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## G = C2×C28.48D4order 448 = 26·7

### Direct product of C2 and C28.48D4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — C2×C28.48D4
 Chief series C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — C22×Dic14 — C2×C28.48D4
 Lower central C7 — C2×C14 — C2×C28.48D4
 Upper central C1 — C23 — C23×C4

Generators and relations for C2×C28.48D4
G = < a,b,c,d | a2=b28=c4=1, d2=b14, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b14c-1 >

Subgroups: 1092 in 322 conjugacy classes, 143 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C23, C23, C14, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×Q8, C24, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C2×C4⋊C4, C22⋊Q8, C23×C4, C22×Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C2×C22⋊Q8, Dic7⋊C4, C4⋊Dic7, C23.D7, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, C22×C28, C22×C28, C23×C14, C2×Dic7⋊C4, C28.48D4, C2×C4⋊Dic7, C2×C23.D7, C22×Dic14, C23×C28, C2×C28.48D4
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, C24, D14, C22⋊Q8, C22×D4, C22×Q8, C2×C4○D4, Dic14, C7⋊D4, C22×D7, C2×C22⋊Q8, C2×Dic14, C4○D28, C2×C7⋊D4, C23×D7, C28.48D4, C22×Dic14, C2×C4○D28, C22×C7⋊D4, C2×C28.48D4

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

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

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

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

124 conjugacy classes

 class 1 2A ··· 2G 2H 2I 2J 2K 4A ··· 4H 4I ··· 4P 7A 7B 7C 14A ··· 14AS 28A ··· 28AV order 1 2 ··· 2 2 2 2 2 4 ··· 4 4 ··· 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 ··· 1 2 2 2 2 2 ··· 2 28 ··· 28 2 2 2 2 ··· 2 2 ··· 2

124 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 type + + + + + + + + - + + + - image C1 C2 C2 C2 C2 C2 C2 D4 Q8 D7 C4○D4 D14 D14 C7⋊D4 Dic14 C4○D28 kernel C2×C28.48D4 C2×Dic7⋊C4 C28.48D4 C2×C4⋊Dic7 C2×C23.D7 C22×Dic14 C23×C28 C2×C28 C22×C14 C23×C4 C2×C14 C22×C4 C24 C2×C4 C23 C22 # reps 1 2 8 1 2 1 1 4 4 3 4 18 3 24 24 24

Matrix representation of C2×C28.48D4 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 1 0 0 0 0 0 0 1
,
 21 0 0 0 0 0 18 18 0 0 0 0 0 0 10 0 0 0 0 0 15 3 0 0 0 0 0 0 9 0 0 0 0 0 15 13
,
 14 17 0 0 0 0 9 15 0 0 0 0 0 0 11 20 0 0 0 0 23 18 0 0 0 0 0 0 21 23 0 0 0 0 6 8
,
 14 17 0 0 0 0 14 15 0 0 0 0 0 0 18 9 0 0 0 0 9 11 0 0 0 0 0 0 8 6 0 0 0 0 4 21

G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[21,18,0,0,0,0,0,18,0,0,0,0,0,0,10,15,0,0,0,0,0,3,0,0,0,0,0,0,9,15,0,0,0,0,0,13],[14,9,0,0,0,0,17,15,0,0,0,0,0,0,11,23,0,0,0,0,20,18,0,0,0,0,0,0,21,6,0,0,0,0,23,8],[14,14,0,0,0,0,17,15,0,0,0,0,0,0,18,9,0,0,0,0,9,11,0,0,0,0,0,0,8,4,0,0,0,0,6,21] >;

C2×C28.48D4 in GAP, Magma, Sage, TeX

C_2\times C_{28}._{48}D_4
% in TeX

G:=Group("C2xC28.48D4");
// GroupNames label

G:=SmallGroup(448,1237);
// by ID

G=gap.SmallGroup(448,1237);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,184,675,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^28=c^4=1,d^2=b^14,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^14*c^-1>;
// generators/relations

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