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## G = C14×C22.D4order 448 = 26·7

### Direct product of C14 and C22.D4

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C14×C22.D4
 Chief series C1 — C2 — C22 — C2×C14 — C22×C14 — D4×C14 — C7×C22.D4 — C14×C22.D4
 Lower central C1 — C22 — C14×C22.D4
 Upper central C1 — C22×C14 — C14×C22.D4

Generators and relations for C14×C22.D4
G = < a,b,c,d,e | a14=b2=c2=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, dbd-1=ebe=bc=cb, cd=dc, ce=ec, ede=cd-1 >

Subgroups: 530 in 342 conjugacy classes, 178 normal (22 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, C23, C14, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, C28, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C22.D4, C23×C4, C22×D4, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C22×C14, C2×C22.D4, C7×C22⋊C4, C7×C4⋊C4, C22×C28, C22×C28, C22×C28, D4×C14, D4×C14, C23×C14, C14×C22⋊C4, C14×C22⋊C4, C14×C4⋊C4, C7×C22.D4, C23×C28, D4×C2×C14, C14×C22.D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C4○D4, C24, C2×C14, C22.D4, C22×D4, C2×C4○D4, C7×D4, C22×C14, C2×C22.D4, D4×C14, C7×C4○D4, C23×C14, C7×C22.D4, D4×C2×C14, C14×C4○D4, C14×C22.D4

Smallest permutation representation of C14×C22.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)
(15 178)(16 179)(17 180)(18 181)(19 182)(20 169)(21 170)(22 171)(23 172)(24 173)(25 174)(26 175)(27 176)(28 177)(29 152)(30 153)(31 154)(32 141)(33 142)(34 143)(35 144)(36 145)(37 146)(38 147)(39 148)(40 149)(41 150)(42 151)(85 104)(86 105)(87 106)(88 107)(89 108)(90 109)(91 110)(92 111)(93 112)(94 99)(95 100)(96 101)(97 102)(98 103)(127 158)(128 159)(129 160)(130 161)(131 162)(132 163)(133 164)(134 165)(135 166)(136 167)(137 168)(138 155)(139 156)(140 157)
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 183)(10 184)(11 185)(12 186)(13 187)(14 188)(15 178)(16 179)(17 180)(18 181)(19 182)(20 169)(21 170)(22 171)(23 172)(24 173)(25 174)(26 175)(27 176)(28 177)(29 152)(30 153)(31 154)(32 141)(33 142)(34 143)(35 144)(36 145)(37 146)(38 147)(39 148)(40 149)(41 150)(42 151)(43 219)(44 220)(45 221)(46 222)(47 223)(48 224)(49 211)(50 212)(51 213)(52 214)(53 215)(54 216)(55 217)(56 218)(57 125)(58 126)(59 113)(60 114)(61 115)(62 116)(63 117)(64 118)(65 119)(66 120)(67 121)(68 122)(69 123)(70 124)(71 198)(72 199)(73 200)(74 201)(75 202)(76 203)(77 204)(78 205)(79 206)(80 207)(81 208)(82 209)(83 210)(84 197)(85 104)(86 105)(87 106)(88 107)(89 108)(90 109)(91 110)(92 111)(93 112)(94 99)(95 100)(96 101)(97 102)(98 103)(127 158)(128 159)(129 160)(130 161)(131 162)(132 163)(133 164)(134 165)(135 166)(136 167)(137 168)(138 155)(139 156)(140 157)
(1 155 223 147)(2 156 224 148)(3 157 211 149)(4 158 212 150)(5 159 213 151)(6 160 214 152)(7 161 215 153)(8 162 216 154)(9 163 217 141)(10 164 218 142)(11 165 219 143)(12 166 220 144)(13 167 221 145)(14 168 222 146)(15 207 103 117)(16 208 104 118)(17 209 105 119)(18 210 106 120)(19 197 107 121)(20 198 108 122)(21 199 109 123)(22 200 110 124)(23 201 111 125)(24 202 112 126)(25 203 99 113)(26 204 100 114)(27 205 101 115)(28 206 102 116)(29 194 129 52)(30 195 130 53)(31 196 131 54)(32 183 132 55)(33 184 133 56)(34 185 134 43)(35 186 135 44)(36 187 136 45)(37 188 137 46)(38 189 138 47)(39 190 139 48)(40 191 140 49)(41 192 127 50)(42 193 128 51)(57 172 74 92)(58 173 75 93)(59 174 76 94)(60 175 77 95)(61 176 78 96)(62 177 79 97)(63 178 80 98)(64 179 81 85)(65 180 82 86)(66 181 83 87)(67 182 84 88)(68 169 71 89)(69 170 72 90)(70 171 73 91)
(1 17)(2 18)(3 19)(4 20)(5 21)(6 22)(7 23)(8 24)(9 25)(10 26)(11 27)(12 28)(13 15)(14 16)(29 200)(30 201)(31 202)(32 203)(33 204)(34 205)(35 206)(36 207)(37 208)(38 209)(39 210)(40 197)(41 198)(42 199)(43 96)(44 97)(45 98)(46 85)(47 86)(48 87)(49 88)(50 89)(51 90)(52 91)(53 92)(54 93)(55 94)(56 95)(57 161)(58 162)(59 163)(60 164)(61 165)(62 166)(63 167)(64 168)(65 155)(66 156)(67 157)(68 158)(69 159)(70 160)(71 150)(72 151)(73 152)(74 153)(75 154)(76 141)(77 142)(78 143)(79 144)(80 145)(81 146)(82 147)(83 148)(84 149)(99 217)(100 218)(101 219)(102 220)(103 221)(104 222)(105 223)(106 224)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)(113 132)(114 133)(115 134)(116 135)(117 136)(118 137)(119 138)(120 139)(121 140)(122 127)(123 128)(124 129)(125 130)(126 131)(169 192)(170 193)(171 194)(172 195)(173 196)(174 183)(175 184)(176 185)(177 186)(178 187)(179 188)(180 189)(181 190)(182 191)

