direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C28.53D4, M4(2).29D14, C23.12Dic14, C28.49(C4⋊C4), (C2×C28).27Q8, C28.440(C2×D4), (C2×C28).168D4, C14⋊2(C8.C4), C28.67(C22×C4), (C2×C4).36Dic14, (C22×C14).15Q8, C4.20(Dic7⋊C4), (C2×C28).414C23, (C22×C4).348D14, (C2×M4(2)).15D7, C22.3(C2×Dic14), (C14×M4(2)).26C2, C4.Dic7.40C22, C22.26(Dic7⋊C4), (C22×C28).182C22, (C7×M4(2)).32C22, (C2×C7⋊C8).9C4, C4.89(C2×C4×D7), C7⋊3(C2×C8.C4), C7⋊C8.20(C2×C4), C14.51(C2×C4⋊C4), (C2×C4).158(C4×D7), C4.130(C2×C7⋊D4), (C22×C7⋊C8).12C2, (C2×C14).10(C2×Q8), (C2×C14).53(C4⋊C4), (C2×C28).102(C2×C4), (C2×C7⋊C8).266C22, C2.18(C2×Dic7⋊C4), (C2×C4).277(C7⋊D4), (C2×C4).510(C22×D7), (C2×C4.Dic7).23C2, SmallGroup(448,657)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C28.53D4
G = < a,b,c,d | a2=b28=1, c4=b14, d2=b21, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b13, dcd-1=b14c3 >
Subgroups: 292 in 106 conjugacy classes, 63 normal (41 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C8, C2×C4, C23, C14, C14, C14, C2×C8, M4(2), M4(2), C22×C4, C28, C2×C14, C2×C14, C8.C4, C22×C8, C2×M4(2), C2×M4(2), C7⋊C8, C7⋊C8, C56, C2×C28, C22×C14, C2×C8.C4, C2×C7⋊C8, C2×C7⋊C8, C2×C7⋊C8, C4.Dic7, C4.Dic7, C2×C56, C7×M4(2), C7×M4(2), C22×C28, C28.53D4, C22×C7⋊C8, C2×C4.Dic7, C14×M4(2), C2×C28.53D4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, D14, C8.C4, C2×C4⋊C4, Dic14, C4×D7, C7⋊D4, C22×D7, C2×C8.C4, Dic7⋊C4, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C28.53D4, C2×Dic7⋊C4, C2×C28.53D4
►On 224 points
Generators in S224
(1 190)(2 191)(3 192)(4 193)(5 194)(6 195)(7 196)(8 169)(9 170)(10 171)(11 172)(12 173)(13 174)(14 175)(15 176)(16 177)(17 178)(18 179)(19 180)(20 181)(21 182)(22 183)(23 184)(24 185)(25 186)(26 187)(27 188)(28 189)(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)(57 152)(58 153)(59 154)(60 155)(61 156)(62 157)(63 158)(64 159)(65 160)(66 161)(67 162)(68 163)(69 164)(70 165)(71 166)(72 167)(73 168)(74 141)(75 142)(76 143)(77 144)(78 145)(79 146)(80 147)(81 148)(82 149)(83 150)(84 151)(85 198)(86 199)(87 200)(88 201)(89 202)(90 203)(91 204)(92 205)(93 206)(94 207)(95 208)(96 209)(97 210)(98 211)(99 212)(100 213)(101 214)(102 215)(103 216)(104 217)(105 218)(106 219)(107 220)(108 221)(109 222)(110 223)(111 224)(112 197)
(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 45 169 121 15 31 183 135)(2 30 170 134 16 44 184 120)(3 43 171 119 17 29 185 133)(4 56 172 132 18 42 186 118)(5 41 173 117 19 55 187 131)(6 54 174 130 20 40 188 116)(7 39 175 115 21 53 189 129)(8 52 176 128 22 38 190 114)(9 37 177 113 23 51 191 127)(10 50 178 126 24 36 192 140)(11 35 179 139 25 49 193 125)(12 48 180 124 26 34 194 138)(13 33 181 137 27 47 195 123)(14 46 182 122 28 32 196 136)(57 208 145 88 71 222 159 102)(58 221 146 101 72 207 160 87)(59 206 147 86 73 220 161 100)(60 219 148 99 74 205 162 85)(61 204 149 112 75 218 163 98)(62 217 150 97 76 203 164 111)(63 202 151 110 77 216 165 96)(64 215 152 95 78 201 166 109)(65 200 153 108 79 214 167 94)(66 213 154 93 80 199 168 107)(67 198 155 106 81 212 141 92)(68 211 156 91 82 197 142 105)(69 224 157 104 83 210 143 90)(70 209 158 89 84 223 144 103)
