metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊C4⋊7C4, C14.60(C4×D4), (C2×C28).252D4, (C22×C4).43D14, C22.113(D4×D7), C14.91(C4⋊D4), (C2×Dic7).178D4, C2.20(D28⋊C4), C14.C42⋊42C2, C2.6(Dic7⋊D4), C2.7(D14.5D4), C14.52(C4.4D4), C2.3(C28.23D4), C22.59(C4○D28), (C22×C28).30C22, C7⋊7(C24.C22), (C23×D7).19C22, C23.298(C22×D7), C14.38(C42⋊C2), C14.28(C42⋊2C2), C22.60(D4⋊2D7), (C22×C14).354C23, C22.30(Q8⋊2D7), C14.52(C22.D4), (C22×Dic7).193C22, (C2×C4⋊C4)⋊8D7, (C14×C4⋊C4)⋊25C2, (C2×C4×Dic7)⋊25C2, (C2×C4).42(C4×D7), C2.14(C4×C7⋊D4), C22.139(C2×C4×D7), (C2×C28).186(C2×C4), (C2×D14⋊C4).13C2, C2.7(C4⋊C4⋊D7), (C2×C14).335(C2×D4), C22.69(C2×C7⋊D4), C2.14(C4⋊C4⋊7D7), (C2×C4).100(C7⋊D4), (C2×Dic7).64(C2×C4), (C22×D7).22(C2×C4), (C2×C14).157(C4○D4), (C2×C14).122(C22×C4), SmallGroup(448,524)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊C4⋊7C4
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=c-1 >
Subgroups: 964 in 190 conjugacy classes, 69 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×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C24.C22, C4×Dic7, D14⋊C4, D14⋊C4, C7×C4⋊C4, C22×Dic7, C22×C28, C23×D7, C14.C42, C2×C4×Dic7, C2×D14⋊C4, C14×C4⋊C4, D14⋊C4⋊7C4
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, C7⋊D4, C22×D7, C24.C22, C2×C4×D7, C4○D28, D4×D7, D4⋊2D7, Q8⋊2D7, C2×C7⋊D4, C4⋊C4⋊7D7, D28⋊C4, D14.5D4, C4⋊C4⋊D7, C4×C7⋊D4, Dic7⋊D4, C28.23D4, D14⋊C4⋊7C4
►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)
(1 184)(2 183)(3 196)(4 195)(5 194)(6 193)(7 192)(8 191)(9 190)(10 189)(11 188)(12 187)(13 186)(14 185)(15 44)(16 43)(17 56)(18 55)(19 54)(20 53)(21 52)(22 51)(23 50)(24 49)(25 48)(26 47)(27 46)(28 45)(29 157)(30 156)(31 155)(32 168)(33 167)(34 166)(35 165)(36 164)(37 163)(38 162)(39 161)(40 160)(41 159)(42 158)(57 97)(58 96)(59 95)(60 94)(61 93)(62 92)(63 91)(64 90)(65 89)(66 88)(67 87)(68 86)(69 85)(70 98)(71 170)(72 169)(73 182)(74 181)(75 180)(76 179)(77 178)(78 177)(79 176)(80 175)(81 174)(82 173)(83 172)(84 171)(99 126)(100 125)(101 124)(102 123)(103 122)(104 121)(105 120)(106 119)(107 118)(108 117)(109 116)(110 115)(111 114)(112 113)(127 200)(128 199)(129 198)(130 197)(131 210)(132 209)(133 208)(134 207)(135 206)(136 205)(137 204)(138 203)(139 202)(140 201)(141 222)(142 221)(143 220)(144 219)(145 218)(146 217)(147 216)(148 215)(149 214)(150 213)(151 212)(152 211)(153 224)(154 223)
