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G = (C2×C28).31D4order 448 = 26·7

5th non-split extension by C2×C28 of D4 acting via D4/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C2×C28).31D4, (C2×C4).20D28, (C22×D7)⋊1Q8, C14.6C22≀C2, C71(C23⋊Q8), C22.42(Q8×D7), (C2×Dic7).12D4, C22.157(D4×D7), (C22×C4).72D14, C22.82(C2×D28), C2.9(C22⋊D28), C14.C425C2, C2.8(D142Q8), C2.7(C4.D28), (C22×Dic14)⋊1C2, C2.C4212D7, C14.26(C22⋊Q8), (C23×D7).5C22, C2.10(D14⋊Q8), C14.20(C4.4D4), C22.90(C4○D28), (C22×C28).17C22, C23.361(C22×D7), C22.88(D42D7), (C22×C14).298C23, C2.10(Dic7.D4), (C22×Dic7).20C22, (C2×D14⋊C4).6C2, (C2×C14).69(C2×Q8), (C2×C14).206(C2×D4), (C2×C14).60(C4○D4), (C7×C2.C42)⋊10C2, SmallGroup(448,207)

Series: Derived Chief Lower central Upper central

C1C22×C14 — (C2×C28).31D4
C1C7C14C2×C14C22×C14C23×D7C2×D14⋊C4 — (C2×C28).31D4
C7C22×C14 — (C2×C28).31D4
C1C23C2.C42

Generators and relations for (C2×C28).31D4
 G = < a,b,c,d | a2=b28=c4=1, d2=b14, cbc-1=ab=ba, ac=ca, ad=da, dbd-1=b-1, dcd-1=b14c-1 >

Subgroups: 1148 in 202 conjugacy classes, 61 normal (25 characteristic)
C1, C2 [×3], C2 [×4], C2 [×2], C4 [×9], C22 [×3], C22 [×4], C22 [×10], C7, C2×C4 [×2], C2×C4 [×19], Q8 [×8], C23, C23 [×8], D7 [×2], C14 [×3], C14 [×4], C22⋊C4 [×6], C22×C4, C22×C4 [×2], C22×C4 [×3], C2×Q8 [×6], C24, Dic7 [×5], C28 [×4], D14 [×10], C2×C14 [×3], C2×C14 [×4], C2.C42, C2.C42 [×2], C2×C22⋊C4 [×3], C22×Q8, Dic14 [×8], C2×Dic7 [×4], C2×Dic7 [×7], C2×C28 [×2], C2×C28 [×8], C22×D7 [×2], C22×D7 [×6], C22×C14, C23⋊Q8, D14⋊C4 [×6], C2×Dic14 [×6], C22×Dic7, C22×Dic7 [×2], C22×C28, C22×C28 [×2], C23×D7, C14.C42 [×2], C7×C2.C42, C2×D14⋊C4, C2×D14⋊C4 [×2], C22×Dic14, (C2×C28).31D4
Quotients: C1, C2 [×7], C22 [×7], D4 [×6], Q8 [×2], C23, D7, C2×D4 [×3], C2×Q8, C4○D4 [×3], D14 [×3], C22≀C2, C22⋊Q8 [×3], C4.4D4 [×3], D28 [×2], C22×D7, C23⋊Q8, C2×D28, C4○D28 [×2], D4×D7 [×2], D42D7, Q8×D7, C4.D28, C22⋊D28, Dic7.D4 [×2], D14⋊Q8 [×2], D142Q8, (C2×C28).31D4

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

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

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

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

82 conjugacy classes

class 1 2A···2G2H2I4A···4F4G···4L7A7B7C14A···14U28A···28AJ
order12···2224···44···477714···1428···28
size11···128284···428···282222···24···4

82 irreducible representations

dim1111122222222444
type+++++++-++++--
imageC1C2C2C2C2D4D4Q8D7C4○D4D14D28C4○D28D4×D7D42D7Q8×D7
kernel(C2×C28).31D4C14.C42C7×C2.C42C2×D14⋊C4C22×Dic14C2×Dic7C2×C28C22×D7C2.C42C2×C14C22×C4C2×C4C22C22C22C22
# reps121314223691224633

Matrix representation of (C2×C28).31D4 in GL6(𝔽29)

100000
010000
001000
000100
0000280
0000028
,
26110000
2100000
00272400
0051200
0000170
0000212
,
2240000
1270000
0012000
0001200
00001618
00001013
,
1170000
16180000
0012000
0071700
00001311
0000316

G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[26,21,0,0,0,0,11,0,0,0,0,0,0,0,27,5,0,0,0,0,24,12,0,0,0,0,0,0,17,2,0,0,0,0,0,12],[2,1,0,0,0,0,24,27,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,16,10,0,0,0,0,18,13],[11,16,0,0,0,0,7,18,0,0,0,0,0,0,12,7,0,0,0,0,0,17,0,0,0,0,0,0,13,3,0,0,0,0,11,16] >;

(C2×C28).31D4 in GAP, Magma, Sage, TeX

(C_2\times C_{28})._{31}D_4
% in TeX

G:=Group("(C2xC28).31D4");
// GroupNames label

G:=SmallGroup(448,207);
// by ID

G=gap.SmallGroup(448,207);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,64,926,387,268,18822]);
// Polycyclic

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

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