metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊C4⋊5C4, C14.24(C4×D4), C22.63(D4×D7), C14.5(C4⋊D4), (C2×Dic7).84D4, C2.C42⋊3D7, C2.4(D14⋊D4), C2.6(D28⋊C4), C14.C42⋊3C2, (C22×C4).299D14, (C23×D7).1C22, C14.6(C42⋊C2), C2.9(Dic7⋊4D4), C2.4(D14.5D4), C14.18(C4.4D4), C22.37(C4○D28), C2.10(C42⋊D7), (C22×C28).14C22, C7⋊1(C24.C22), C23.259(C22×D7), C14.20(C42⋊2C2), C22.38(D4⋊2D7), (C22×C14).294C23, C2.3(Dic7.D4), C22.19(Q8⋊2D7), C14.39(C22.D4), (C22×Dic7).17C22, (C2×C4×Dic7)⋊17C2, (C2×C4).60(C4×D7), C22.92(C2×C4×D7), (C2×Dic7⋊C4)⋊2C2, (C2×D14⋊C4).4C2, (C2×C28).144(C2×C4), C2.3(C4⋊C4⋊D7), (C2×C14).203(C2×D4), (C2×Dic7).9(C2×C4), (C22×D7).7(C2×C4), (C2×C14).53(C22×C4), (C2×C14).133(C4○D4), (C7×C2.C42)⋊21C2, SmallGroup(448,203)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊C4⋊5C4
G = < a,b,c,d | a14=b2=c4=d4=1, bab=a-1, ac=ca, ad=da, cbc-1=a7b, dbd-1=bc2, dcd-1=a7c >
Subgroups: 988 in 190 conjugacy classes, 67 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, D14, C2×C14, C2.C42, C2.C42, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C24.C22, C4×Dic7, Dic7⋊C4, D14⋊C4, D14⋊C4, C22×Dic7, C22×C28, C23×D7, C14.C42, C7×C2.C42, C2×C4×Dic7, C2×Dic7⋊C4, C2×D14⋊C4, D14⋊C4⋊5C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, D14, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C4.4D4, C42⋊2C2, C4×D7, C22×D7, C24.C22, C2×C4×D7, C4○D28, D4×D7, D4⋊2D7, Q8⋊2D7, C42⋊D7, Dic7⋊4D4, D14⋊D4, Dic7.D4, D28⋊C4, D14.5D4, C4⋊C4⋊D7, D14⋊C4⋊5C4
►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 26)(2 25)(3 24)(4 23)(5 22)(6 21)(7 20)(8 19)(9 18)(10 17)(11 16)(12 15)(13 28)(14 27)(29 44)(30 43)(31 56)(32 55)(33 54)(34 53)(35 52)(36 51)(37 50)(38 49)(39 48)(40 47)(41 46)(42 45)(57 70)(58 69)(59 68)(60 67)(61 66)(62 65)(63 64)(71 76)(72 75)(73 74)(77 84)(78 83)(79 82)(80 81)(85 94)(86 93)(87 92)(88 91)(89 90)(95 98)(96 97)(99 112)(100 111)(101 110)(102 109)(103 108)(104 107)(105 106)(113 138)(114 137)(115 136)(116 135)(117 134)(118 133)(119 132)(120 131)(121 130)(122 129)(123 128)(124 127)(125 140)(126 139)(141 158)(142 157)(143 156)(144 155)(145 168)(146 167)(147 166)(148 165)(149 164)(150 163)(151 162)(152 161)(153 160)(154 159)(169 179)(170 178)(171 177)(172 176)(173 175)(180 182)(183 189)(184 188)(185 187)(190 196)(191 195)(192 194)(197 209)(198 208)(199 207)(200 206)(201 205)(202 204)(211 215)(212 214)(216 224)(217 223)(218 222)(219 221)
(1 155 27 152)(2 156 28 153)(3 157 15 154)(4 158 16 141)(5 159 17 142)(6 160 18 143)(7 161 19 144)(8 162 20 145)(9 163 21 146)(10 164 22 147)(11 165 23 148)(12 166 24 149)(13 167 25 150)(14 168 26 151)(29 128 43 115)(30 129 44 116)(31 130 45 117)(32 131 46 118)(33 132 47 119)(34 133 48 120)(35 134 49 121)(36 135 50 122)(37 136 51 123)(38 137 52 124)(39 138 53 125)(40 139 54 126)(41 140 55 113)(42 127 56 114)(57 224 81 207)(58 211 82 208)(59 212 83 209)(60 213 84 210)(61 214 71 197)(62 215 72 198)(63 216 73 199)(64 217 74 200)(65 218 75 201)(66 219 76 202)(67 220 77 203)(68 221 78 204)(69 222 79 205)(70 223 80 206)(85 185 101 180)(86 186 102 181)(87 187 103 182)(88 188 104 169)(89 189 105 170)(90 190 106 171)(91 191 107 172)(92 192 108 173)(93 193 109 174)(94 194 110 175)(95 195 111 176)(96 196 112 177)(97 183 99 178)(98 184 100 179)