(1 208 22 201 15 222 8 215)(2 221 23 214 16 207 9 200)(3 206 24 199 17 220 10 213)(4 219 25 212 18 205 11 198)(5 204 26 197 19 218 12 211)(6 217 27 210 20 203 13 224)(7 202 28 223 21 216 14 209)(29 73 50 66 43 59 36 80)(30 58 51 79 44 72 37 65)(31 71 52 64 45 57 38 78)(32 84 53 77 46 70 39 63)(33 69 54 62 47 83 40 76)(34 82 55 75 48 68 41 61)(35 67 56 60 49 81 42 74)(85 193 106 186 99 179 92 172)(86 178 107 171 100 192 93 185)(87 191 108 184 101 177 94 170)(88 176 109 169 102 190 95 183)(89 189 110 182 103 175 96 196)(90 174 111 195 104 188 97 181)(91 187 112 180 105 173 98 194)(113 167 134 160 127 153 120 146)(114 152 135 145 128 166 121 159)(115 165 136 158 129 151 122 144)(116 150 137 143 130 164 123 157)(117 163 138 156 131 149 124 142)(118 148 139 141 132 162 125 155)(119 161 140 154 133 147 126 168)
G:=sub<Sym(224)| (1,190)(2,191)(3,192)(4,193)(5,194)(6,195)(7,196)(8,169)(9,170)(10,171)(11,172)(12,173)(13,174)(14,175)(15,176)(16,177)(17,178)(18,179)(19,180)(20,181)(21,182)(22,183)(23,184)(24,185)(25,186)(26,187)(27,188)(28,189)(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)(57,152)(58,153)(59,154)(60,155)(61,156)(62,157)(63,158)(64,159)(65,160)(66,161)(67,162)(68,163)(69,164)(70,165)(71,166)(72,167)(73,168)(74,141)(75,142)(76,143)(77,144)(78,145)(79,146)(80,147)(81,148)(82,149)(83,150)(84,151)(85,198)(86,199)(87,200)(88,201)(89,202)(90,203)(91,204)(92,205)(93,206)(94,207)(95,208)(96,209)(97,210)(98,211)(99,212)(100,213)(101,214)(102,215)(103,216)(104,217)(105,218)(106,219)(107,220)(108,221)(109,222)(110,223)(111,224)(112,197), (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), (1,45,169,121,15,31,183,135)(2,30,170,134,16,44,184,120)(3,43,171,119,17,29,185,133)(4,56,172,132,18,42,186,118)(5,41,173,117,19,55,187,131)(6,54,174,130,20,40,188,116)(7,39,175,115,21,53,189,129)(8,52,176,128,22,38,190,114)(9,37,177,113,23,51,191,127)(10,50,178,126,24,36,192,140)(11,35,179,139,25,49,193,125)(12,48,180,124,26,34,194,138)(13,33,181,137,27,47,195,123)(14,46,182,122,28,32,196,136)(57,208,145,88,71,222,159,102)(58,221,146,101,72,207,160,87)(59,206,147,86,73,220,161,100)(60,219,148,99,74,205,162,85)(61,204,149,112,75,218,163,98)(62,217,150,97,76,203,164,111)(63,202,151,110,77,216,165,96)(64,215,152,95,78,201,166,109)(65,200,153,108,79,214,167,94)(66,213,154,93,80,199,168,107)(67,198,155,106,81,212,141,92)(68,211,156,91,82,197,142,105)(69,224,157,104,83,210,143,90)(70,209,158,89,84,223,144,103), (1,208,22,201,15,222,8,215)(2,221,23,214,16,207,9,200)(3,206,24,199,17,220,10,213)(4,219,25,212,18,205,11,198)(5,204,26,197,19,218,12,211)(6,217,27,210,20,203,13,224)(7,202,28,223,21,216,14,209)(29,73,50,66,43,59,36,80)(30,58,51,79,44,72,37,65)(31,71,52,64,45,57,38,78)(32,84,53,77,46,70,39,63)(33,69,54,62,47,83,40,76)(34,82,55,75,48,68,41,61)(35,67,56,60,49,81,42,74)(85,193,106,186,99,179,92,172)(86,178,107,171,100,192,93,185)(87,191,108,184,101,177,94,170)(88,176,109,169,102,190,95,183)(89,189,110,182,103,175,96,196)(90,174,111,195,104,188,97,181)(91,187,112,180,105,173,98,194)(113,167,134,160,127,153,120,146)(114,152,135,145,128,166,121,159)(115,165,136,158,129,151,122,144)(116,150,137,143,130,164,123,157)(117,163,138,156,131,149,124,142)(118,148,139,141,132,162,125,155)(119,161,140,154,133,147,126,168)>;
