direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C42⋊C2, (C2×C42)⋊3C14, C42⋊13(C2×C14), (C22×C4)⋊10C28, (C4×C28)⋊48C22, (C22×C28)⋊21C4, C2.3(C23×C28), (C23×C28).24C2, (C23×C4).11C14, C4.30(C22×C28), C24.32(C2×C14), C23.34(C2×C28), C14.55(C23×C4), C28.188(C22×C4), (C2×C14).334C24, (C2×C28).706C23, C22.7(C23×C14), C22.25(C22×C28), (C23×C14).89C22, C23.67(C22×C14), (C22×C28).609C22, (C22×C14).467C23, (C2×C4×C28)⋊5C2, (C14×C4⋊C4)⋊51C2, (C2×C4⋊C4)⋊24C14, C4⋊C4⋊18(C2×C14), (C2×C4)⋊11(C2×C28), (C2×C28)⋊40(C2×C4), C2.1(C14×C4○D4), (C7×C4⋊C4)⋊75C22, C14.220(C2×C4○D4), C22.26(C7×C4○D4), (C2×C22⋊C4).15C14, (C14×C22⋊C4).35C2, C22⋊C4.27(C2×C14), (C22×C4).97(C2×C14), (C2×C14).226(C4○D4), (C2×C4).133(C22×C14), (C22×C14).120(C2×C4), (C2×C14).164(C22×C4), (C7×C22⋊C4).158C22, SmallGroup(448,1297)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×C42⋊C2
G = < a,b,c,d | a14=b4=c4=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=bc2, cd=dc >
Subgroups: 402 in 330 conjugacy classes, 258 normal (18 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, C23, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, C28, C28, C2×C14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C42⋊C2, C23×C4, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C2×C42⋊C2, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C22×C28, C22×C28, C23×C14, C2×C4×C28, C14×C22⋊C4, C14×C4⋊C4, C7×C42⋊C2, C23×C28, C14×C42⋊C2
Quotients: C1, C2, C4, C22, C7, C2×C4, C23, C14, C22×C4, C4○D4, C24, C28, C2×C14, C42⋊C2, C23×C4, C2×C4○D4, C2×C28, C22×C14, C2×C42⋊C2, C22×C28, C7×C4○D4, C23×C14, C7×C42⋊C2, C23×C28, C14×C4○D4, C14×C42⋊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 28 107 206)(2 15 108 207)(3 16 109 208)(4 17 110 209)(5 18 111 210)(6 19 112 197)(7 20 99 198)(8 21 100 199)(9 22 101 200)(10 23 102 201)(11 24 103 202)(12 25 104 203)(13 26 105 204)(14 27 106 205)(29 165 94 61)(30 166 95 62)(31 167 96 63)(32 168 97 64)(33 155 98 65)(34 156 85 66)(35 157 86 67)(36 158 87 68)(37 159 88 69)(38 160 89 70)(39 161 90 57)(40 162 91 58)(41 163 92 59)(42 164 93 60)(43 119 169 142)(44 120 170 143)(45 121 171 144)(46 122 172 145)(47 123 173 146)(48 124 174 147)(49 125 175 148)(50 126 176 149)(51 113 177 150)(52 114 178 151)(53 115 179 152)(54 116 180 153)(55 117 181 154)(56 118 182 141)(71 189 222 128)(72 190 223 129)(73 191 224 130)(74 192 211 131)(75 193 212 132)(76 194 213 133)(77 195 214 134)(78 196 215 135)(79 183 216 136)(80 184 217 137)(81 185 218 138)(82 186 219 139)(83 187 220 140)(84 188 221 127)
(1 222 174 32)(2 223 175 33)(3 224 176 34)(4 211 177 35)(5 212 178 36)(6 213 179 37)(7 214 180 38)(8 215 181 39)(9 216 182 40)(10 217 169 41)(11 218 170 42)(12 219 171 29)(13 220 172 30)(14 221 173 31)(15 129 148 155)(16 130 149 156)(17 131 150 157)(18 132 151 158)(19 133 152 159)(20 134 153 160)(21 135 154 161)(22 136 141 162)(23 137 142 163)(24 138 143 164)(25 139 144 165)(26 140 145 166)(27 127 146 167)(28 128 147 168)(43 92 102 80)(44 93 103 81)(45 94 104 82)(46 95 105 83)(47 96 106 84)(48 97 107 71)(49 98 108 72)(50 85 109 73)(51 86 110 74)(52 87 111 75)(53 88 112 76)(54 89 99 77)(55 90 100 78)(56 91 101 79)(57 199 196 117)(58 200 183 118)(59 201 184 119)(60 202 185 120)(61 203 186 121)(62 204 187 122)(63 205 188 123)(64 206 189 124)(65 207 190 125)(66 208 191 126)(67 209 192 113)(68 210 193 114)(69 197 194 115)(70 198 195 116)