(1 97 37 57)(2 98 38 58)(3 85 39 59)(4 86 40 60)(5 87 41 61)(6 88 42 62)(7 89 29 63)(8 90 30 64)(9 91 31 65)(10 92 32 66)(11 93 33 67)(12 94 34 68)(13 95 35 69)(14 96 36 70)(15 101 53 83)(16 102 54 84)(17 103 55 71)(18 104 56 72)(19 105 43 73)(20 106 44 74)(21 107 45 75)(22 108 46 76)(23 109 47 77)(24 110 48 78)(25 111 49 79)(26 112 50 80)(27 99 51 81)(28 100 52 82)(113 204 142 175)(114 205 143 176)(115 206 144 177)(116 207 145 178)(117 208 146 179)(118 209 147 180)(119 210 148 181)(120 197 149 182)(121 198 150 169)(122 199 151 170)(123 200 152 171)(124 201 153 172)(125 202 154 173)(126 203 141 174)(127 222 160 195)(128 223 161 196)(129 224 162 183)(130 211 163 184)(131 212 164 185)(132 213 165 186)(133 214 166 187)(134 215 167 188)(135 216 168 189)(136 217 155 190)(137 218 156 191)(138 219 157 192)(139 220 158 193)(140 221 159 194)
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), (1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,28)(14,27)(29,44)(30,43)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,76)(72,75)(73,74)(77,84)(78,83)(79,82)(80,81)(85,94)(86,93)(87,92)(88,91)(89,90)(95,98)(96,97)(99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(113,138)(114,137)(115,136)(116,135)(117,134)(118,133)(119,132)(120,131)(121,130)(122,129)(123,128)(124,127)(125,140)(126,139)(141,158)(142,157)(143,156)(144,155)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)(153,160)(154,159)(169,179)(170,178)(171,177)(172,176)(173,175)(180,182)(183,189)(184,188)(185,187)(190,196)(191,195)(192,194)(197,209)(198,208)(199,207)(200,206)(201,205)(202,204)(211,215)(212,214)(216,224)(217,223)(218,222)(219,221), (1,155,27,152)(2,156,28,153)(3,157,15,154)(4,158,16,141)(5,159,17,142)(6,160,18,143)(7,161,19,144)(8,162,20,145)(9,163,21,146)(10,164,22,147)(11,165,23,148)(12,166,24,149)(13,167,25,150)(14,168,26,151)(29,128,43,115)(30,129,44,116)(31,130,45,117)(32,131,46,118)(33,132,47,119)(34,133,48,120)(35,134,49,121)(36,135,50,122)(37,136,51,123)(38,137,52,124)(39,138,53,125)(40,139,54,126)(41,140,55,113)(42,127,56,114)(57,224,81,207)(58,211,82,208)(59,212,83,209)(60,213,84,210)(61,214,71,197)(62,215,72,198)(63,216,73,199)(64,217,74,200)(65,218,75,201)(66,219,76,202)(67,220,77,203)(68,221,78,204)(69,222,79,205)(70,223,80,206)(85,185,101,180)(86,186,102,181)(87,187,103,182)(88,188,104,169)(89,189,105,170)(90,190,106,171)(91,191,107,172)(92,192,108,173)(93,193,109,174)(94,194,110,175)(95,195,111,176)(96,196,112,177)(97,183,99,178)(98,184,100,179), (1,97,37,57)(2,98,38,58)(3,85,39,59)(4,86,40,60)(5,87,41,61)(6,88,42,62)(7,89,29,63)(8,90,30,64)(9,91,31,65)(10,92,32,66)(11,93,33,67)(12,94,34,68)(13,95,35,69)(14,96,36,70)(15,101,53,83)(16,102,54,84)(17,103,55,71)(18,104,56,72)(19,105,43,73)(20,106,44,74)(21,107,45,75)(22,108,46,76)(23,109,47,77)(24,110,48,78)(25,111,49,79)(26,112,50,80)(27,99,51,81)(28,100,52,82)(113,204,142,175)(114,205,143,176)(115,206,144,177)(116,207,145,178)(117,208,146,179)(118,209,147,180)(119,210,148,181)(120,197,149,182)(121,198,150,169)(122,199,151,170)(123,200,152,171)(124,201,153,172)(125,202,154,173)(126,203,141,174)(127,222,160,195)(128,223,161,196)(129,224,162,183)(130,211,163,184)(131,212,164,185)(132,213,165,186)(133,214,166,187)(134,215,167,188)(135,216,168,189)(136,217,155,190)(137,218,156,191)(138,219,157,192)(139,220,158,193)(140,221,159,194)>;
