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## G = (C2×D28).14C4order 448 = 26·7

### 10th non-split extension by C2×D28 of C4 acting via C4/C2=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — (C2×D28).14C4
 Chief series C1 — C7 — C14 — C28 — C2×C28 — C2×C4×D7 — C2×C4○D28 — (C2×D28).14C4
 Lower central C7 — C2×C14 — (C2×D28).14C4
 Upper central C1 — C2×C4 — C2×M4(2)

Generators and relations for (C2×D28).14C4
G = < a,b,c,d,e | a2=b8=c2=d7=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b5, bd=db, ebe=ab5, cd=dc, ece=b4c, ede=d-1 >

Subgroups: 740 in 158 conjugacy classes, 63 normal (25 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C2×C8, C2×C8, M4(2), C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C22⋊C8, C22×C8, C2×M4(2), C2×C4○D4, C7⋊C8, C56, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, (C22×C8)⋊C2, C2×C7⋊C8, C2×C7⋊C8, C2×C56, C7×M4(2), C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, D14⋊C8, C22×C7⋊C8, C14×M4(2), C2×C4○D28, (C2×D28).14C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, D14, C2×C22⋊C4, C8○D4, C4×D7, D28, C7⋊D4, C22×D7, (C22×C8)⋊C2, D14⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, D28.C4, C2×D14⋊C4, (C2×D28).14C4

Smallest permutation representation of (C2×D28).14C4
On 224 points
Generators in S224
(1 42)(2 43)(3 44)(4 45)(5 46)(6 47)(7 48)(8 41)(9 138)(10 139)(11 140)(12 141)(13 142)(14 143)(15 144)(16 137)(17 108)(18 109)(19 110)(20 111)(21 112)(22 105)(23 106)(24 107)(25 125)(26 126)(27 127)(28 128)(29 121)(30 122)(31 123)(32 124)(33 189)(34 190)(35 191)(36 192)(37 185)(38 186)(39 187)(40 188)(49 183)(50 184)(51 177)(52 178)(53 179)(54 180)(55 181)(56 182)(57 115)(58 116)(59 117)(60 118)(61 119)(62 120)(63 113)(64 114)(65 167)(66 168)(67 161)(68 162)(69 163)(70 164)(71 165)(72 166)(73 169)(74 170)(75 171)(76 172)(77 173)(78 174)(79 175)(80 176)(81 195)(82 196)(83 197)(84 198)(85 199)(86 200)(87 193)(88 194)(89 147)(90 148)(91 149)(92 150)(93 151)(94 152)(95 145)(96 146)(97 130)(98 131)(99 132)(100 133)(101 134)(102 135)(103 136)(104 129)(153 202)(154 203)(155 204)(156 205)(157 206)(158 207)(159 208)(160 201)(209 222)(210 223)(211 224)(212 217)(213 218)(214 219)(215 220)(216 221)
(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 46)(2 43)(3 48)(4 45)(5 42)(6 47)(7 44)(8 41)(9 138)(10 143)(11 140)(12 137)(13 142)(14 139)(15 144)(16 141)(17 108)(18 105)(19 110)(20 107)(21 112)(22 109)(23 106)(24 111)(25 121)(26 126)(27 123)(28 128)(29 125)(30 122)(31 127)(32 124)(33 189)(34 186)(35 191)(36 188)(37 185)(38 190)(39 187)(40 192)(49 179)(50 184)(51 181)(52 178)(53 183)(54 180)(55 177)(56 182)(57 115)(58 120)(59 117)(60 114)(61 119)(62 116)(63 113)(64 118)(65 163)(66 168)(67 165)(68 162)(69 167)(70 164)(71 161)(72 166)(73 169)(74 174)(75 171)(76 176)(77 173)(78 170)(79 175)(80 172)(81 199)(82 196)(83 193)(84 198)(85 195)(86 200)(87 197)(88 194)(89 147)(90 152)(91 149)(92 146)(93 151)(94 148)(95 145)(96 150)(97 134)(98 131)(99 136)(100 133)(101 130)(102 135)(103 132)(104 129)(153 202)(154 207)(155 204)(156 201)(157 206)(158 203)(159 208)(160 205)(209 218)(210 223)(211 220)(212 217)(213 222)(214 219)(215 224)(216 221)
(1 67 53 172 141 99 18)(2 68 54 173 142 100 19)(3 69 55 174 143 101 20)(4 70 56 175 144 102 21)(5 71 49 176 137 103 22)(6 72 50 169 138 104 23)(7 65 51 170 139 97 24)(8 66 52 171 140 98 17)(9 129 106 47 166 184 73)(10 130 107 48 167 177 74)(11 131 108 41 168 178 75)(12 132 109 42 161 179 76)(13 133 110 43 162 180 77)(14 134 111 44 163 181 78)(15 135 112 45 164 182 79)(16 136 105 46 165 183 80)(25 36 199 146 160 209 116)(26 37 200 147 153 210 117)(27 38 193 148 154 211 118)(28 39 194 149 155 212 119)(29 40 195 150 156 213 120)(30 33 196 151 157 214 113)(31 34 197 152 158 215 114)(32 35 198 145 159 216 115)(57 124 191 84 95 208 221)(58 125 192 85 96 201 222)(59 126 185 86 89 202 223)(60 127 186 87 90 203 224)(61 128 187 88 91 204 217)(62 121 188 81 92 205 218)(63 122 189 82 93 206 219)(64 123 190 83 94 207 220)
(1 91)(2 146)(3 93)(4 148)(5 95)(6 150)(7 89)(8 152)(9 62)(10 117)(11 64)(12 119)(13 58)(14 113)(15 60)(16 115)(17 158)(18 204)(19 160)(20 206)(21 154)(22 208)(23 156)(24 202)(25 173)(26 74)(27 175)(28 76)(29 169)(30 78)(31 171)(32 80)(33 181)(34 52)(35 183)(36 54)(37 177)(38 56)(39 179)(40 50)(41 94)(42 149)(43 96)(44 151)(45 90)(46 145)(47 92)(48 147)(49 191)(51 185)(53 187)(55 189)(57 137)(59 139)(61 141)(63 143)(65 86)(66 197)(67 88)(68 199)(69 82)(70 193)(71 84)(72 195)(73 121)(75 123)(77 125)(79 127)(81 166)(83 168)(85 162)(87 164)(97 223)(98 215)(99 217)(100 209)(101 219)(102 211)(103 221)(104 213)(105 159)(106 205)(107 153)(108 207)(109 155)(110 201)(111 157)(112 203)(114 140)(116 142)(118 144)(120 138)(122 174)(124 176)(126 170)(128 172)(129 218)(130 210)(131 220)(132 212)(133 222)(134 214)(135 224)(136 216)(161 194)(163 196)(165 198)(167 200)(178 190)(180 192)(182 186)(184 188)

