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## G = (C2×C28).290D4order 448 = 26·7

### 264th non-split extension by C2×C28 of D4 acting via D4/C2=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22×C14 — (C2×C28).290D4
 Chief series C1 — C7 — C14 — C2×C14 — C22×C14 — C23×D7 — C2×D14⋊C4 — (C2×C28).290D4
 Lower central C7 — C22×C14 — (C2×C28).290D4
 Upper central C1 — C23 — C2×C4⋊C4

Generators and relations for (C2×C28).290D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=ab-1, dbd=ab13, dcd=ac-1 >

Subgroups: 932 in 170 conjugacy classes, 57 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C24, Dic7, C28, D14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.11D4, D14⋊C4, C7×C4⋊C4, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, C14.C42, C14.C42, C2×D14⋊C4, C2×D14⋊C4, C14×C4⋊C4, (C2×C28).290D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C22.D4, C4.4D4, C422C2, C7⋊D4, C22×D7, C23.11D4, C4○D28, D4×D7, D42D7, Q82D7, C2×C7⋊D4, D14.5D4, C4⋊C4⋊D7, C23.23D14, C282D4, C28.23D4, (C2×C28).290D4

Smallest permutation representation of (C2×C28).290D4
On 224 points
Generators in S224
(1 161)(2 162)(3 163)(4 164)(5 165)(6 166)(7 167)(8 168)(9 141)(10 142)(11 143)(12 144)(13 145)(14 146)(15 147)(16 148)(17 149)(18 150)(19 151)(20 152)(21 153)(22 154)(23 155)(24 156)(25 157)(26 158)(27 159)(28 160)(29 104)(30 105)(31 106)(32 107)(33 108)(34 109)(35 110)(36 111)(37 112)(38 85)(39 86)(40 87)(41 88)(42 89)(43 90)(44 91)(45 92)(46 93)(47 94)(48 95)(49 96)(50 97)(51 98)(52 99)(53 100)(54 101)(55 102)(56 103)(57 218)(58 219)(59 220)(60 221)(61 222)(62 223)(63 224)(64 197)(65 198)(66 199)(67 200)(68 201)(69 202)(70 203)(71 204)(72 205)(73 206)(74 207)(75 208)(76 209)(77 210)(78 211)(79 212)(80 213)(81 214)(82 215)(83 216)(84 217)(113 180)(114 181)(115 182)(116 183)(117 184)(118 185)(119 186)(120 187)(121 188)(122 189)(123 190)(124 191)(125 192)(126 193)(127 194)(128 195)(129 196)(130 169)(131 170)(132 171)(133 172)(134 173)(135 174)(136 175)(137 176)(138 177)(139 178)(140 179)
(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 54 74 138)(2 100 75 176)(3 52 76 136)(4 98 77 174)(5 50 78 134)(6 96 79 172)(7 48 80 132)(8 94 81 170)(9 46 82 130)(10 92 83 196)(11 44 84 128)(12 90 57 194)(13 42 58 126)(14 88 59 192)(15 40 60 124)(16 86 61 190)(17 38 62 122)(18 112 63 188)(19 36 64 120)(20 110 65 186)(21 34 66 118)(22 108 67 184)(23 32 68 116)(24 106 69 182)(25 30 70 114)(26 104 71 180)(27 56 72 140)(28 102 73 178)(29 204 113 158)(31 202 115 156)(33 200 117 154)(35 198 119 152)(37 224 121 150)(39 222 123 148)(41 220 125 146)(43 218 127 144)(45 216 129 142)(47 214 131 168)(49 212 133 166)(51 210 135 164)(53 208 137 162)(55 206 139 160)(85 223 189 149)(87 221 191 147)(89 219 193 145)(91 217 195 143)(93 215 169 141)(95 213 171 167)(97 211 173 165)(99 209 175 163)(101 207 177 161)(103 205 179 159)(105 203 181 157)(107 201 183 155)(109 199 185 153)(111 197 187 151)
(1 15)(2 160)(3 13)(4 158)(5 11)(6 156)(7 9)(8 154)(10 152)(12 150)(14 148)(16 146)(17 27)(18 144)(19 25)(20 142)(21 23)(22 168)(24 166)(26 164)(28 162)(29 135)(30 187)(31 133)(32 185)(33 131)(34 183)(35 129)(36 181)(37 127)(38 179)(39 125)(40 177)(41 123)(42 175)(43 121)(44 173)(45 119)(46 171)(47 117)(48 169)(49 115)(50 195)(51 113)(52 193)(53 139)(54 191)(55 137)(56 189)(57 224)(58 76)(59 222)(60 74)(61 220)(62 72)(63 218)(64 70)(65 216)(66 68)(67 214)(69 212)(71 210)(73 208)(75 206)(77 204)(78 84)(79 202)(80 82)(81 200)(83 198)(85 140)(86 192)(87 138)(88 190)(89 136)(90 188)(91 134)(92 186)(93 132)(94 184)(95 130)(96 182)(97 128)(98 180)(99 126)(100 178)(101 124)(102 176)(103 122)(104 174)(105 120)(106 172)(107 118)(108 170)(109 116)(110 196)(111 114)(112 194)(141 167)(143 165)(145 163)(147 161)(149 159)(151 157)(153 155)(197 203)(199 201)(205 223)(207 221)(209 219)(211 217)(213 215)