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), (15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,183)(10,184)(11,185)(12,186)(13,187)(14,188)(15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(43,219)(44,220)(45,221)(46,222)(47,223)(48,224)(49,211)(50,212)(51,213)(52,214)(53,215)(54,216)(55,217)(56,218)(57,125)(58,126)(59,113)(60,114)(61,115)(62,116)(63,117)(64,118)(65,119)(66,120)(67,121)(68,122)(69,123)(70,124)(71,198)(72,199)(73,200)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,208)(82,209)(83,210)(84,197)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,155,223,147)(2,156,224,148)(3,157,211,149)(4,158,212,150)(5,159,213,151)(6,160,214,152)(7,161,215,153)(8,162,216,154)(9,163,217,141)(10,164,218,142)(11,165,219,143)(12,166,220,144)(13,167,221,145)(14,168,222,146)(15,207,103,117)(16,208,104,118)(17,209,105,119)(18,210,106,120)(19,197,107,121)(20,198,108,122)(21,199,109,123)(22,200,110,124)(23,201,111,125)(24,202,112,126)(25,203,99,113)(26,204,100,114)(27,205,101,115)(28,206,102,116)(29,194,129,52)(30,195,130,53)(31,196,131,54)(32,183,132,55)(33,184,133,56)(34,185,134,43)(35,186,135,44)(36,187,136,45)(37,188,137,46)(38,189,138,47)(39,190,139,48)(40,191,140,49)(41,192,127,50)(42,193,128,51)(57,172,74,92)(58,173,75,93)(59,174,76,94)(60,175,77,95)(61,176,78,96)(62,177,79,97)(63,178,80,98)(64,179,81,85)(65,180,82,86)(66,181,83,87)(67,182,84,88)(68,169,71,89)(69,170,72,90)(70,171,73,91), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,15)(14,16)(29,200)(30,201)(31,202)(32,203)(33,204)(34,205)(35,206)(36,207)(37,208)(38,209)(39,210)(40,197)(41,198)(42,199)(43,96)(44,97)(45,98)(46,85)(47,86)(48,87)(49,88)(50,89)(51,90)(52,91)(53,92)(54,93)(55,94)(56,95)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,155)(66,156)(67,157)(68,158)(69,159)(70,160)(71,150)(72,151)(73,152)(74,153)(75,154)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,127)(123,128)(124,129)(125,130)(126,131)(169,192)(170,193)(171,194)(172,195)(173,196)(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)(181,190)(182,191)>;