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

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

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

88 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 4C 4D 4E 4F 4G 4H 7A 7B 7C 8A 8B 8C 8D 8E ··· 8L 14A ··· 14I 14J ··· 14O 28A ··· 28L 28M ··· 28R 56A ··· 56X order 1 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 7 7 7 8 8 8 8 8 ··· 8 14 ··· 14 14 ··· 14 28 ··· 28 28 ··· 28 56 ··· 56 size 1 1 1 1 2 2 28 28 1 1 1 1 2 2 28 28 2 2 2 4 4 4 4 14 ··· 14 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4 4 ··· 4

88 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 type + + + + + + + + + + image C1 C2 C2 C2 C2 C4 C4 C4 D4 D7 D14 D14 C8○D4 C4×D7 D28 C7⋊D4 C4×D7 D28.C4 kernel (C2×D28).14C4 D14⋊C8 C22×C7⋊C8 C14×M4(2) C2×C4○D28 C2×Dic14 C2×D28 C2×C7⋊D4 C2×C28 C2×M4(2) C2×C8 C22×C4 C14 C2×C4 C2×C4 C2×C4 C23 C2 # reps 1 4 1 1 1 2 2 4 4 3 6 3 8 6 12 12 6 12

Matrix representation of (C2×D28).14C4 in GL4(𝔽113) generated by

 112 0 0 0 0 112 0 0 0 0 1 0 0 0 0 1
,
 58 75 0 0 38 55 0 0 0 0 98 2 0 0 106 15
,
 112 0 0 0 0 112 0 0 0 0 1 0 0 0 15 112
,
 0 1 0 0 112 9 0 0 0 0 1 0 0 0 0 1
,
 104 1 0 0 33 9 0 0 0 0 69 36 0 0 31 44
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[58,38,0,0,75,55,0,0,0,0,98,106,0,0,2,15],[112,0,0,0,0,112,0,0,0,0,1,15,0,0,0,112],[0,112,0,0,1,9,0,0,0,0,1,0,0,0,0,1],[104,33,0,0,1,9,0,0,0,0,69,31,0,0,36,44] >;

(C2×D28).14C4 in GAP, Magma, Sage, TeX

(C_2\times D_{28})._{14}C_4
% in TeX

G:=Group("(C2xD28).14C4");
// GroupNames label

G:=SmallGroup(448,663);
// by ID

G=gap.SmallGroup(448,663);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,422,387,58,136,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^8=c^2=d^7=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^5,b*d=d*b,e*b*e=a*b^5,c*d=d*c,e*c*e=b^4*c,e*d*e=d^-1>;
// generators/relations

׿
×
𝔽