direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C42⋊2C2, (C2×C42)⋊4C14, C42⋊14(C2×C14), (C4×C28)⋊49C22, C24.17(C2×C14), (C2×C14).348C24, (C2×C28).712C23, (C23×C14).14C22, C22.22(C23×C14), (C22×C14).86C23, C23.72(C22×C14), (C22×C28).510C22, (C2×C4×C28)⋊6C2, (C2×C4⋊C4)⋊17C14, (C14×C4⋊C4)⋊44C2, C4⋊C4⋊13(C2×C14), (C7×C4⋊C4)⋊69C22, C2.11(C14×C4○D4), C14.230(C2×C4○D4), C22.34(C7×C4○D4), (C2×C22⋊C4).12C14, C22⋊C4.11(C2×C14), (C14×C22⋊C4).32C2, (C2×C4).16(C22×C14), (C2×C14).234(C4○D4), (C22×C4).102(C2×C14), (C7×C22⋊C4).145C22, SmallGroup(448,1311)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×C42⋊2C2
G = < a,b,c,d | a14=b4=c4=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=bc2, dcd=b2c-1 >
Subgroups: 354 in 246 conjugacy classes, 162 normal (12 characteristic)
C1, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C24, C28, C2×C14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C42⋊2C2, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C2×C42⋊2C2, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C22×C28, C23×C14, C2×C4×C28, C14×C22⋊C4, C14×C4⋊C4, C7×C42⋊2C2, C14×C42⋊2C2
Quotients: C1, C2, C22, C7, C23, C14, C4○D4, C24, C2×C14, C42⋊2C2, C2×C4○D4, C22×C14, C2×C42⋊2C2, C7×C4○D4, C23×C14, C7×C42⋊2C2, C14×C4○D4, C14×C42⋊2C2
►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)
(1 159 184 52)(2 160 185 53)(3 161 186 54)(4 162 187 55)(5 163 188 56)(6 164 189 43)(7 165 190 44)(8 166 191 45)(9 167 192 46)(10 168 193 47)(11 155 194 48)(12 156 195 49)(13 157 196 50)(14 158 183 51)(15 66 220 143)(16 67 221 144)(17 68 222 145)(18 69 223 146)(19 70 224 147)(20 57 211 148)(21 58 212 149)(22 59 213 150)(23 60 214 151)(24 61 215 152)(25 62 216 153)(26 63 217 154)(27 64 218 141)(28 65 219 142)(29 133 108 78)(30 134 109 79)(31 135 110 80)(32 136 111 81)(33 137 112 82)(34 138 99 83)(35 139 100 84)(36 140 101 71)(37 127 102 72)(38 128 103 73)(39 129 104 74)(40 130 105 75)(41 131 106 76)(42 132 107 77)(85 175 207 121)(86 176 208 122)(87 177 209 123)(88 178 210 124)(89 179 197 125)(90 180 198 126)(91 181 199 113)(92 182 200 114)(93 169 201 115)(94 170 202 116)(95 171 203 117)(96 172 204 118)(97 173 205 119)(98 174 206 120)
(1 88 27 74)(2 89 28 75)(3 90 15 76)(4 91 16 77)(5 92 17 78)(6 93 18 79)(7 94 19 80)(8 95 20 81)(9 96 21 82)(10 97 22 83)(11 98 23 84)(12 85 24 71)(13 86 25 72)(14 87 26 73)(29 163 182 68)(30 164 169 69)(31 165 170 70)(32 166 171 57)(33 167 172 58)(34 168 173 59)(35 155 174 60)(36 156 175 61)(37 157 176 62)(38 158 177 63)(39 159 178 64)(40 160 179 65)(41 161 180 66)(42 162 181 67)(43 115 146 109)(44 116 147 110)(45 117 148 111)(46 118 149 112)(47 119 150 99)(48 120 151 100)(49 121 152 101)(50 122 153 102)(51 123 154 103)(52 124 141 104)(53 125 142 105)(54 126 143 106)(55 113 144 107)(56 114 145 108)(127 196 208 216)(128 183 209 217)(129 184 210 218)(130 185 197 219)(131 186 198 220)(132 187 199 221)(133 188 200 222)(134 189 201 223)(135 190 202 224)(136 191 203 211)(137 192 204 212)(138 193 205 213)(139 194 206 214)(140 195 207 215)
