direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C28.17D4, C24.37D14, C28.251(C2×D4), (C2×C28).209D4, (C2×D4).229D14, C14⋊3(C4.4D4), (C22×D4).11D7, (C2×C14).292C24, (C2×C28).540C23, (C4×Dic7)⋊67C22, (C22×C4).378D14, C14.140(C22×D4), C23.D7⋊58C22, (C22×Dic14)⋊20C2, (C2×Dic14)⋊67C22, (D4×C14).269C22, (C23×C14).74C22, C23.134(C22×D7), C22.306(C23×D7), C22.78(D4⋊2D7), (C22×C28).273C22, (C22×C14).228C23, (C2×Dic7).282C23, (C22×Dic7).231C22, (D4×C2×C14).8C2, C7⋊4(C2×C4.4D4), (C2×C4×Dic7)⋊11C2, C4.23(C2×C7⋊D4), C14.104(C2×C4○D4), (C2×C14).579(C2×D4), C2.68(C2×D4⋊2D7), (C2×C23.D7)⋊25C2, C2.13(C22×C7⋊D4), (C2×C4).153(C7⋊D4), (C2×C4).623(C22×D7), C22.109(C2×C7⋊D4), (C2×C14).176(C4○D4), SmallGroup(448,1250)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1172 in 330 conjugacy classes, 127 normal (15 characteristic)
C1, C2, C2 [×6], C2 [×4], C4 [×4], C4 [×8], C22, C22 [×6], C22 [×20], C7, C2×C4 [×6], C2×C4 [×16], D4 [×8], Q8 [×8], C23, C23 [×4], C23 [×12], C14, C14 [×6], C14 [×4], C42 [×4], C22⋊C4 [×16], C22×C4, C22×C4 [×4], C2×D4 [×4], C2×D4 [×4], C2×Q8 [×8], C24 [×2], Dic7 [×8], C28 [×4], C2×C14, C2×C14 [×6], C2×C14 [×20], C2×C42, C2×C22⋊C4 [×4], C4.4D4 [×8], C22×D4, C22×Q8, Dic14 [×8], C2×Dic7 [×8], C2×Dic7 [×8], C2×C28 [×6], C7×D4 [×8], C22×C14, C22×C14 [×4], C22×C14 [×12], C2×C4.4D4, C4×Dic7 [×4], C23.D7 [×16], C2×Dic14 [×4], C2×Dic14 [×4], C22×Dic7 [×4], C22×C28, D4×C14 [×4], D4×C14 [×4], C23×C14 [×2], C2×C4×Dic7, C28.17D4 [×8], C2×C23.D7 [×4], C22×Dic14, D4×C2×C14, C2×C28.17D4
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×4], C24, D14 [×7], C4.4D4 [×4], C22×D4, C2×C4○D4 [×2], C7⋊D4 [×4], C22×D7 [×7], C2×C4.4D4, D4⋊2D7 [×4], C2×C7⋊D4 [×6], C23×D7, C28.17D4 [×4], C2×D4⋊2D7 [×2], C22×C7⋊D4, C2×C28.17D4
Generators and relations
G = < a,b,c,d | a2=b28=c4=1, d2=b14, ab=ba, ac=ca, ad=da, cbc-1=b13, dbd-1=b-1, dcd-1=b14c-1 >
►On 224 points
Generators in S224
(1 143)(2 144)(3 145)(4 146)(5 147)(6 148)(7 149)(8 150)(9 151)(10 152)(11 153)(12 154)(13 155)(14 156)(15 157)(16 158)(17 159)(18 160)(19 161)(20 162)(21 163)(22 164)(23 165)(24 166)(25 167)(26 168)(27 141)(28 142)(29 175)(30 176)(31 177)(32 178)(33 179)(34 180)(35 181)(36 182)(37 183)(38 184)(39 185)(40 186)(41 187)(42 188)(43 189)(44 190)(45 191)(46 192)(47 193)(48 194)(49 195)(50 196)(51 169)(52 170)(53 171)(54 172)(55 173)(56 174)(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)(85 117)(86 118)(87 119)(88 120)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)(97 129)(98 130)(99 131)(100 132)(101 133)(102 134)(103 135)(104 136)(105 137)(106 138)(107 139)(108 140)(109 113)(110 114)(111 115)(112 116)
(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 90 173 73)(2 103 174 58)(3 88 175 71)(4 101 176 84)(5 86 177 69)(6 99 178 82)(7 112 179 67)(8 97 180 80)(9 110 181 65)(10 95 182 78)(11 108 183 63)(12 93 184 76)(13 106 185 61)(14 91 186 74)(15 104 187 59)(16 89 188 72)(17 102 189 57)(18 87 190 70)(19 100 191 83)(20 85 192 68)(21 98 193 81)(22 111 194 66)(23 96 195 79)(24 109 196 64)(25 94 169 77)(26 107 170 62)(27 92 171 75)(28 105 172 60)(29 221 145 120)(30 206 146 133)(31 219 147 118)(32 204 148 131)(33 217 149 116)(34 202 150 129)(35 215 151 114)(36 200 152 127)(37 213 153 140)(38 198 154 125)(39 211 155 138)(40 224 156 123)(41 209 157 136)(42 222 158 121)(43 207 159 134)(44 220 160 119)(45 205 161 132)(46 218 162 117)(47 203 163 130)(48 216 164 115)(49 201 165 128)(50 214 166 113)(51 199 167 126)(52 212 168 139)(53 197 141 124)(54 210 142 137)(55 223 143 122)(56 208 144 135)