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), (1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,28)(14,27)(29,44)(30,43)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,76)(72,75)(73,74)(77,84)(78,83)(79,82)(80,81)(85,94)(86,93)(87,92)(88,91)(89,90)(95,98)(96,97)(99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(113,138)(114,137)(115,136)(116,135)(117,134)(118,133)(119,132)(120,131)(121,130)(122,129)(123,128)(124,127)(125,140)(126,139)(141,158)(142,157)(143,156)(144,155)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)(153,160)(154,159)(169,179)(170,178)(171,177)(172,176)(173,175)(180,182)(183,189)(184,188)(185,187)(190,196)(191,195)(192,194)(197,209)(198,208)(199,207)(200,206)(201,205)(202,204)(211,215)(212,214)(216,224)(217,223)(218,222)(219,221), (1,155,27,152)(2,156,28,153)(3,157,15,154)(4,158,16,141)(5,159,17,142)(6,160,18,143)(7,161,19,144)(8,162,20,145)(9,163,21,146)(10,164,22,147)(11,165,23,148)(12,166,24,149)(13,167,25,150)(14,168,26,151)(29,128,43,115)(30,129,44,116)(31,130,45,117)(32,131,46,118)(33,132,47,119)(34,133,48,120)(35,134,49,121)(36,135,50,122)(37,136,51,123)(38,137,52,124)(39,138,53,125)(40,139,54,126)(41,140,55,113)(42,127,56,114)(57,224,81,207)(58,211,82,208)(59,212,83,209)(60,213,84,210)(61,214,71,197)(62,215,72,198)(63,216,73,199)(64,217,74,200)(65,218,75,201)(66,219,76,202)(67,220,77,203)(68,221,78,204)(69,222,79,205)(70,223,80,206)(85,185,101,180)(86,186,102,181)(87,187,103,182)(88,188,104,169)(89,189,105,170)(90,190,106,171)(91,191,107,172)(92,192,108,173)(93,193,109,174)(94,194,110,175)(95,195,111,176)(96,196,112,177)(97,183,99,178)(98,184,100,179), (1,97,37,57)(2,98,38,58)(3,85,39,59)(4,86,40,60)(5,87,41,61)(6,88,42,62)(7,89,29,63)(8,90,30,64)(9,91,31,65)(10,92,32,66)(11,93,33,67)(12,94,34,68)(13,95,35,69)(14,96,36,70)(15,101,53,83)(16,102,54,84)(17,103,55,71)(18,104,56,72)(19,105,43,73)(20,106,44,74)(21,107,45,75)(22,108,46,76)(23,109,47,77)(24,110,48,78)(25,111,49,79)(26,112,50,80)(27,99,51,81)(28,100,52,82)(113,204,142,175)(114,205,143,176)(115,206,144,177)(116,207,145,178)(117,208,146,179)(118,209,147,180)(119,210,148,181)(120,197,149,182)(121,198,150,169)(122,199,151,170)(123,200,152,171)(124,201,153,172)(125,202,154,173)(126,203,141,174)(127,222,160,195)(128,223,161,196)(129,224,162,183)(130,211,163,184)(131,212,164,185)(132,213,165,186)(133,214,166,187)(134,215,167,188)(135,216,168,189)(136,217,155,190)(137,218,156,191)(138,219,157,192)(139,220,158,193)(140,221,159,194) );
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)], [(1,26),(2,25),(3,24),(4,23),(5,22),(6,21),(7,20),(8,19),(9,18),(10,17),(11,16),(12,15),(13,28),(14,27),(29,44),(30,43),(31,56),(32,55),(33,54),(34,53),(35,52),(36,51),(37,50),(38,49),(39,48),(40,47),(41,46),(42,45),(57,70),(58,69),(59,68),(60,67),(61,66),(62,65),(63,64),(71,76),(72,75),(73,74),(77,84),(78,83),(79,82),(80,81),(85,94),(86,93),(87,92),(88,91),(89,90),(95,98),(96,97),(99,112),(100,111),(101,110),(102,109),(103,108),(104,107),(105,106),(113,138),(114,137),(115,136),(116,135),(117,134),(118,133),(119,132),(120,131),(121,130),(122,129),(123,128),(124,127),(125,140),(126,139),(141,158),(142,157),(143,156),(144,155),(145,168),(146,167),(147,166),(148,165),(149,164),(150,163),(151,162),(152,161),(153,160),(154,159),(169,179),(170,178),(171,177),(172,176),(173,175),(180,182),(183,189),(184,188),(185,187),(190,196),(191,195),(192,194),(197,209),(198,208),(199,207),(200,206),(201,205),(202,204),(211,215),(212,214),(216,224),(217,223