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G = C14×C4⋊1D4  order 448 = 26·7

Direct product of C14 and C4⋊1D4

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: C14×C4⋊1D4, C4⋊1(D4×C14), (C2×C28)⋊33D4, C28⋊12(C2×D4), C42⋊18(C2×C14), (C2×C42)⋊11C14, (C4×C28)⋊59C22, (C22×D4)⋊5C14, (D4×C14)⋊63C22, C24.18(C2×C14), C22.63(D4×C14), (C2×C14).350C24, (C2×C28).961C23, C14.186(C22×D4), C23.8(C22×C14), C22.24(C23×C14), (C23×C14).15C22, (C22×C14).88C23, (C22×C28).596C22, (C2×C4×C28)⋊24C2, (C2×C4)⋊7(C7×D4), (D4×C2×C14)⋊20C2, C2.10(D4×C2×C14), (C2×D4)⋊11(C2×C14), (C2×C14).684(C2×D4), (C2×C4).136(C22×C14), (C22×C4).124(C2×C14), SmallGroup(448,1313)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C22 — C14×C4⋊1D4
Chief series
C1 — C2 — C22 — C2×C14 — C22×C14 — D4×C14 — C7×C4⋊1D4 — C14×C4⋊1D4
Lower central
C1 — C22 — C14×C4⋊1D4
Upper central
C1 — C22×C14 — C14×C4⋊1D4

Subgroups: 882 in 498 conjugacy classes, 210 normal (10 characteristic)
C1, C2 [×7], C2 [×8], C4 [×12], C22, C22 [×6], C22 [×40], C7, C2×C4 [×18], D4 [×48], C23, C23 [×8], C23 [×24], C14 [×7], C14 [×8], C42 [×4], C22×C4 [×3], C2×D4 [×24], C2×D4 [×24], C24 [×4], C28 [×12], C2×C14, C2×C14 [×6], C2×C14 [×40], C2×C42, C4⋊1D4 [×8], C22×D4 [×6], C2×C28 [×18], C7×D4 [×48], C22×C14, C22×C14 [×8], C22×C14 [×24], C2×C4⋊1D4, C4×C28 [×4], C22×C28 [×3], D4×C14 [×24], D4×C14 [×24], C23×C14 [×4], C2×C4×C28, C7×C4⋊1D4 [×8], D4×C2×C14 [×6], C14×C4⋊1D4

Quotients:
C1, C2 [×15], C22 [×35], C7, D4 [×12], C23 [×15], C14 [×15], C2×D4 [×18], C24, C2×C14 [×35], C4⋊1D4 [×4], C22×D4 [×3], C7×D4 [×12], C22×C14 [×15], C2×C4⋊1D4, D4×C14 [×18], C23×C14, C7×C4⋊1D4 [×4], D4×C2×C14 [×3], C14×C4⋊1D4

Generators and relations
 G = < a,b,c,d | a14=b4=c4=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >

Smallest permutation representation
►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)

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

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

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

Matrix representation ►G ⊆ GL6(𝔽29)

600000
060000
007000
000700
0000130
0000013
,
120000
28280000
0028200
0028100
0000280
0000028
,
2800000
0280000
001000
000100
000012
00002828
,
28270000
010000
0012700
0002800
00002827
000001

G:=sub<GL(6,GF(29))| [6,0,0,0,0,0,0,6,0,0,0,0,0,0,7,0,0,0,0,0,0,7,0,0,0,0,0,0,13,0,0,0,0,0,0,13],[1,28,0,0,0,0,2,28,0,0,0,0,0,0,28,28,0,0,0,0,2,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,28,0,0,0,0,2,28],[28,0,0,0,0,0,27,1,0,0,0,0,0,0,1,0,0,0,0,0,27,28,0,0,0,0,0,0,28,0,0,0,0,0,27,1] >;
 

196 conjugacy classes

class 1 2A···2G2H···2O4A···4L7A···7F14A···14AP14AQ···14CL28A···28BT
order12···22···24···47···714···1414···1428···28
size11···14···42···21···11···14···42···2

196 irreducible representations

dim1111111122
type+++++
imageC1C2C2C2C7C14C14C14D4C7×D4
kernelC14×C4⋊1D4C2×C4×C28C7×C4⋊1D4D4×C2×C14C2×C4⋊1D4C2×C42C4⋊1D4C22×D4C2×C28C2×C4
# reps11866648361272

In GAP, Magma, Sage, TeX 

C_{14}\times C_4\rtimes_1D_4
 
% in TeX
 
G:=Group("C14xC4:1D4");
 
// GroupNames label
 
G:=SmallGroup(448,1313);
 
// by ID
 
G=gap.SmallGroup(448,1313);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,792,4790,1192]);
 
// 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^-1,d*c*d=c^-1>;
 
// generators/relations
 

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