(1 97 15 111)(2 96 16 110)(3 95 17 109)(4 94 18 108)(5 93 19 107)(6 92 20 106)(7 91 21 105)(8 90 22 104)(9 89 23 103)(10 88 24 102)(11 87 25 101)(12 86 26 100)(13 85 27 99)(14 112 28 98)(29 200 43 214)(30 199 44 213)(31 198 45 212)(32 197 46 211)(33 224 47 210)(34 223 48 209)(35 222 49 208)(36 221 50 207)(37 220 51 206)(38 219 52 205)(39 218 53 204)(40 217 54 203)(41 216 55 202)(42 215 56 201)(57 182 71 196)(58 181 72 195)(59 180 73 194)(60 179 74 193)(61 178 75 192)(62 177 76 191)(63 176 77 190)(64 175 78 189)(65 174 79 188)(66 173 80 187)(67 172 81 186)(68 171 82 185)(69 170 83 184)(70 169 84 183)(113 145 127 159)(114 144 128 158)(115 143 129 157)(116 142 130 156)(117 141 131 155)(118 168 132 154)(119 167 133 153)(120 166 134 152)(121 165 135 151)(122 164 136 150)(123 163 137 149)(124 162 138 148)(125 161 139 147)(126 160 140 146)
G:=sub<Sym(224)| (1,143)(2,144)(3,145)(4,146)(5,147)(6,148)(7,149)(8,150)(9,151)(10,152)(11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,159)(18,160)(19,161)(20,162)(21,163)(22,164)(23,165)(24,166)(25,167)(26,168)(27,141)(28,142)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(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)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,113)(110,114)(111,115)(112,116), (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), (1,90,173,73)(2,103,174,58)(3,88,175,71)(4,101,176,84)(5,86,177,69)(6,99,178,82)(7,112,179,67)(8,97,180,80)(9,110,181,65)(10,95,182,78)(11,108,183,63)(12,93,184,76)(13,106,185,61)(14,91,186,74)(15,104,187,59)(16,89,188,72)(17,102,189,57)(18,87,190,70)(19,100,191,83)(20,85,192,68)(21,98,193,81)(22,111,194,66)(23,96,195,79)(24,109,196,64)(25,94,169,77)(26,107,170,62)(27,92,171,75)(28,105,172,60)(29,221,145,120)(30,206,146,133)(31,219,147,118)(32,204,148,131)(33,217,149,116)(34,202,150,129)(35,215,151,114)(36,200,152,127)(37,213,153,140)(38,198,154,125)(39,211,155,138)(40,224,156,123)(41,209,157,136)(42,222,158,121)(43,207,159,134)(44,220,160,119)(45,205,161,132)(46,218,162,117)(47,203,163,130)(48,216,164,115)(49,201,165,128)(50,214,166,113)(51,199,167,126)(52,212,168,139)(53,197,141,124)(54,210,142,137)(55,223,143,122)(56,208,144,135), (1,97,15,111)(2,96,16,110)(3,95,17,109)(4,94,18,108)(5,93,19,107)(6,92,20,106)(7,91,21,105)(8,90,22,104)(9,89,23,103)(10,88,24,102)(11,87,25,101)(12,86,26,100)(13,85,27,99)(14,112,28,98)(29,200,43,214)(30,199,44,213)(31,198,45,212)(32,197,46,211)(33,224,47,210)(34,223,48,209)(35,222,49,208)(36,221,50,207)(37,220,51,206)(38,219,52,205)(39,218,53,204)(40,217,54,203)(41,216,55,202)(42,215,56,201)(57,182,71,196)(58,181,72,195)(59,180,73,194)(60,179,74,193)(61,178,75,192)(62,177,76,191)(63,176,77,190)(64,175,78,189)(65,174,79,188)(66,173,80,187)(67,172,81,186)(68,171,82,185)(69,170,83,184)(70,169,84,183)(113,145,127,159)(114,144,128,158)(115,143,129,157)(116,142,130,156)(117,141,131,155)(118,168,132,154)(119,167,133,153)(120,166,134,152)(121,165,135,151)(122,164,136,150)(123,163,137,149)(124,162,138,148)(125,161,139,147)(126,160,140,146)>;