(1 223 208 155)(2 224 209 156)(3 211 210 157)(4 212 197 158)(5 213 198 159)(6 214 199 160)(7 215 200 161)(8 216 201 162)(9 217 202 163)(10 218 203 164)(11 219 204 165)(12 220 205 166)(13 221 206 167)(14 222 207 168)(15 94 122 178)(16 95 123 179)(17 96 124 180)(18 97 125 181)(19 98 126 182)(20 85 113 169)(21 86 114 170)(22 87 115 171)(23 88 116 172)(24 89 117 173)(25 90 118 174)(26 91 119 175)(27 92 120 176)(28 93 121 177)(29 189 152 138)(30 190 153 139)(31 191 154 140)(32 192 141 127)(33 193 142 128)(34 194 143 129)(35 195 144 130)(36 196 145 131)(37 183 146 132)(38 184 147 133)(39 185 148 134)(40 186 149 135)(41 187 150 136)(42 188 151 137)(43 66 102 83)(44 67 103 84)(45 68 104 71)(46 69 105 72)(47 70 106 73)(48 57 107 74)(49 58 108 75)(50 59 109 76)(51 60 110 77)(52 61 111 78)(53 62 112 79)(54 63 99 80)(55 64 100 81)(56 65 101 82)
(1 24 134 50)(2 25 135 51)(3 26 136 52)(4 27 137 53)(5 28 138 54)(6 15 139 55)(7 16 140 56)(8 17 127 43)(9 18 128 44)(10 19 129 45)(11 20 130 46)(12 21 131 47)(13 22 132 48)(14 23 133 49)(29 80 213 177)(30 81 214 178)(31 82 215 179)(32 83 216 180)(33 84 217 181)(34 71 218 182)(35 72 219 169)(36 73 220 170)(37 74 221 171)(38 75 222 172)(39 76 223 173)(40 77 224 174)(41 78 211 175)(42 79 212 176)(57 167 87 146)(58 168 88 147)(59 155 89 148)(60 156 90 149)(61 157 91 150)(62 158 92 151)(63 159 93 152)(64 160 94 153)(65 161 95 154)(66 162 96 141)(67 163 97 142)(68 164 98 143)(69 165 85 144)(70 166 86 145)(99 198 121 189)(100 199 122 190)(101 200 123 191)(102 201 124 192)(103 202 125 193)(104 203 126 194)(105 204 113 195)(106 205 114 196)(107 206 115 183)(108 207 116 184)(109 208 117 185)(110 209 118 186)(111 210 119 187)(112 197 120 188)
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), (1,184)(2,183)(3,196)(4,195)(5,194)(6,193)(7,192)(8,191)(9,190)(10,189)(11,188)(12,187)(13,186)(14,185)(15,44)(16,43)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,157)(30,156)(31,155)(32,168)(33,167)(34,166)(35,165)(36,164)(37,163)(38,162)(39,161)(40,160)(41,159)(42,158)(57,97)(58,96)(59,95)(60,94)(61,93)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,98)(71,170)(72,169)(73,182)(74,181)(75,180)(76,179)(77,178)(78,177)(79,176)(80,175)(81,174)(82,173)(83,172)(84,171)(99,126)(100,125)(101,124)(102,123)(103,122)(104,121)(105,120)(106,119)(107,118)(108,117)(109,116)(110,115)(111,114)(112,113)(127,200)(128,199)(129,198)(130,197)(131,210)(132,209)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)(139,202)(140,201)(141,222)(142,221)(143,220)(144,219)(145,218)(146,217)(147,216)(148,215)(149,214)(150,213)(151,212)(152,211)(153,224)(154,223), (1,223,208,155)(2,224,209,156)(3,211,210,157)(4,212,197,158)(5,213,198,159)(6,214,199,160)(7,215,200,161)(8,216,201,162)(9,217,202,163)(10,218,203,164)(11,219,204,165)(12,220,205,166)(13,221,206,167)(14,222,207,168)(15,94,122,178)(16,95,123,179)(17,96,124,180)(18,97,125,181)(19,98,126,182)(20,85,113,169)(21,86,114,170)(22,87,115,171)(23,88,116,172)(24,89,117,173)(25,90,118,174)(26,91,119,175)(27,92,120,176)(28,93,121,177)(29,189,152,138)(30,190,153,139)(31,191,154,140)(32,192,141,127)(33,193,142,128)(34,194,143,129)(35,195,144