(1 107)(2 108)(3 109)(4 110)(5 111)(6 112)(7 99)(8 100)(9 101)(10 102)(11 103)(12 104)(13 105)(14 106)(15 125)(16 126)(17 113)(18 114)(19 115)(20 116)(21 117)(22 118)(23 119)(24 120)(25 121)(26 122)(27 123)(28 124)(29 94)(30 95)(31 96)(32 97)(33 98)(34 85)(35 86)(36 87)(37 88)(38 89)(39 90)(40 91)(41 92)(42 93)(43 169)(44 170)(45 171)(46 172)(47 173)(48 174)(49 175)(50 176)(51 177)(52 178)(53 179)(54 180)(55 181)(56 182)(57 135)(58 136)(59 137)(60 138)(61 139)(62 140)(63 127)(64 128)(65 129)(66 130)(67 131)(68 132)(69 133)(70 134)(71 222)(72 223)(73 224)(74 211)(75 212)(76 213)(77 214)(78 215)(79 216)(80 217)(81 218)(82 219)(83 220)(84 221)(141 200)(142 201)(143 202)(144 203)(145 204)(146 205)(147 206)(148 207)(149 208)(150 209)(151 210)(152 197)(153 198)(154 199)(155 190)(156 191)(157 192)(158 193)(159 194)(160 195)(161 196)(162 183)(163 184)(164 185)(165 186)(166 187)(167 188)(168 189)
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), (1,28,107,206)(2,15,108,207)(3,16,109,208)(4,17,110,209)(5,18,111,210)(6,19,112,197)(7,20,99,198)(8,21,100,199)(9,22,101,200)(10,23,102,201)(11,24,103,202)(12,25,104,203)(13,26,105,204)(14,27,106,205)(29,165,94,61)(30,166,95,62)(31,167,96,63)(32,168,97,64)(33,155,98,65)(34,156,85,66)(35,157,86,67)(36,158,87,68)(37,159,88,69)(38,160,89,70)(39,161,90,57)(40,162,91,58)(41,163,92,59)(42,164,93,60)(43,119,169,142)(44,120,170,143)(45,121,171,144)(46,122,172,145)(47,123,173,146)(48,124,174,147)(49,125,175,148)(50,126,176,149)(51,113,177,150)(52,114,178,151)(53,115,179,152)(54,116,180,153)(55,117,181,154)(56,118,182,141)(71,189,222,128)(72,190,223,129)(73,191,224,130)(74,192,211,131)(75,193,212,132)(76,194,213,133)(77,195,214,134)(78,196,215,135)(79,183,216,136)(80,184,217,137)(81,185,218,138)(82,186,219,139)(83,187,220,140)(84,188,221,127), (1,222,174,32)(2,223,175,33)(3,224,176,34)(4,211,177,35)(5,212,178,36)(6,213,179,37)(7,214,180,38)(8,215,181,39)(9,216,182,40)(10,217,169,41)(11,218,170,42)(12,219,171,29)(13,220,172,30)(14,221,173,31)(15,129,148,155)(16,130,149,156)(17,131,150,157)(18,132,151,158)(19,133,152,159)(20,134,153,160)(21,135,154,161)(22,136,141,162)(23,137,142,163)(24,138,143,164)(25,139,144,165)(26,140,145,166)(27,127,146,167)(28,128,147,168)(43,92,102,80)(44,93,103,81)(45,94,104,82)(46,95,105,83)(47,96,106,84)(48,97,107,71)(49,98,108,72)(50,85,109,73)(51,86,110,74)(52,87,111,75)(53,88,112,76)(54,89,99,77)(55,90,100,78)(56,91,101,79)(57,199,196,117)(58,200,183,118)(59,201,184,119)(60,202,185,120)(61,203,186,121)(62,204,187,122)(63,205,188,123)(64,206,189,124)(65,207,190,125)(66,208,191,126)(67,209,192,113)(68,210,193,114)(69,197,194,115)(70,198,195,116), (1,107)(2,108)(3,109)(4,110)(5,111)(6,112)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,125)(16,126)(17,113)(18,114)(19,115)(20,116)(21,117)(22,118)(23,119)(24,120)(25,121)(26,122)(27,123)(28,124)(29,94)(30,95)(31,96)(32,97)(33,98)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,92)(42,93)(43,169)(44,170)(45,171)(46,172)(47,173)(48,174)(49,175)(50,176)(51,177)(52,178)(53,179)(54,180)(55,181)(56,182)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,127)(64,128)(65,129)(66,130)(67,131)(68,132)(69,133)(70,134)(71,222)(72,223)(73,224)(74,211)(75,212)(76,213)(77,214)(78,215)(79,216)(80,217)(81,218)(82,219)(83,220)(84,221)(141,200)(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)(151,210)(152,197)(153,198)(154,199)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)>;