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), (15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,183)(10,184)(11,185)(12,186)(13,187)(14,188)(15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(43,219)(44,220)(45,221)(46,222)(47,223)(48,224)(49,211)(50,212)(51,213)(52,214)(53,215)(54,216)(55,217)(56,218)(57,125)(58,126)(59,113)(60,114)(61,115)(62,116)(63,117)(64,118)(65,119)(66,120)(67,121)(68,122)(69,123)(70,124)(71,198)(72,199)(73,200)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,208)(82,209)(83,210)(84,197)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,155,223,147)(2,156,224,148)(3,157,211,149)(4,158,212,150)(5,159,213,151)(6,160,214,152)(7,161,215,153)(8,162,216,154)(9,163,217,141)(10,164,218,142)(11,165,219,143)(12,166,220,144)(13,167,221,145)(14,168,222,146)(15,207,103,117)(16,208,104,118)(17,209,105,119)(18,210,106,120)(19,197,107,121)(20,198,108,122)(21,199,109,123)(22,200,110,124)(23,201,111,125)(24,202,112,126)(25,203,99,113)(26,204,100,114)(27,205,101,115)(28,206,102,116)(29,194,129,52)(30,195,130,53)(31,196,131,54)(32,183,132,55)(33,184,133,56)(34,185,134,43)(35,186,135,44)(36,187,136,45)(37,188,137,46)(38,189,138,47)(39,190,139,48)(40,191,140,49)(41,192,127,50)(42,193,128,51)(57,172,74,92)(58,173,75,93)(59,174,76,94)(60,175,77,95)(61,176,78,96)(62,177,79,97)(63,178,80,98)(64,179,81,85)(65,180,82,86)(66,181,83,87)(67,182,84,88)(68,169,71,89)(69,170,72,90)(70,171,73,91), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,15)(14,16)(29,200)(30,201)(31,202)(32,203)(33,204)(34,205)(35,206)(36,207)(37,208)(38,209)(39,210)(40,197)(41,198)(42,199)(43,96)(44,97)(45,98)(46,85)(47,86)(48,87)(49,88)(50,89)(51,90)(52,91)(53,92)(54,93)(55,94)(56,95)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,155)(66,156)(67,157)(68,158)(69,159)(70,160)(71,150)(72,151)(73,152)(74,153)(75,154)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,127)(123,128)(124,129)(125,130)(126,131)(169,192)(170,193)(171,194)(172,195)(173,196)(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)(181,190)(182,191) );

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)], [(15,178),(16,179),(17,180),(18,181),(19,182),(20,169),(21,170),(22,171),(23,172),(24,173),(25,174),(26,175),(27,176),(28,177),(29,152),(30,153),(31,154),(32,141),(33,142),(34,143),(35,144),(36,145),(37,146),(38,147),(39,148),(40,149),(41,150),(42,151),(85,104),(86,105),(87,106),(88,107),(89,108),(90,109),(91,110),(92,111),(93,112),(94,99),(95,100),(96,101),(97,102),(98,103),(127,158),(128,159),(129,160),(130,161),(131,162),(132,163),(133,164),(134,165),(135,166),(136,167),(137,168),(138,155),(139,156),(140,157)], [(1,189),(2,190),(3,191),(4,192),(5,193),(6,194),(7,195),(8,196),(9,183),(10,184),(11,185),(12,186),(13,187),(14,188),(15,178),(16,179),(17,180),(18,181),(19,182),(20,169),(21,170),(22,171),(23,172),(24,173),(25,174),(26,175),(27,176),(28,177),(29,152),(30,153),(31,154),(32,141),(33,142),(34,143),(35,144),(36,145),(37,146),(38,147),(39,148),(40,149),(41,150),(42,151),(43,219),(44,220),(45,221),(46,222),(47,223),(48,224),(49,211),(50,212),(51,213),(52,214),(53,215),(54,216),(55,217),(56,218),(57,125),(58,126),(59,113),(60,114),(61,115),(62,116),(63,117),(64,118),(65,119),(66,120),(67,121),(68,122),(69,123),(70,124),(71,198),(72,199),(73,200),(74,201),(75,202),(76,203),(77,204),(78,205),(79,206),(80,207),(81,208),(82,209),(83,210),(84,197),(85,104),(86,105),(87,106),(88,107),(89,108),(90,109),(91,110),(92,111),(93,112),(94,99),(95,100),(96,101),(97,102),(98,103),(127,158),(128,159),(129,160),(130,161),(131,162),(132,163),(133,164),(134,165),(135,166),(136,167),(137,168),(138,155),(139,156),(140,157)], [(1,155,223,147),(2,156,224,148),(3,157,211,149),(4,158,212,150),(5,159,213,151),(6,160,214,152),(7,161,215,153),(8,162,216,154),(9,163,217,141),(10,164,218,142),(11,165,219,143),(12,166,220,144),(13,167,221,145),(14,168,222,146),(15,207,103,117),(16,208,104,118),(17,209,105,119),(18,210,106,120),(19,197,107,121),(20,198,108,122),(21,199,109,123),(22,200,110,124),(23,201,111,125),(24,202,112,126),(25,203,99,113),(26,204,100,114),(27,205,101,115),(28,206,102,116),(29,194,129,52),(30,195,130,53),(31,196,131,54),(32,183,132,55),(33,184,133,56),(34,185,134,43),(35,186,135,44),(36,187,136,45),(37,188,137,46),(38,189,138,47),(39,190,139,48),(40,191,140,49),(41,192,127,50),(42,193,128,51),(57,172,74,92),(58,173,75,93),(59,174,76,94),(60,175,77,95),(61,176,78,96),(62,177,79,97),(63,178,80,98),(64,179,81,85),(65,180,82,86),(66,181,83,87),(67,182,84,88),(68,169,71,89),(69,170,72,90),(70,171,73,91)], [(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,15),(14,16),(29,200),(30,201),(31,202),(32,203),(33,204),(34,205),(35,206),(36,207),(37,208),(38,209),(39,210),(40,197),(41,198),(42,199),(43,96),(44,97),(45,98),(46,85),(47,86),(48,87),(49,88),(50,89),(51,90),(52,91),(53,92),(54,93),(55,94),(56,95),(57,161),(58,162),(59,163),(60,164),(61,165),(62,166),(63,167),(64,168),(65,155),(66,156),(67,157),(68,158),(69,159),(70,160),(71,150),(72,151),(73,152),(74,153),(75,154),(76,141),(77,142),(78,143),(79,144),(80,145),(81,146),(82,147),(83,148),(84,149),(99,217),(100,218),(101,219),(102,220),(103,221),(104,222),(105,223),(106,224),(107,211),(108,212),(109,213),(110,214),(111,215),(112,216),(113,132),(114,133),(115,134),(116,135),(117,136),(118,137),(119,138),(120,139),(121,140),(122,127),(123,128),(124,129),(125,130),(126,131),(169,192),(170,193),(171,194),(172,195),(173,196),(174,183),(175,184),(176,185),(177,186),(178,187),(179,188),(180,189),(181,190),(182,191)]])