,130)(36,196,145,131)(37,183,146,132)(38,184,147,133)(39,185,148,134)(40,186,149,135)(41,187,150,136)(42,188,151,137)(43,66,102,83)(44,67,103,84)(45,68,104,71)(46,69,105,72)(47,70,106,73)(48,57,107,74)(49,58,108,75)(50,59,109,76)(51,60,110,77)(52,61,111,78)(53,62,112,79)(54,63,99,80)(55,64,100,81)(56,65,101,82), (1,24,134,50)(2,25,135,51)(3,26,136,52)(4,27,137,53)(5,28,138,54)(6,15,139,55)(7,16,140,56)(8,17,127,43)(9,18,128,44)(10,19,129,45)(11,20,130,46)(12,21,131,47)(13,22,132,48)(14,23,133,49)(29,80,213,177)(30,81,214,178)(31,82,215,179)(32,83,216,180)(33,84,217,181)(34,71,218,182)(35,72,219,169)(36,73,220,170)(37,74,221,171)(38,75,222,172)(39,76,223,173)(40,77,224,174)(41,78,211,175)(42,79,212,176)(57,167,87,146)(58,168,88,147)(59,155,89,148)(60,156,90,149)(61,157,91,150)(62,158,92,151)(63,159,93,152)(64,160,94,153)(65,161,95,154)(66,162,96,141)(67,163,97,142)(68,164,98,143)(69,165,85,144)(70,166,86,145)(99,198,121,189)(100,199,122,190)(101,200,123,191)(102,201,124,192)(103,202,125,193)(104,203,126,194)(105,204,113,195)(106,205,114,196)(107,206,115,183)(108,207,116,184)(109,208,117,185)(110,209,118,186)(111,210,119,187)(112,197,120,188)>;
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), (1,184)(2,183)(3,196)(4,195)(5,194)(6,193)(7,192)(8,191)(9,190)(10,189)(11,188)(12,187)(13,186)(14,185)(15,44)(16,43)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,157)(30,156)(31,155)(32,168)(33,167)(34,166)(35,165)(36,164)(37,163)(38,162)(39,161)(40,160)(41,159)(42,158)(57,97)(58,96)(59,95)(60,94)(61,93)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,98)(71,170)(72,169)(73,182)(74,181)(75,180)(76,179)(77,178)(78,177)(79,176)(80,175)(81,174)(82,173)(83,172)(84,171)(99,126)(100,125)(101,124)(102,123)(103,122)(104,121)(105,120)(106,119)(107,118)(108,117)(109,116)(110,115)(111,114)(112,113)(127,200)(128,199)(129,198)(130,197)(131,210)(132,209)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)(139,202)(140,201)(141,222)(142,221)(143,220)(144,219)(145,218)(146,217)(147,216)(148,215)(149,214)(150,213)(151,212)(152,211)(153,224)(154,223), (1,223,208,155)(2,224,209,156)(3,211,210,157)(4,212,197,158)(5,213,198,159)(6,214,199,160)(7,215,200,161)(8,216,201,162)(9,217,202,163)(10,218,203,164)(11,219,204,165)(12,220,205,166)(13,221,206,167)(14,222,207,168)(15,94,122,178)(16,95,123,179)(17,96,124,180)(18,97,125,181)(19,98,126,182)(20,85,113,169)(21,86,114,170)(22,87,115,171)(23,88,116,172)(24,89,117,173)(25,90,118,174)(26,91,119,175)(27,92,120,176)(28,93,121,177)(29,189,152,138)(30,190,153,139)(31,191,154,140)(32,192,141,127)(33,193,142,128)(34,194,143,129)(35,195,144,130)(36,196,145,131)(37,183,146,132)(38,184,147,133)(39,185,148,134)(40,186,149,135)(41,187,150,136)(42,188,151,137)(43,66,102,83)(44,