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## G = (C2×C4)⋊6D28order 448 = 26·7

### 1st semidirect product of C2×C4 and D28 acting via D28/C28=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — (C2×C4)⋊6D28
 Chief series C1 — C7 — C14 — C2×C14 — C22×C14 — C23×D7 — C22×D28 — (C2×C4)⋊6D28
 Lower central C7 — C2×C14 — (C2×C4)⋊6D28
 Upper central C1 — C23 — C2×C42

Generators and relations for (C2×C4)⋊6D28
G = < a,b,c,d | a2=b4=c28=d2=1, dbd=ab=ba, ac=ca, ad=da, bc=cb, dcd=c-1 >

Subgroups: 1540 in 258 conjugacy classes, 87 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C22×D4, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C24.3C22, C4⋊Dic7, D14⋊C4, C4×C28, C2×D28, C2×D28, C22×Dic7, C22×C28, C22×C28, C23×D7, C2×C4⋊Dic7, C2×D14⋊C4, C2×C4×C28, C22×D28, (C2×C4)⋊6D28
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C4○D4, D14, C2×C22⋊C4, C4×D4, C4⋊D4, C4.4D4, C41D4, C4×D7, D28, C7⋊D4, C22×D7, C24.3C22, D14⋊C4, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C4×D28, C284D4, C4.D28, C2×D14⋊C4, C287D4, (C2×C4)⋊6D28

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

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

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

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

124 conjugacy classes

 class 1 2A ··· 2G 2H 2I 2J 2K 4A ··· 4L 4M 4N 4O 4P 7A 7B 7C 14A ··· 14U 28A ··· 28BT order 1 2 ··· 2 2 2 2 2 4 ··· 4 4 4 4 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 ··· 1 28 28 28 28 2 ··· 2 28 28 28 28 2 2 2 2 ··· 2 2 ··· 2

124 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 2 type + + + + + + + + + image C1 C2 C2 C2 C2 C4 D4 D7 C4○D4 D14 C4×D7 D28 C7⋊D4 C4○D28 kernel (C2×C4)⋊6D28 C2×C4⋊Dic7 C2×D14⋊C4 C2×C4×C28 C22×D28 C2×D28 C2×C28 C2×C42 C2×C14 C22×C4 C2×C4 C2×C4 C2×C4 C22 # reps 1 1 4 1 1 8 8 3 4 9 12 36 12 24

Matrix representation of (C2×C4)⋊6D28 in GL6(𝔽29)

 28 0 0 0 0 0 0 28 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 3 27 0 0 0 0 4 26 0 0 0 0 0 0 17 0 0 0 0 0 0 17 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 15 18 0 0 0 0 22 11 0 0 0 0 0 0 18 7 0 0 0 0 15 22 0 0 0 0 0 0 9 4 0 0 0 0 25 8
,
 17 25 0 0 0 0 14 12 0 0 0 0 0 0 6 10 0 0 0 0 11 23 0 0 0 0 0 0 10 7 0 0 0 0 19 19

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[3,4,0,0,0,0,27,26,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[15,22,0,0,0,0,18,11,0,0,0,0,0,0,18,15,0,0,0,0,7,22,0,0,0,0,0,0,9,25,0,0,0,0,4,8],[17,14,0,0,0,0,25,12,0,0,0,0,0,0,6,11,0,0,0,0,10,23,0,0,0,0,0,0,10,19,0,0,0,0,7,19] >;

(C2×C4)⋊6D28 in GAP, Magma, Sage, TeX

(C_2\times C_4)\rtimes_6D_{28}
% in TeX

G:=Group("(C2xC4):6D28");
// GroupNames label

G:=SmallGroup(448,473);
// by ID

G=gap.SmallGroup(448,473);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,758,58,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^4=c^28=d^2=1,d*b*d=a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*c*d=c^-1>;
// generators/relations

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