G:=Group( (1,190)(2,191)(3,192)(4,193)(5,194)(6,195)(7,196)(8,169)(9,170)(10,171)(11,172)(12,173)(13,174)(14,175)(15,176)(16,177)(17,178)(18,179)(19,180)(20,181)(21,182)(22,183)(23,184)(24,185)(25,186)(26,187)(27,188)(28,189)(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)(57,152)(58,153)(59,154)(60,155)(61,156)(62,157)(63,158)(64,159)(65,160)(66,161)(67,162)(68,163)(69,164)(70,165)(71,166)(72,167)(73,168)(74,141)(75,142)(76,143)(77,144)(78,145)(79,146)(80,147)(81,148)(82,149)(83,150)(84,151)(85,198)(86,199)(87,200)(88,201)(89,202)(90,203)(91,204)(92,205)(93,206)(94,207)(95,208)(96,209)(97,210)(98,211)(99,212)(100,213)(101,214)(102,215)(103,216)(104,217)(105,218)(106,219)(107,220)(108,221)(109,222)(110,223)(111,224)(112,197), (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), (1,45,169,121,15,31,183,135)(2,30,170,134,16,44,184,120)(3,43,171,119,17,29,185,133)(4,56,172,132,18,42,186,118)(5,41,173,117,19,55,187,131)(6,54,174,130,20,40,188,116)(7,39,175,115,21,53,189,129)(8,52,176,128,22,38,190,114)(9,37,177,113,23,51,191,127)(10,50,178,126,24,36,192,140)(11,35,179,139,25,49,193,125)(12,48,180,124,26,34,194,138)(13,33,181,137,27,47,195,123)(14,46,182,122,28,32,196,136)(57,208,145,88,71,222,159,102)(58,221,146,101,72,207,160,87)(59,206,147,86,73,220,161,100)(60,219,148,99,74,205,162,85)(61,204,149,112,75,218,163,98)(62,217,150,97,76,203,164,111)(63,202,151,110,77,216,165,96)(64,215,152,95,78,201,166,109)(65,200,153,108,79,214,167,94)(66,213,154,93,80,199,168,107)(67,198,155,106,81,212,141,92)(68,211,156,91,82,197,142,105)(69,224,157,104,83,210,143,90)(70,209,158,89,84,223,144,103), (1,208,22,201,15,222,8,215)(2,221,23,214,16,207,9,200)(3,206,24,199,17,220,10,213)(4,219,25,212,18,205,11,198)(5,204,26,197,19,218,12,211)(6,217,27,210,20,203,13,224)(7,202,28,223,21,216,14,209)(29,73,50,66,43,59,36,80)(30,58,51,79,44,72,37,65)(31,71,52,64,45,57,38,78)(32,84,53,77,46,70,39,63)(33,69,54,62,47,83,40,76)(34,82,55,75,48,68,41,61)(35,67,56,60,49,81,42,74)(85,193,106,186,99,179,92,172)(86,178,107,171,100,192,93,185)(87,191,108,184,101,177,94,170)(88,176,109,169,102,190,95,183)(89,189,110,182,103,175,96,196)(90,174,111,195,104,188,97,181)(91,187,112,180,105,173,98,194)(113,167,134,160,127,153,120,146)(114,152,135,145,128,166,121,159)(115,165,136,158,129,151,122,144)(116,150,137,143,130,164,123,157)(117,163,138,156,131,149,124,142)(118,148,139,141,132,162,125,155)(119,161,140,154,133,147,126,168) );
G=PermutationGroup([[(1,190),(2,191),(3,192),(4,193),(5,194),(6,195),(7,196),(8,169),(9,170),(10,171),(11,172),(12,173),(13,174),(14,175),(15,176),(16,177),(17,178),(18,179),(19,180),(20,181),(21,182),(22,183),(23,184),(24,185),(25,186),(26,187),(27,188),(28,189),(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),(57,152),(58,153),(59,154),(60,155),(61,156),(62,157),(63,158),(64,159),(65,160),(66,161),(67,162),(68,163),(69,164),(70,165),(71,166),(72,167),(73,168),(74,141),(75,142),(76,143),(77,144),(78,145),(79,146),(80,147),(81,148),(82,149),(83,150),(84,151),(85,198),(86,199),(87,200),(88,201),(89,202),(90,203),(91,204),(92,205),(93,206),(94,207),(95,208),(96,209),(97,210),(98,211),(99,212),(100,213),(101,214),(102,215),(103,216),(104,217),(105,218),(106,219),(107,220),(108,221),(109,222),(110,223),(111,224),(112,197)], [(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)], [(1,45,169,121,15,