G:=Group( (1,143)(2,144)(3,145)(4,146)(5,147)(6,148)(7,149)(8,150)(9,151)(10,152)(11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,159)(18,160)(19,161)(20,162)(21,163)(22,164)(23,165)(24,166)(25,167)(26,168)(27,141)(28,142)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(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)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,139)(108,140)(109,113)(110,114)(111,115)(112,116), (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), (1,90,173,73)(2,103,174,58)(3,88,175,71)(4,101,176,84)(5,86,177,69)(6,99,178,82)(7,112,179,67)(8,97,180,80)(9,110,181,65)(10,95,182,78)(11,108,183,63)(12,93,184,76)(13,106,185,61)(14,91,186,74)(15,104,187,59)(16,89,188,72)(17,102,189,57)(18,87,190,70)(19,100,191,83)(20,85,192,68)(21,98,193,81)(22,111,194,66)(23,96,195,79)(24,109,196,64)(25,94,169,77)(26,107,170,62)(27,92,171,75)(28,105,172,60)(29,221,145,120)(30,206,146,133)(31,219,147,118)(32,204,148,131)(33,217,149,116)(34,202,150,129)(35,215,151,114)(36,200,152,127)(37,213,153,140)(38,198,154,125)(39,211,155,138)(40,224,156,123)(41,209,157,136)(42,222,158,121)(43,207,159,134)(44,220,160,119)(45,205,161,132)(46,218,162,117)(47,203,163,130)(48,216,164,115)(49,201,165,128)(50,214,166,113)(51,199,167,126)(52,212,168,139)(53,197,141,124)(54,210,142,137)(55,223,143,122)(56,208,144,135), (1,97,15,111)(2,96,16,110)(3,95,17,109)(4,94,18,108)(5,93,19,107)(6,92,20,106)(7,91,21,105)(8,90,22,104)(9,89,23,103)(10,88,24,102)(11,87,25,101)(12,86,26,100)(13,85,27,99)(14,112,28,98)(29,200,43,214)(30,199,44,213)(31,198,45,212)(32,197,46,211)(33,224,47,210)(34,223,48,209)(35,222,49,208)(36,221,50,207)(37,220,51,206)(38,219,52,205)(39,218,53,204)(40,217,54,203)(41,216,55,202)(42,215,56,201)(57,182,71,196)(58,181,72,195)(59,180,73,194)(60,179,74,193)(61,178,75,192)(62,177,76,191)(63,176,77,190)(64,175,78,189)(65,174,79,188)(66,173,80,187)(67,172,81,186)(68,171,82,185)(69,170,83,184)(70,169,84,183)(113,145,127,159)(114,144,128,158)(115,143,129,157)(116,142,130,156)(117,141,131,155)(118,168,132,154)(119,167,133,153)(120,166,134,152)(121,165,135,151)(122,164,136,150)(123,163,137,149)(124,162,138,148)(125,161,139,147)(126,160,140,146) );
G=PermutationGroup([(1,143),(2,144),(3,145),(4,146),(5,147),(6,148),(7,149),(8,150),(9,151),(10,152),(11,153),(12,154),(13,155),(14,156),(15,157),(16,158),(17,159),(18,160),(19,161),(20,162),(21,163),(22,164),(23,165),(24,166),(25,167),(26,168),(27,141),(28,142),(29,175),(30,176),(31,177),(32,178),(33,179),(34,180),(35,181),(36,182),(37,183),(38,184),(39,185),(40,186),(41,187),(42,188),(43,189),(44,190),(45,191),(46,192),(47,193),(48,194),(49,195),(50,196),(51,169),(52,170),(53,171),(54,172),(55,173),(56,174),(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),(85,117),(86,118),(87,119),(88,120),(89,121),(90,122),(91,123),(92,124),(93,125),(94,126),(95,127),(96,128),(97,129),(98,130),(99,131),(100,132),(101,133),(102,134),(103,135),(104,136),(105,137),(106,138),(107,139),(108,140),(109,113),(110,114),(111,115),(112,116)], [(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)], [(1,90,173,73),(2,103,174