108,152,86)(32,109,153,87)(33,110,154,88)(34,111,141,89)(35,112,142,90)(36,99,143,91)(37,100,144,92)(38,101,145,93)(39,102,146,94)(40,103,147,95)(41,104,148,96)(42,105,149,97)(43,206,137,113)(44,207,138,114)(45,208,139,115)(46,209,140,116)(47,210,127,117)(48,197,128,118)(49,198,129,119)(50,199,130,120)(51,200,131,121)(52,201,132,122)(53,202,133,123)(54,203,134,124)(55,204,135,125)(56,205,136,126)(71,174,193,224)(72,175,194,211)(73,176,195,212)(74,177,196,213)(75,178,183,214)(76,179,184,215)(77,180,185,216)(78,181,186,217)(79,182,187,218)(80,169,188,219)(81,170,189,220)(82,171,190,221)(83,172,191,222)(84,173,192,223), (1,159)(2,160)(3,161)(4,162)(5,163)(6,164)(7,165)(8,166)(9,167)(10,168)(11,155)(12,156)(13,157)(14,158)(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,130)(44,131)(45,132)(46,133)(47,134)(48,135)(49,136)(50,137)(51,138)(52,139)(53,140)(54,127)(55,128)(56,129)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,186)(72,187)(73,188)(74,189)(75,190)(76,191)(77,192)(78,193)(79,194)(80,195)(81,196)(82,183)(83,184)(84,185)(85,100)(86,101)(87,102)(88,103)(89,104)(90,105)(91,106)(92,107)(93,108)(94,109)(95,110)(96,111)(97,112)(98,99)(113,120)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(141,148)(142,149)(143,150)(144,151)(145,152)(146,153)(147,154)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)(197,204)(198,205)(199,206)(200,207)(201,208)(202,209)(203,210)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224) );
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)], [(1,108,196,51,166,86,74,131),(2,109,183,52,167,87,75,132),(3,110,184,53,168,88,76,133),(4,111,185,54,155,89,77,134),(5,112,186,55,156,90,78,135),(6,99,187,56,157,91,79,136),(7,100,188,43,158,92,80,137),(8,101,189,44,159,93,81,138),(9,102,190,45,160,94,82,139),(10,103,191,46,161,95,83,140),(11,104,192,47,162,96,84,127),(12,105,193,48,163,97,71,128),(13,106,194,49,164,98,72,129),(14,107,195,50,165,85,73,130),(15,34,180,124,63,141,216,203),(16,35,181,125,64,142,217,204),(17,36,182,126,65,143,218,205),(18,37,169,113,66,144,219,206),(19,38,170,114,67,145,220,207),(20,39,171,115,68,146,221,208),(21,40,172,116,69,147,222,209),(22,41,173,117,70,148,223,210),(23,42,174,118,57,149,224,197),(24,29,175,119,58,150,211,198),(25,30,176,120,59,151,212,199),(26,31,177,121,60,152,213,200),(27,32,178,122,61,153,214,201),(28,33,179,123,62,154,215,202)], [(1,60,166,26),(2,61,167,27),(3,62,168,28),(4,63,155,15),(5,64,156,16),(6,65,157,17),(7,66,158,18),(8,67,159,19),(9,68,160,20),(10,69,161,21),(11,70,162,22),(12,57,163,23),(13,58,164,24),(14,59,165,25),(29,106,150,98),(30,107,151,85),(31,108,152,86),(32,109,153,87),(33,110,154,88),(34,111,141,89),(35,112,142,90),(36,99,143,91),(37,100,144,92),(38,101,145,93),(39,102,146,94),(40,103,147,95),(41,104,148,96),(42,105,149,97),(43,206,137,113),(44,207,138,114),(45,208,139,115),(46,209,140,116),(47,210,127,117),(48,197,128,118),(49,198,129,119),