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

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

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

82 conjugacy classes

 class 1 2A ··· 2G 2H 2I 4A ··· 4F 4G ··· 4L 7A 7B 7C 14A ··· 14U 28A ··· 28AJ order 1 2 ··· 2 2 2 4 ··· 4 4 ··· 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 ··· 1 28 28 4 ··· 4 28 ··· 28 2 2 2 2 ··· 2 4 ··· 4

82 irreducible representations

 dim 1 1 1 1 2 2 2 2 2 2 2 4 4 4 type + + + + + + + + + - + image C1 C2 C2 C2 D4 D4 D7 C4○D4 D14 C7⋊D4 C4○D28 D4×D7 D4⋊2D7 Q8⋊2D7 kernel (C2×C28).290D4 C14.C42 C2×D14⋊C4 C14×C4⋊C4 C2×C28 C22×D7 C2×C4⋊C4 C2×C14 C22×C4 C2×C4 C22 C22 C22 C22 # reps 1 3 3 1 2 2 3 10 9 12 24 3 3 6

Matrix representation of (C2×C28).290D4 in GL6(𝔽29)

 1 0 0 0 0 0 0 1 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
,
 11 21 0 0 0 0 8 18 0 0 0 0 0 0 21 26 0 0 0 0 2 19 0 0 0 0 0 0 11 3 0 0 0 0 26 7
,
 0 28 0 0 0 0 28 0 0 0 0 0 0 0 9 13 0 0 0 0 5 20 0 0 0 0 0 0 17 0 0 0 0 0 16 12
,
 28 0 0 0 0 0 0 28 0 0 0 0 0 0 10 1 0 0 0 0 17 19 0 0 0 0 0 0 1 0 0 0 0 0 18 28

G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[11,8,0,0,0,0,21,18,0,0,0,0,0,0,21,2,0,0,0,0,26,19,0,0,0,0,0,0,11,26,0,0,0,0,3,7],[0,28,0,0,0,0,28,0,0,0,0,0,0,0,9,5,0,0,0,0,13,20,0,0,0,0,0,0,17,16,0,0,0,0,0,12],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,10,17,0,0,0,0,1,19,0,0,0,0,0,0,1,18,0,0,0,0,0,28] >;

(C2×C28).290D4 in GAP, Magma, Sage, TeX

(C_2\times C_{28})._{290}D_4
% in TeX

G:=Group("(C2xC28).290D4");
// GroupNames label

G:=SmallGroup(448,527);
// by ID

G=gap.SmallGroup(448,527);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,254,387,100,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=a*b^-1,d*b*d=a*b^13,d*c*d=a*c^-1>;
// generators/relations

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