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