direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C28⋊2D4, C24.39D14, C28⋊7(C2×D4), D14⋊4(C2×D4), (C2×C28)⋊12D4, (C2×D4)⋊36D14, (C22×D4)⋊6D7, C14⋊4(C4⋊D4), (C22×D7)⋊12D4, (D4×C14)⋊43C22, C4⋊Dic7⋊77C22, C22.147(D4×D7), (C2×C14).295C24, (C2×C28).542C23, (C22×C4).379D14, C14.142(C22×D4), C23.D7⋊61C22, (C23×C14).76C22, C22.308(C23×D7), C23.337(C22×D7), C22.79(D4⋊2D7), (C22×C28).275C22, (C22×C14).419C23, (C2×Dic7).152C23, (C22×D7).239C23, (C23×D7).113C22, (C22×Dic7).163C22, (D4×C2×C14)⋊4C2, C7⋊5(C2×C4⋊D4), C4⋊3(C2×C7⋊D4), C2.102(C2×D4×D7), (D7×C22×C4)⋊6C2, (C2×C4×D7)⋊57C22, (C2×C4)⋊13(C7⋊D4), (C2×C4⋊Dic7)⋊45C2, C14.105(C2×C4○D4), C2.69(C2×D4⋊2D7), (C2×C14).580(C2×D4), (C2×C7⋊D4)⋊44C22, (C22×C7⋊D4)⋊13C2, (C2×C23.D7)⋊28C2, C2.15(C22×C7⋊D4), (C2×C4).625(C22×D7), C22.110(C2×C7⋊D4), (C2×C14).177(C4○D4), SmallGroup(448,1253)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1876 in 426 conjugacy classes, 135 normal (21 characteristic)
C1, C2 [×3], C2 [×4], C2 [×8], C4 [×4], C4 [×6], C22, C22 [×6], C22 [×36], C7, C2×C4 [×6], C2×C4 [×20], D4 [×24], C23, C23 [×4], C23 [×22], D7 [×4], C14 [×3], C14 [×4], C14 [×4], C22⋊C4 [×8], C4⋊C4 [×4], C22×C4, C22×C4 [×11], C2×D4 [×4], C2×D4 [×20], C24 [×2], C24, Dic7 [×6], C28 [×4], D14 [×4], D14 [×12], C2×C14, C2×C14 [×6], C2×C14 [×20], C2×C22⋊C4 [×2], C2×C4⋊C4, C4⋊D4 [×8], C23×C4, C22×D4, C22×D4 [×2], C4×D7 [×8], C2×Dic7 [×6], C2×Dic7 [×6], C7⋊D4 [×16], C2×C28 [×6], C7×D4 [×8], C22×D7 [×6], C22×D7 [×4], C22×C14, C22×C14 [×4], C22×C14 [×12], C2×C4⋊D4, C4⋊Dic7 [×4], C23.D7 [×8], C2×C4×D7 [×4], C2×C4×D7 [×4], C22×Dic7, C22×Dic7 [×2], C2×C7⋊D4 [×8], C2×C7⋊D4 [×8], C22×C28, D4×C14 [×4], D4×C14 [×4], C23×D7, C23×C14 [×2], C2×C4⋊Dic7, C28⋊2D4 [×8], C2×C23.D7 [×2], D7×C22×C4, C22×C7⋊D4 [×2], D4×C2×C14, C2×C28⋊2D4
Quotients:
C1, C2 [×15], C22 [×35], D4 [×8], C23 [×15], D7, C2×D4 [×12], C4○D4 [×2], C24, D14 [×7], C4⋊D4 [×4], C22×D4 [×2], C2×C4○D4, C7⋊D4 [×4], C22×D7 [×7], C2×C4⋊D4, D4×D7 [×2], D4⋊2D7 [×2], C2×C7⋊D4 [×6], C23×D7, C28⋊2D4 [×4], C2×D4×D7, C2×D4⋊2D7, C22×C7⋊D4, C2×C28⋊2D4
Generators and relations
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd=b13, dcd=c-1 >
►On 224 points
Generators in S224