67,103,84)(45,68,104,71)(46,69,105,72)(47,70,106,73)(48,57,107,74)(49,58,108,75)(50,59,109,76)(51,60,110,77)(52,61,111,78)(53,62,112,79)(54,63,99,80)(55,64,100,81)(56,65,101,82), (1,24,134,50)(2,25,135,51)(3,26,136,52)(4,27,137,53)(5,28,138,54)(6,15,139,55)(7,16,140,56)(8,17,127,43)(9,18,128,44)(10,19,129,45)(11,20,130,46)(12,21,131,47)(13,22,132,48)(14,23,133,49)(29,80,213,177)(30,81,214,178)(31,82,215,179)(32,83,216,180)(33,84,217,181)(34,71,218,182)(35,72,219,169)(36,73,220,170)(37,74,221,171)(38,75,222,172)(39,76,223,173)(40,77,224,174)(41,78,211,175)(42,79,212,176)(57,167,87,146)(58,168,88,147)(59,155,89,148)(60,156,90,149)(61,157,91,150)(62,158,92,151)(63,159,93,152)(64,160,94,153)(65,161,95,154)(66,162,96,141)(67,163,97,142)(68,164,98,143)(69,165,85,144)(70,166,86,145)(99,198,121,189)(100,199,122,190)(101,200,123,191)(102,201,124,192)(103,202,125,193)(104,203,126,194)(105,204,113,195)(106,205,114,196)(107,206,115,183)(108,207,116,184)(109,208,117,185)(110,209,118,186)(111,210,119,187)(112,197,120,188) );
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)], [(1,184),(2,183),(3,196),(4,195),(5,194),(6,193),(7,192),(8,191),(9,190),(10,189),(11,188),(12,187),(13,186),(14,185),(15,44),(16,43),(17,56),(18,55),(19,54),(20,53),(21,52),(22,51),(23,50),(24,49),(25,48),(26,47),(27,46),(28,45),(29,157),(30,156),(31,155),(32,168),(33,167),(34,166),(35,165),(36,164),(37,163),(38,162),(39,161),(40,160),(41,159),(42,158),(57,97),(58,96),(59,95),(60,94),(61,93),(62,92),(63,91),(64,90),(65,89),(66,88),(67,87),(68,86),(69,85),(70,98),(71,170),(72,169),(73,182),(74,181),(75,180),(76,179),(77,178),(78,177),(79,176),(80,175),(81,174),(82,173),(83,172),(84,171),(99,126),(100,125),(101,124),(102,123),(103,122),(104,121),(105,120),(106,119),(107,118),(108,117),(109,116),(110,115),(111,114),(112,113),(127,200),(128,199),(129,198),(130,197),(131,210),(132,209),(133,208),(134,207),(135,206),(136,205),(137,204),(138,203),(139,202),(140,201),(141,222),(142,221),(143,220),(144,219),(145,218),(146,217),(147,216),(148,215),(149,214),(150,213),(151,212),(152,211),(153,224),(154,223)], [(1,223,208,155),(2,224,209,156),(3,211,210,157),(4,212,197,158),(5,213,198,159),(6,214,199,160),(7,215,200,161),(8,216,201,162),(9,217,202,163),(10,218,203,164),(11,219,204,165),(12,220,205,166),(13,221,206,167),(14,222,207,168),(15,94,122,178),(16,95,123,179),(17,96,124,180),(18,97,125,181),(19,98,126,182),(20,85,113,169),(21,86,114,170),(22,87,115,171),(23,88,116,172),(24,89,117,173),(25,90,118,174),(26,91,119,175),(27,92,120,176),(28,93,121,177),(29,189,152,138),(30,190,153,139),(31,191,154,140),(32,192,141,127),(33,193,142,128),(34,194,143,129),(35,195,144,130),(36,196,145,131),(37,183,146,132),(38,184,147,133),(39,185,148,134),(40,186