,58),(3,88,175,71),(4,101,176,84),(5,86,177,69),(6,99,178,82),(7,112,179,67),(8,97,180,80),(9,110,181,65),(10,95,182,78),(11,108,183,63),(12,93,184,76),(13,106,185,61),(14,91,186,74),(15,104,187,59),(16,89,188,72),(17,102,189,57),(18,87,190,70),(19,100,191,83),(20,85,192,68),(21,98,193,81),(22,111,194,66),(23,96,195,79),(24,109,196,64),(25,94,169,77),(26,107,170,62),(27,92,171,75),(28,105,172,60),(29,221,145,120),(30,206,146,133),(31,219,147,118),(32,204,148,131),(33,217,149,116),(34,202,150,129),(35,215,151,114),(36,200,152,127),(37,213,153,140),(38,198,154,125),(39,211,155,138),(40,224,156,123),(41,209,157,136),(42,222,158,121),(43,207,159,134),(44,220,160,119),(45,205,161,132),(46,218,162,117),(47,203,163,130),(48,216,164,115),(49,201,165,128),(50,214,166,113),(51,199,167,126),(52,212,168,139),(53,197,141,124),(54,210,142,137),(55,223,143,122),(56,208,144,135)], [(1,97,15,111),(2,96,16,110),(3,95,17,109),(4,94,18,108),(5,93,19,107),(6,92,20,106),(7,91,21,105),(8,90,22,104),(9,89,23,103),(10,88,24,102),(11,87,25,101),(12,86,26,100),(13,85,27,99),(14,112,28,98),(29,200,43,214),(30,199,44,213),(31,198,45,212),(32,197,46,211),(33,224,47,210),(34,223,48,209),(35,222,49,208),(36,221,50,207),(37,220,51,206),(38,219,52,205),(39,218,53,204),(40,217,54,203),(41,216,55,202),(42,215,56,201),(57,182,71,196),(58,181,72,195),(59,180,73,194),(60,179,74,193),(61,178,75,192),(62,177,76,191),(63,176,77,190),(64,175,78,189),(65,174,79,188),(66,173,80,187),(67,172,81,186),(68,171,82,185),(69,170,83,184),(70,169,84,183),(113,145,127,159),(114,144,128,158),(115,143,129,157),(116,142,130,156),(117,141,131,155),(118,168,132,154),(119,167,133,153),(120,166,134,152),(121,165,135,151),(122,164,136,150),(123,163,137,149),(124,162,138,148),(125,161,139,147),(126,160,140,146)])
Matrix representation ►G ⊆ GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 24 | 27 | 0 | 0 |
| 0 | 0 | 23 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 0 | 27 | 28 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 4 | 0 | 0 |
| 0 | 14 | 1 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 17 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 14 | 1 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 5 | 17 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,24,0,0,0,0,27,23,0,0,0,0,0,1,27,0,0,0,1,28],[1,0,0,0,0,0,28,14,0,0,0,4,1,0,0,0,0,0,17,0,0,0,0,0,17],[28,0,0,0,0,0,28,14,0,0,0,0,1,0,0,0,0,0,12,5,0,0,0,0,17] >;
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 14V | ··· | 14AS | 28A | ··· | 28L |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | D4⋊2D7 |
| kernel | C2×C28.17D4 | C2×C4×Dic7 | C28.17D4 | C2×C23.D7 | C22×Dic14 | D4×C2×C14 | C2×C28 | C22×D4 | C2×C14 | C22×C4 | C2×D4 | C24 | C2×C4 | C22 |
| # reps | 1 | 1 | 8 | 4 | 1 | 1 | 4 | 3 | 8 | 3 | 12 | 6 | 24 | 12 |
In GAP, Magma, Sage, TeX
C_2\times C_{28}._{17}D_4 % in TeX
G:=Group("C2xC28.17D4"); // GroupNames label
G:=SmallGroup(448,1250);
// by ID
G=gap.SmallGroup(448,1250);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,1571,185,18822]);
// 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=b^13,d*b*d^-1=b^-1,d*c*d^-1=b^14*c^-1>;
// generators/relations
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