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), (1,28,107,206)(2,15,108,207)(3,16,109,208)(4,17,110,209)(5,18,111,210)(6,19,112,197)(7,20,99,198)(8,21,100,199)(9,22,101,200)(10,23,102,201)(11,24,103,202)(12,25,104,203)(13,26,105,204)(14,27,106,205)(29,165,94,61)(30,166,95,62)(31,167,96,63)(32,168,97,64)(33,155,98,65)(34,156,85,66)(35,157,86,67)(36,158,87,68)(37,159,88,69)(38,160,89,70)(39,161,90,57)(40,162,91,58)(41,163,92,59)(42,164,93,60)(43,119,169,142)(44,120,170,143)(45,121,171,144)(46,122,172,145)(47,123,173,146)(48,124,174,147)(49,125,175,148)(50,126,176,149)(51,113,177,150)(52,114,178,151)(53,115,179,152)(54,116,180,153)(55,117,181,154)(56,118,182,141)(71,189,222,128)(72,190,223,129)(73,191,224,130)(74,192,211,131)(75,193,212,132)(76,194,213,133)(77,195,214,134)(78,196,215,135)(79,183,216,136)(80,184,217,137)(81,185,218,138)(82,186,219,139)(83,187,220,140)(84,188,221,127), (1,222,174,32)(2,223,175,33)(3,224,176,34)(4,211,177,35)(5,212,178,36)(6,213,179,37)(7,214,180,38)(8,215,181,39)(9,216,182,40)(10,217,169,41)(11,218,170,42)(12,219,171,29)(13,220,172,30)(14,221,173,31)(15,129,148,155)(16,130,149,156)(17,131,150,157)(18,132,151,158)(19,133,152,159)(20,134,153,160)(21,135,154,161)(22,136,141,162)(23,137,142,163)(24,138,143,164)(25,139,144,165)(26,140,145,166)(27,127,146,167)(28,128,147,168)(43,92,102,80)(44,93,103,81)(45,94,104,82)(46,95,105,83)(47,96,106,84)(48,97,107,71)(49,98,108,72)(50,85,109,73)(51,86,110,74)(52,87,111,75)(53,88,112,76)(54,89,99,77)(55,90,100,78)(56,91,101,79)(57,199,196,117)(58,200,183,118)(59,201,184,119)(60,202,185,120)(61,203,186,121)(62,204,187,122)(63,205,188,123)(64,206,189,124)(65,207,190,125)(66,208,191,126)(67,209,192,113)(68,210,193,114)(69,197,194,115)(70,198,195,116), (1,107)(2,108)(3,109)(4,110)(5,111)(6,112)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,125)(16,126)(17,113)(18,114)(19,115)(20,116)(21,117)(22,118)(23,119)(24,120)(25,121)(26,122)(27,123)(28,124)(29,94)(30,95)(31,96)(32,97)(33,98)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,92)(42,93)(43,169)(44,170)(45,171)(46,172)(47,173)(48,174)(49,175)(50,176)(51,177)(52,178)(53,179)(54,180)(55,181)(56,182)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,127)(64,128)(65,129)(66,130)(67,131)(68,132)(69,133)(70,134)(71,222)(72,223)(73,224)(74,211)(75,212)(76,213)(77,214)(78,215)(79,216)(80,217)(81,218)(82,219)(83,220)(84,221)(141,200)(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)(151,210)(152,197)(153,198)(154,199)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189) );
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)], [(1,28,107,206),(2,15,108,207),(3,16,109,208),(4,17,110,209),(5,18,111,210),(6,19,112,197),(7,20,99,198),(8,21,100,199),(9,22,101,200),(10,23,102,201),(11,24,103,202),(12,25,104,203),(13,26,105,204),(14,27,106,205),(29,165,94,61),(30,166,95,62),(31,167,96,63),(32,168,97,64),(33,155,98,65),(34,156,85,66),(35,157,86,67),(36,158,87,68),(37,159,88,69),(38,160,89,70),(39,161,90,57),(40,162,91,58),(41,163,92,59),(42,164,93,60),(43,119,169,142),(44,120,170,143),(45,121,171,144),(46,122,172,145),(47,123,173,146),(48,124,174,147),(49,125,175,148),(50,126,176,149),(51,113,177,150),(52,114,178,151),(53,115,179,152),(54,116,180,153),(55,117,181,154),(56,118,182,141),(71,189,222,128),(72,190,223,129),(73,191,224,130),(74,192,211,131),(75,193,212,132),(76,194,213,133),(77,195,214,134),(78,196,215,135),(79,183,216,136),(80,184,217