,149,135),(41,187,150,136),(42,188,151,137),(43,66,102,83),(44,67,103,84),(45,68,104,71),(46,69,105,72),(47,70,106,73),(48,57,107,74),(49,58,108,75),(50,59,109,76),(51,60,110,77),(52,61,111,78),(53,62,112,79),(54,63,99,80),(55,64,100,81),(56,65,101,82)], [(1,24,134,50),(2,25,135,51),(3,26,136,52),(4,27,137,53),(5,28,138,54),(6,15,139,55),(7,16,140,56),(8,17,127,43),(9,18,128,44),(10,19,129,45),(11,20,130,46),(12,21,131,47),(13,22,132,48),(14,23,133,49),(29,80,213,177),(30,81,214,178),(31,82,215,179),(32,83,216,180),(33,84,217,181),(34,71,218,182),(35,72,219,169),(36,73,220,170),(37,74,221,171),(38,75,222,172),(39,76,223,173),(40,77,224,174),(41,78,211,175),(42,79,212,176),(57,167,87,146),(58,168,88,147),(59,155,89,148),(60,156,90,149),(61,157,91,150),(62,158,92,151),(63,159,93,152),(64,160,94,153),(65,161,95,154),(66,162,96,141),(67,163,97,142),(68,164,98,143),(69,165,85,144),(70,166,86,145),(99,198,121,189),(100,199,122,190),(101,200,123,191),(102,201,124,192),(103,202,125,193),(104,203,126,194),(105,204,113,195),(106,205,114,196),(107,206,115,183),(108,207,116,184),(109,208,117,185),(110,209,118,186),(111,210,119,187),(112,197,120,188)]])
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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | C4○D4 | D14 | C4×D7 | C7⋊D4 | C4○D28 | D4×D7 | D4⋊2D7 | Q8⋊2D7 |
| kernel | D14⋊C4⋊7C4 | C14.C42 | C2×C4×Dic7 | C2×D14⋊C4 | C14×C4⋊C4 | D14⋊C4 | C2×Dic7 | C2×C28 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 3 | 1 | 8 | 2 | 2 | 3 | 8 | 9 | 12 | 12 | 12 | 3 | 3 | 6 |
Matrix representation of D14⋊C4⋊7C4 ►in GL6(𝔽29)
| 8 | 21 | 0 | 0 | 0 | 0 |
| 8 | 3 | 0 | 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 | 1 |
| 26 | 28 | 0 | 0 | 0 | 0 |
| 8 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 8 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 17 | 28 |
| 24 | 16 | 0 | 0 | 0 | 0 |
| 13 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 2 | 0 | 0 |
| 0 | 0 | 12 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 28 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 2 |
| 0 | 0 | 0 | 0 | 0 | 17 |
G:=sub<GL(6,GF(29))| [8,8,0,0,0,0,21,3,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[26,8,0,0,0,0,28,3,0,0,0,0,0,0,28,8,0,0,0,0,0,1,0,0,0,0,0,0,1,17,0,0,0,0,0,28],[24,13,0,0,0,0,16,5,0,0,0,0,0,0,8,12,0,0,0,0,2,21,0,0,0,0,0,0,17,28,0,0,0,0,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,2,17] >;
D14⋊C4⋊7C4 in GAP, Magma, Sage, TeX
D_{14}\rtimes C_4\rtimes_7C_4 % in TeX
G:=Group("D14:C4:7C4"); // GroupNames label
G:=SmallGroup(448,524);
// by ID
G=gap.SmallGroup(448,524);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,758,387,58,18822]);
// 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=c^-1>;
// generators/relations