(1 191)(2 192)(3 193)(4 194)(5 195)(6 196)(7 183)(8 184)(9 185)(10 186)(11 187)(12 188)(13 189)(14 190)(15 213)(16 214)(17 215)(18 216)(19 217)(20 218)(21 219)(22 220)(23 221)(24 222)(25 223)(26 224)(27 211)(28 212)(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(43 62)(44 63)(45 64)(46 65)(47 66)(48 67)(49 68)(50 69)(51 70)(52 57)(53 58)(54 59)(55 60)(56 61)(71 92)(72 93)(73 94)(74 95)(75 96)(76 97)(77 98)(78 85)(79 86)(80 87)(81 88)(82 89)(83 90)(84 91)(99 106)(100 107)(101 108)(102 109)(103 110)(104 111)(105 112)(113 120)(114 121)(115 122)(116 123)(117 124)(118 125)(119 126)(127 201)(128 202)(129 203)(130 204)(131 205)(132 206)(133 207)(134 208)(135 209)(136 210)(137 197)(138 198)(139 199)(140 200)(141 166)(142 167)(143 168)(144 155)(145 156)(146 157)(147 158)(148 159)(149 160)(150 161)(151 162)(152 163)(153 164)(154 165)(169 176)(170 177)(171 178)(172 179)(173 180)(174 181)(175 182)
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), (1,159,184,52)(2,160,185,53)(3,161,186,54)(4,162,187,55)(5,163,188,56)(6,164,189,43)(7,165,190,44)(8,166,191,45)(9,167,192,46)(10,168,193,47)(11,155,194,48)(12,156,195,49)(13,157,196,50)(14,158,183,51)(15,66,220,143)(16,67,221,144)(17,68,222,145)(18,69,223,146)(19,70,224,147)(20,57,211,148)(21,58,212,149)(22,59,213,150)(23,60,214,151)(24,61,215,152)(25,62,216,153)(26,63,217,154)(27,64,218,141)(28,65,219,142)(29,133,108,78)(30,134,109,79)(31,135,110,80)(32,136,111,81)(33,137,112,82)(34,138,99,83)(35,139,100,84)(36,140,101,71)(37,127,102,72)(38,128,103,73)(39,129,104,74)(40,130,105,75)(41,131,106,76)(42,132,107,77)(85,175,207,121)(86,176,208,122)(87,177,209,123)(88,178,210,124)(89,179,197,125)(90,180,198,126)(91,181,199,113)(92,182,200,114)(93,169,201,115)(94,170,202,116)(95,171,203,117)(96,172,204,118)(97,173,205,119)(98,174,206,120), (1,88,27,74)(2,89,28,75)(3,90,15,76)(4,91,16,77)(5,92,17,78)(6,93,18,79)(7,94,19,80)(8,95,20,81)(9,96,21,82)(10,97,22,83)(11,98,23,84)(12,85,24,71)(13,86,25,72)(14,87,26,73)(29,163,182,68)(30,164,169,69)(31,165,170,70)(32,166,171,57)(33,167,172,58)(34,168,173,59)(35,155,174,60)(36,156,175,61)(37,157,176,62)(38,158,177,63)(39,159,178,64)(40,160,179,65)(41,161,180,66)(42,162,181,67)(43,115,146,109)(44,116,147,110)(45,117,148,111)(46,118,149,112)(47,119,150,99)(48,120,151,100)(49,121,152,101)(50,122,153,102)(51,123,154,103)(52,124,141,104)(53,125,142,105)(54,126,143,106)(55,113,144,107)(56,114,145,108)(127,196,208,216)(128,183,209,217)(129,184,210,218)(130,185,197,219)(131,186,198,220)(132,187,199,221)(133,188,200,222)(134,189,201,223)(135,190,202,224)(136,191,203,211)(137,192,204,212)(138,193,205,213)(139,194,206,214)(140,195,207,215), (1,191)(2,192)(3,193)(4,194)(5,195)(6,196)(7,183)(8,184)(9,185)(10,186)(11,187)(12,188)(13,189)(14,190)(15,213)(16,214)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,211)(28,212)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,57)(53,58)(54,59)(55,60)(56,61)(71,92)(72,93)(73,94)(74,95)(75,96)(76,97)(77,98)(78,85)(79,86)(80,87)(81,88)(82,89)(83,90)(84,91)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(113,120)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(127,201)(128,202)(129,203)(130,204)(131,205)(132,206)(133,207)(134,208)(135,209)(136,210)(137,197)(138,198)(139,199)(140,200)(141,166)(142,167)(143,168)(144,155)(145,156)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)>;