,137),(81,185,218,138),(82,186,219,139),(83,187,220,140),(84,188,221,127)], [(1,222,174,32),(2,223,175,33),(3,224,176,34),(4,211,177,35),(5,212,178,36),(6,213,179,37),(7,214,180,38),(8,215,181,39),(9,216,182,40),(10,217,169,41),(11,218,170,42),(12,219,171,29),(13,220,172,30),(14,221,173,31),(15,129,148,155),(16,130,149,156),(17,131,150,157),(18,132,151,158),(19,133,152,159),(20,134,153,160),(21,135,154,161),(22,136,141,162),(23,137,142,163),(24,138,143,164),(25,139,144,165),(26,140,145,166),(27,127,146,167),(28,128,147,168),(43,92,102,80),(44,93,103,81),(45,94,104,82),(46,95,105,83),(47,96,106,84),(48,97,107,71),(49,98,108,72),(50,85,109,73),(51,86,110,74),(52,87,111,75),(53,88,112,76),(54,89,99,77),(55,90,100,78),(56,91,101,79),(57,199,196,117),(58,200,183,118),(59,201,184,119),(60,202,185,120),(61,203,186,121),(62,204,187,122),(63,205,188,123),(64,206,189,124),(65,207,190,125),(66,208,191,126),(67,209,192,113),(68,210,193,114),(69,197,194,115),(70,198,195,116)], [(1,107),(2,108),(3,109),(4,110),(5,111),(6,112),(7,99),(8,100),(9,101),(10,102),(11,103),(12,104),(13,105),(14,106),(15,125),(16,126),(17,113),(18,114),(19,115),(20,116),(21,117),(22,118),(23,119),(24,120),(25,121),(26,122),(27,123),(28,124),(29,94),(30,95),(31,96),(32,97),(33,98),(34,85),(35,86),(36,87),(37,88),(38,89),(39,90),(40,91),(41,92),(42,93),(43,169),(44,170),(45,171),(46,172),(47,173),(48,174),(49,175),(50,176),(51,177),(52,178),(53,179),(54,180),(55,181),(56,182),(57,135),(58,136),(59,137),(60,138),(61,139),(62,140),(63,127),(64,128),(65,129),(66,130),(67,131),(68,132),(69,133),(70,134),(71,222),(72,223),(73,224),(74,211),(75,212),(76,213),(77,214),(78,215),(79,216),(80,217),(81,218),(82,219),(83,220),(84,221),(141,200),(142,201),(143,202),(144,203),(145,204),(146,205),(147,206),(148,207),(149,208),(150,209),(151,210),(152,197),(153,198),(154,199),(155,190),(156,191),(157,192),(158,193),(159,194),(160,195),(161,196),(162,183),(163,184),(164,185),(165,186),(166,187),(167,188),(168,189)]])
280 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 4I | ··· | 4AB | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 28A | ··· | 28AV | 28AW | ··· | 28FL |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 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 | 2 | 2 |
| type | + | + | + | + | + | + | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C7 | C14 | C14 | C14 | C14 | C14 | C28 | C4○D4 | C7×C4○D4 |
| kernel | C14×C42⋊C2 | C2×C4×C28 | C14×C22⋊C4 | C14×C4⋊C4 | C7×C42⋊C2 | C23×C28 | C22×C28 | C2×C42⋊C2 | C2×C42 | C2×C22⋊C4 | C2×C4⋊C4 | C42⋊C2 | C23×C4 | C22×C4 | C2×C14 | C22 |
| # reps | 1 | 2 | 2 | 2 | 8 | 1 | 16 | 6 | 12 | 12 | 12 | 48 | 6 | 96 | 8 | 48 |
Matrix representation of C14×C42⋊C2 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 5 | 0 |
| 0 | 0 | 0 | 5 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 28 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,1,0,0,0,0,5,0,0,0,0,5],[17,0,0,0,0,17,0,0,0,0,1,0,0,0,27,28],[28,0,0,0,0,1,0,0,0,0,17,0,0,0,0,17],[1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,28] >;
C14×C42⋊C2 in GAP, Magma, Sage, TeX
C_{14}\times C_4^2\rtimes C_2 % in TeX
G:=Group("C14xC4^2:C2"); // GroupNames label
G:=SmallGroup(448,1297);
// by ID
G=gap.SmallGroup(448,1297);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1568,1597,604]);
// 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,c*d=d*c>;
// generators/relations