(50,199,130,120),(51,200,131,121),(52,201,132,122),(53,202,133,123),(54,203,134,124),(55,204,135,125),(56,205,136,126),(71,174,193,224),(72,175,194,211),(73,176,195,212),(74,177,196,213),(75,178,183,214),(76,179,184,215),(77,180,185,216),(78,181,186,217),(79,182,187,218),(80,169,188,219),(81,170,189,220),(82,171,190,221),(83,172,191,222),(84,173,192,223)], [(1,159),(2,160),(3,161),(4,162),(5,163),(6,164),(7,165),(8,166),(9,167),(10,168),(11,155),(12,156),(13,157),(14,158),(15,22),(16,23),(17,24),(18,25),(19,26),(20,27),(21,28),(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(43,130),(44,131),(45,132),(46,133),(47,134),(48,135),(49,136),(50,137),(51,138),(52,139),(53,140),(54,127),(55,128),(56,129),(57,64),(58,65),(59,66),(60,67),(61,68),(62,69),(63,70),(71,186),(72,187),(73,188),(74,189),(75,190),(76,191),(77,192),(78,193),(79,194),(80,195),(81,196),(82,183),(83,184),(84,185),(85,100),(86,101),(87,102),(88,103),(89,104),(90,105),(91,106),(92,107),(93,108),(94,109),(95,110),(96,111),(97,112),(98,99),(113,120),(114,121),(115,122),(116,123),(117,124),(118,125),(119,126),(141,148),(142,149),(143,150),(144,151),(145,152),(146,153),(147,154),(169,176),(170,177),(171,178),(172,179),(173,180),(174,181),(175,182),(197,204),(198,205),(199,206),(200,207),(201,208),(202,209),(203,210),(211,218),(212,219),(213,220),(214,221),(215,222),(216,223),(217,224)]])
280 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 4A | 4B | 4C | 4D | 4E | ··· | 4J | 7A | ··· | 7F | 8A | ··· | 8H | 8I | ··· | 8T | 14A | ··· | 14R | 14S | ··· | 14BB | 28A | ··· | 28X | 28Y | ··· | 28BH | 56A | ··· | 56AV | 56AW | ··· | 56DP |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 |
280 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + | |||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | C7 | C14 | C14 | C14 | C14 | C28 | C28 | C28 | C8○D4 | C7×C8○D4 |
| kernel | C14×C8○D4 | C22×C56 | C14×M4(2) | C7×C8○D4 | C14×C4○D4 | D4×C14 | Q8×C14 | C7×C4○D4 | C2×C8○D4 | C22×C8 | C2×M4(2) | C8○D4 | C2×C4○D4 | C2×D4 | C2×Q8 | C4○D4 | C14 | C2 |
| # reps | 1 | 3 | 3 | 8 | 1 | 6 | 2 | 8 | 6 | 18 | 18 | 48 | 6 | 36 | 12 | 48 | 8 | 48 |
Matrix representation of C14×C8○D4 ►in GL3(𝔽113) generated by
| 112 | 0 | 0 |
| 0 | 7 | 0 |
| 0 | 0 | 7 |
| 98 | 0 | 0 |
| 0 | 69 | 0 |
| 0 | 0 | 69 |
| 112 | 0 | 0 |
| 0 | 74 | 2 |
| 0 | 30 | 39 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 39 | 112 |
G:=sub<GL(3,GF(113))| [112,0,0,0,7,0,0,0,7],[98,0,0,0,69,0,0,0,69],[112,0,0,0,74,30,0,2,39],[1,0,0,0,1,39,0,0,112] >;
C14×C8○D4 in GAP, Magma, Sage, TeX
C_{14}\times C_8\circ D_4 % in TeX
G:=Group("C14xC8oD4"); // GroupNames label
G:=SmallGroup(448,1350);
// by ID
G=gap.SmallGroup(448,1350);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,784,2403,124]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^8=d^2=1,c^2=b^4,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=b^4*c>;
// generators/relations