31,183,135),(2,30,170,134,16,44,184,120),(3,43,171,119,17,29,185,133),(4,56,172,132,18,42,186,118),(5,41,173,117,19,55,187,131),(6,54,174,130,20,40,188,116),(7,39,175,115,21,53,189,129),(8,52,176,128,22,38,190,114),(9,37,177,113,23,51,191,127),(10,50,178,126,24,36,192,140),(11,35,179,139,25,49,193,125),(12,48,180,124,26,34,194,138),(13,33,181,137,27,47,195,123),(14,46,182,122,28,32,196,136),(57,208,145,88,71,222,159,102),(58,221,146,101,72,207,160,87),(59,206,147,86,73,220,161,100),(60,219,148,99,74,205,162,85),(61,204,149,112,75,218,163,98),(62,217,150,97,76,203,164,111),(63,202,151,110,77,216,165,96),(64,215,152,95,78,201,166,109),(65,200,153,108,79,214,167,94),(66,213,154,93,80,199,168,107),(67,198,155,106,81,212,141,92),(68,211,156,91,82,197,142,105),(69,224,157,104,83,210,143,90),(70,209,158,89,84,223,144,103)], [(1,208,22,201,15,222,8,215),(2,221,23,214,16,207,9,200),(3,206,24,199,17,220,10,213),(4,219,25,212,18,205,11,198),(5,204,26,197,19,218,12,211),(6,217,27,210,20,203,13,224),(7,202,28,223,21,216,14,209),(29,73,50,66,43,59,36,80),(30,58,51,79,44,72,37,65),(31,71,52,64,45,57,38,78),(32,84,53,77,46,70,39,63),(33,69,54,62,47,83,40,76),(34,82,55,75,48,68,41,61),(35,67,56,60,49,81,42,74),(85,193,106,186,99,179,92,172),(86,178,107,171,100,192,93,185),(87,191,108,184,101,177,94,170),(88,176,109,169,102,190,95,183),(89,189,110,182,103,175,96,196),(90,174,111,195,104,188,97,181),(91,187,112,180,105,173,98,194),(113,167,134,160,127,153,120,146),(114,152,135,145,128,166,121,159),(115,165,136,158,129,151,122,144),(116,150,137,143,130,164,123,157),(117,163,138,156,131,149,124,142),(118,148,139,141,132,162,125,155),(119,161,140,154,133,147,126,168)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | ··· | 8L | 8M | 8N | 8O | 8P | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28R | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | - | - | + | + | + | - | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | Q8 | Q8 | D7 | D14 | D14 | C8.C4 | Dic14 | C4×D7 | C7⋊D4 | Dic14 | C28.53D4 |
| kernel | C2×C28.53D4 | C28.53D4 | C22×C7⋊C8 | C2×C4.Dic7 | C14×M4(2) | C2×C7⋊C8 | C2×C28 | C2×C28 | C22×C14 | C2×M4(2) | M4(2) | C22×C4 | C14 | C2×C4 | C2×C4 | C2×C4 | C23 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 2 | 1 | 1 | 3 | 6 | 3 | 8 | 6 | 12 | 12 | 6 | 12 |
Matrix representation of C2×C28.53D4 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 80 | 104 | 0 | 0 |
| 9 | 112 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 46 | 93 | 0 | 0 |
| 55 | 67 | 0 | 0 |
| 0 | 0 | 95 | 70 |
| 0 | 0 | 0 | 69 |
| 82 | 6 | 0 | 0 |
| 66 | 31 | 0 | 0 |
| 0 | 0 | 101 | 23 |
| 0 | 0 | 111 | 12 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,112,0,0,0,0,112],[80,9,0,0,104,112,0,0,0,0,98,0,0,0,0,98],[46,55,0,0,93,67,0,0,0,0,95,0,0,0,70,69],[82,66,0,0,6,31,0,0,0,0,101,111,0,0,23,12] >;
C2×C28.53D4 in GAP, Magma, Sage, TeX
C_2\times C_{28}._{53}D_4 % in TeX
G:=Group("C2xC28.53D4"); // GroupNames label
G:=SmallGroup(448,657);
// by ID
G=gap.SmallGroup(448,657);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,422,58,136,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=1,c^4=b^14,d^2=b^21,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^13,d*c*d^-1=b^14*c^3>;
// generators/relations