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), (1,159,184,52)(2,160,185,53)(3,161,186,54)(4,162,187,55)(5,163,188,56)(6,164,189,43)(7,165,190,44)(8,166,191,45)(9,167,192,46)(10,168,193,47)(11,155,194,48)(12,156,195,49)(13,157,196,50)(14,158,183,51)(15,66,220,143)(16,67,221,144)(17,68,222,145)(18,69,223,146)(19,70,224,147)(20,57,211,148)(21,58,212,149)(22,59,213,150)(23,60,214,151)(24,61,215,152)(25,62,216,153)(26,63,217,154)(27,64,218,141)(28,65,219,142)(29,133,108,78)(30,134,109,79)(31,135,110,80)(32,136,111,81)(33,137,112,82)(34,138,99,83)(35,139,100,84)(36,140,101,71)(37,127,102,72)(38,128,103,73)(39,129,104,74)(40,130,105,75)(41,131,106,76)(42,132,107,77)(85,175,207,121)(86,176,208,122)(87,177,209,123)(88,178,210,124)(89,179,197,125)(90,180,198,126)(91,181,199,113)(92,182,200,114)(93,169,201,115)(94,170,202,116)(95,171,203,117)(96,172,204,118)(97,173,205,119)(98,174,206,120), (1,88,27,74)(2,89,28,75)(3,90,15,76)(4,91,16,77)(5,92,17,78)(6,93,18,79)(7,94,19,80)(8,95,20,81)(9,96,21,82)(10,97,22,83)(11,98,23,84)(12,85,24,71)(13,86,25,72)(14,87,26,73)(29,163,182,68)(30,164,169,69)(31,165,170,70)(32,166,171,57)(33,167,172,58)(34,168,173,59)(35,155,174,60)(36,156,175,61)(37,157,176,62)(38,158,177,63)(39,159,178,64)(40,160,179,65)(41,161,180,66)(42,162,181,67)(43,115,146,109)(44,116,147,110)(45,117,148,111)(46,118,149,112)(47,119,150,99)(48,120,151,100)(49,121,152,101)(50,122,153,102)(51,123,154,103)(52,124,141,104)(53,125,142,105)(54,126,143,106)(55,113,144,107)(56,114,145,108)(127,196,208,216)(128,183,209,217)(129,184,210,218)(130,185,197,219)(131,186,198,220)(132,187,199,221)(133,188,200,222)(134,189,201,223)(135,190,202,224)(136,191,203,211)(137,192,204,212)(138,193,205,213)(139,194,206,214)(140,195,207,215), (1,191)(2,192)(3,193)(4,194)(5,195)(6,196)(7,183)(8,184)(9,185)(10,186)(11,187)(12,188)(13,189)(14,190)(15,213)(16,214)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,211)(28,212)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,57)(53,58)(54,59)(55,60)(56,61)(71,92)(72,93)(73,94)(74,95)(75,96)(76,97)(77,98)(78,85)(79,86)(80,87)(81,88)(82,89)(83,90)(84,91)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(113,120)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(127,201)(128,202)(129,203)(130,204)(131,205)(132,206)(133,207)(134,208)(135,209)(136,210)(137,197)(138,198)(139,199)(140,200)(141,166)(142,167)(143,168)(144,155)(145,156)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182) );
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)], [(1,159,184,52),(2,160,185,53),(3,161,186,54),(4,162,187,55),(5,163,188,56),(6,164,189,43),(7,165,190,44),(8,166,191,45),(9,167,192,46),(10,168,193,47),(11,155,194,48),(12,156,195,49),(13,157,196,50),(14,158,183,51),(15,66,220,143),(16,67,221,144),(17,68,222,145),(18,69,223,146),(19,70,224,147),(20,57,211,148),(21,58,212,149),(22,59,213,150),(23,60,214,151),(24,61,215,152),(25,62,216,153),(26,63,217,154),(27,64,218,141),(28,65,219,142),(29,133,108,78),(30,134,109,79),(31,135,110,80),(32,136,111,81),(33,137,112,82),(34,138,99,83),(35,139,100,84),(36,140,101,71),(37,127,102,72),(38,128,103,73),(39,129,104,74),(40,130,105,75),(41,131,106,76),(42,132,107,77),(85,175,207,121),(86,176,208,122),(87,177,209,123),(88,178,210,124),(89,179,197,125),(90,180,198,126),(91,181,199,113),(92,182,200,114),(93,169,201,115),(94,170,202,116),(95,171,203,117),(96,172,204,118),(97,173,205,119),(98,174,206,120)], [(1,88,27,74),(2,89,28,75),(3,90,15,76),(4,91,16,77),(5,92,17,78),(6,93,18,79),(7,94,19,80),(8,95,20,81),(9,96,21,82),(10,97,22,83),(11,98,23,84),(12,85,24,71