196 conjugacy classes

 class 1 2A ··· 2G 2H 2I 2J 2K 2L 2M 4A ··· 4H 4I ··· 4N 7A ··· 7F 14A ··· 14AP 14AQ ··· 14BN 14BO ··· 14BZ 28A ··· 28AV 28AW ··· 28CF order 1 2 ··· 2 2 2 2 2 2 2 4 ··· 4 4 ··· 4 7 ··· 7 14 ··· 14 14 ··· 14 14 ··· 14 28 ··· 28 28 ··· 28 size 1 1 ··· 1 2 2 2 2 4 4 2 ··· 2 4 ··· 4 1 ··· 1 1 ··· 1 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4

196 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 type + + + + + + + image C1 C2 C2 C2 C2 C2 C7 C14 C14 C14 C14 C14 D4 C4○D4 C7×D4 C7×C4○D4 kernel C14×C22.D4 C14×C22⋊C4 C14×C4⋊C4 C7×C22.D4 C23×C28 D4×C2×C14 C2×C22.D4 C2×C22⋊C4 C2×C4⋊C4 C22.D4 C23×C4 C22×D4 C22×C14 C2×C14 C23 C22 # reps 1 3 2 8 1 1 6 18 12 48 6 6 4 8 24 48

Matrix representation of C14×C22.D4 in GL6(𝔽29)

 9 0 0 0 0 0 0 9 0 0 0 0 0 0 7 0 0 0 0 0 0 7 0 0 0 0 0 0 13 0 0 0 0 0 0 13
,
 1 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 0 1 0 0 0 0 0 10 28
,
 28 0 0 0 0 0 0 28 0 0 0 0 0 0 28 0 0 0 0 0 0 28 0 0 0 0 0 0 28 0 0 0 0 0 0 28
,
 0 17 0 0 0 0 17 0 0 0 0 0 0 0 0 17 0 0 0 0 17 0 0 0 0 0 0 0 27 12 0 0 0 0 7 2
,
 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 28 0 0 0 0 28 0 0 0 0 0 0 0 5 28 0 0 0 0 24 24

G:=sub<GL(6,GF(29))| [9,0,0,0,0,0,0,9,0,0,0,0,0,0,7,0,0,0,0,0,0,7,0,0,0,0,0,0,13,0,0,0,0,0,0,13],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,10,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,17,0,0,0,0,17,0,0,0,0,0,0,0,0,17,0,0,0,0,17,0,0,0,0,0,0,0,27,7,0,0,0,0,12,2],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,5,24,0,0,0,0,28,24] >;

C14×C22.D4 in GAP, Magma, Sage, TeX

C_{14}\times C_2^2.D_4
% in TeX

G:=Group("C14xC2^2.D4");
// GroupNames label

G:=SmallGroup(448,1307);
// by ID

G=gap.SmallGroup(448,1307);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,4790,604]);
// Polycyclic

G:=Group<a,b,c,d,e|a^14=b^2=c^2=d^4=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,d*b*d^-1=e*b*e=b*c=c*b,c*d=d*c,c*e=e*c,e*d*e=c*d^-1>;
// generators/relations

׿
×
𝔽