),(218,222),(219,221)], [(1,155,27,152),(2,156,28,153),(3,157,15,154),(4,158,16,141),(5,159,17,142),(6,160,18,143),(7,161,19,144),(8,162,20,145),(9,163,21,146),(10,164,22,147),(11,165,23,148),(12,166,24,149),(13,167,25,150),(14,168,26,151),(29,128,43,115),(30,129,44,116),(31,130,45,117),(32,131,46,118),(33,132,47,119),(34,133,48,120),(35,134,49,121),(36,135,50,122),(37,136,51,123),(38,137,52,124),(39,138,53,125),(40,139,54,126),(41,140,55,113),(42,127,56,114),(57,224,81,207),(58,211,82,208),(59,212,83,209),(60,213,84,210),(61,214,71,197),(62,215,72,198),(63,216,73,199),(64,217,74,200),(65,218,75,201),(66,219,76,202),(67,220,77,203),(68,221,78,204),(69,222,79,205),(70,223,80,206),(85,185,101,180),(86,186,102,181),(87,187,103,182),(88,188,104,169),(89,189,105,170),(90,190,106,171),(91,191,107,172),(92,192,108,173),(93,193,109,174),(94,194,110,175),(95,195,111,176),(96,196,112,177),(97,183,99,178),(98,184,100,179)], [(1,97,37,57),(2,98,38,58),(3,85,39,59),(4,86,40,60),(5,87,41,61),(6,88,42,62),(7,89,29,63),(8,90,30,64),(9,91,31,65),(10,92,32,66),(11,93,33,67),(12,94,34,68),(13,95,35,69),(14,96,36,70),(15,101,53,83),(16,102,54,84),(17,103,55,71),(18,104,56,72),(19,105,43,73),(20,106,44,74),(21,107,45,75),(22,108,46,76),(23,109,47,77),(24,110,48,78),(25,111,49,79),(26,112,50,80),(27,99,51,81),(28,100,52,82),(113,204,142,175),(114,205,143,176),(115,206,144,177),(116,207,145,178),(117,208,146,179),(118,209,147,180),(119,210,148,181),(120,197,149,182),(121,198,150,169),(122,199,151,170),(123,200,152,171),(124,201,153,172),(125,202,154,173),(126,203,141,174),(127,222,160,195),(128,223,161,196),(129,224,162,183),(130,211,163,184),(131,212,164,185),(132,213,165,186),(133,214,166,187),(134,215,167,188),(135,216,168,189),(136,217,155,190),(137,218,156,191),(138,219,157,192),(139,220,158,193),(140,221,159,194)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | C4×D7 | C4○D28 | D4×D7 | D4⋊2D7 | Q8⋊2D7 |
| kernel | D14⋊C4⋊5C4 | C14.C42 | C7×C2.C42 | C2×C4×Dic7 | C2×Dic7⋊C4 | C2×D14⋊C4 | D14⋊C4 | C2×Dic7 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 1 | 1 | 3 | 8 | 4 | 3 | 8 | 9 | 12 | 24 | 6 | 3 | 3 |
Matrix representation of D14⋊C4⋊5C4 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 19 | 0 | 0 |
| 0 | 0 | 10 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 22 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 21 | 1 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 26 |
| 0 | 0 | 0 | 0 | 9 | 17 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 15 | 0 | 0 |
| 0 | 0 | 14 | 20 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 20 | 12 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,10,0,0,0,0,19,22,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,18,1,0,0,0,0,0,0,28,0,0,0,0,0,22,1,0,0,0,0,0,0,28,21,0,0,0,0,0,1],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,12,9,0,0,0,0,26,17],[28,16,0,0,0,0,18,1,0,0,0,0,0,0,9,14,0,0,0,0,15,20,0,0,0,0,0,0,17,20,0,0,0,0,0,12] >;
D14⋊C4⋊5C4 in GAP, Magma, Sage, TeX
D_{14}\rtimes C_4\rtimes_5C_4 % in TeX
G:=Group("D14:C4:5C4"); // GroupNames label
G:=SmallGroup(448,203);
// by ID
G=gap.SmallGroup(448,203);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,120,422,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^4=d^4=1,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^2,d*c*d^-1=a^7*c>;
// generators/relations