),(13,86,25,72),(14,87,26,73),(29,163,182,68),(30,164,169,69),(31,165,170,70),(32,166,171,57),(33,167,172,58),(34,168,173,59),(35,155,174,60),(36,156,175,61),(37,157,176,62),(38,158,177,63),(39,159,178,64),(40,160,179,65),(41,161,180,66),(42,162,181,67),(43,115,146,109),(44,116,147,110),(45,117,148,111),(46,118,149,112),(47,119,150,99),(48,120,151,100),(49,121,152,101),(50,122,153,102),(51,123,154,103),(52,124,141,104),(53,125,142,105),(54,126,143,106),(55,113,144,107),(56,114,145,108),(127,196,208,216),(128,183,209,217),(129,184,210,218),(130,185,197,219),(131,186,198,220),(132,187,199,221),(133,188,200,222),(134,189,201,223),(135,190,202,224),(136,191,203,211),(137,192,204,212),(138,193,205,213),(139,194,206,214),(140,195,207,215)], [(1,191),(2,192),(3,193),(4,194),(5,195),(6,196),(7,183),(8,184),(9,185),(10,186),(11,187),(12,188),(13,189),(14,190),(15,213),(16,214),(17,215),(18,216),(19,217),(20,218),(21,219),(22,220),(23,221),(24,222),(25,223),(26,224),(27,211),(28,212),(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(43,62),(44,63),(45,64),(46,65),(47,66),(48,67),(49,68),(50,69),(51,70),(52,57),(53,58),(54,59),(55,60),(56,61),(71,92),(72,93),(73,94),(74,95),(75,96),(76,97),(77,98),(78,85),(79,86),(80,87),(81,88),(82,89),(83,90),(84,91),(99,106),(100,107),(101,108),(102,109),(103,110),(104,111),(105,112),(113,120),(114,121),(115,122),(116,123),(117,124),(118,125),(119,126),(127,201),(128,202),(129,203),(130,204),(131,205),(132,206),(133,207),(134,208),(135,209),(136,210),(137,197),(138,198),(139,199),(140,200),(141,166),(142,167),(143,168),(144,155),(145,156),(146,157),(147,158),(148,159),(149,160),(150,161),(151,162),(152,163),(153,164),(154,165),(169,176),(170,177),(171,178),(172,179),(173,180),(174,181),(175,182)]])
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | ··· | 4L | 4M | ··· | 4R | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BB | 28A | ··· | 28BT | 28BU | ··· | 28DD |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + | |||||||
| image | C1 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C4○D4 | C7×C4○D4 |
| kernel | C14×C42⋊2C2 | C2×C4×C28 | C14×C22⋊C4 | C14×C4⋊C4 | C7×C42⋊2C2 | C2×C42⋊2C2 | C2×C42 | C2×C22⋊C4 | C2×C4⋊C4 | C42⋊2C2 | C2×C14 | C22 |
| # reps | 1 | 1 | 3 | 3 | 8 | 6 | 6 | 18 | 18 | 48 | 12 | 72 |
Matrix representation of C14×C42⋊2C2 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 0 |
| 0 | 0 | 0 | 0 | 0 | 20 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 4 |
| 0 | 0 | 0 | 0 | 11 | 10 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 27 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 24 | 1 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,20,0,0,0,0,0,0,20],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,19,11,0,0,0,0,4,10],[1,27,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[1,0,0,0,0,0,1,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,24,0,0,0,0,0,1] >;
C14×C42⋊2C2 in GAP, Magma, Sage, TeX
C_{14}\times C_4^2\rtimes_2C_2 % in TeX
G:=Group("C14xC4^2:2C2"); // GroupNames label
G:=SmallGroup(448,1311);
// by ID
G=gap.SmallGroup(448,1311);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,2360,4790,604]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^4=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b*c^2,d*c*d=b^2*c^-1>;
// generators/relations