(1 188)(2 189)(3 190)(4 191)(5 192)(6 193)(7 194)(8 195)(9 196)(10 169)(11 170)(12 171)(13 172)(14 173)(15 174)(16 175)(17 176)(18 177)(19 178)(20 179)(21 180)(22 181)(23 182)(24 183)(25 184)(26 185)(27 186)(28 187)(29 147)(30 148)(31 149)(32 150)(33 151)(34 152)(35 153)(36 154)(37 155)(38 156)(39 157)(40 158)(41 159)(42 160)(43 161)(44 162)(45 163)(46 164)(47 165)(48 166)(49 167)(50 168)(51 141)(52 142)(53 143)(54 144)(55 145)(56 146)(57 224)(58 197)(59 198)(60 199)(61 200)(62 201)(63 202)(64 203)(65 204)(66 205)(67 206)(68 207)(69 208)(70 209)(71 210)(72 211)(73 212)(74 213)(75 214)(76 215)(77 216)(78 217)(79 218)(80 219)(81 220)(82 221)(83 222)(84 223)(85 116)(86 117)(87 118)(88 119)(89 120)(90 121)(91 122)(92 123)(93 124)(94 125)(95 126)(96 127)(97 128)(98 129)(99 130)(100 131)(101 132)(102 133)(103 134)(104 135)(105 136)(106 137)(107 138)(108 139)(109 140)(110 113)(111 114)(112 115)
(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 60 150 107)(2 59 151 106)(3 58 152 105)(4 57 153 104)(5 84 154 103)(6 83 155 102)(7 82 156 101)(8 81 157 100)(9 80 158 99)(10 79 159 98)(11 78 160 97)(12 77 161 96)(13 76 162 95)(14 75 163 94)(15 74 164 93)(16 73 165 92)(17 72 166 91)(18 71 167 90)(19 70 168 89)(20 69 141 88)(21 68 142 87)(22 67 143 86)(23 66 144 85)(24 65 145 112)(25 64 146 111)(26 63 147 110)(27 62 148 109)(28 61 149 108)(29 113 185 202)(30 140 186 201)(31 139 187 200)(32 138 188 199)(33 137 189 198)(34 136 190 197)(35 135 191 224)(36 134 192 223)(37 133 193 222)(38 132 194 221)(39 131 195 220)(40 130 196 219)(41 129 169 218)(42 128 170 217)(43 127 171 216)(44 126 172 215)(45 125 173 214)(46 124 174 213)(47 123 175 212)(48 122 176 211)(49 121 177 210)(50 120 178 209)(51 119 179 208)(52 118 180 207)(53 117 181 206)(54 116 182 205)(55 115 183 204)(56 114 184 203)
(1 188)(2 173)(3 186)(4 171)(5 184)(6 169)(7 182)(8 195)(9 180)(10 193)(11 178)(12 191)(13 176)(14 189)(15 174)(16 187)(17 172)(18 185)(19 170)(20 183)(21 196)(22 181)(23 194)(24 179)(25 192)(26 177)(27 190)(28 175)(29 167)(30 152)(31 165)(32 150)(33 163)(34 148)(35 161)(36 146)(37 159)(38 144)(39 157)(40 142)(41 155)(42 168)(43 153)(44 166)(45 151)(46 164)(47 149)(48 162)(49 147)(50 160)(51 145)(52 158)(53 143)(54 156)(55 141)(56 154)(57 127)(58 140)(59 125)(60 138)(61 123)(62 136)(63 121)(64 134)(65 119)(66 132)(67 117)(68 130)(69 115)(70 128)(71 113)(72 126)(73 139)(74 124)(75 137)(76 122)(77 135)(78 120)(79 133)(80 118)(81 131)(82 116)(83 129)(84 114)(85 221)(86 206)(87 219)(88 204)(89 217)(90 202)(91 215)(92 200)(93 213)(94 198)(95 211)(96 224)(97 209)(98 222)(99 207)(100 220)(101 205)(102 218)(103 203)(104 216)(105 201)(106 214)(107 199)(108 212)(109 197)(110 210)(111 223)(112 208)
G:=sub<Sym(224)| (1,188)(2,189)(3,190)(4,191)(5,192)(6,193)(7,194)(8,195)(9,196)(10,169)(11,170)(12,171)(13,172)(14,173)(15,174)(16,175)(17,176)(18,177)(19,178)(20,179)(21,180)(22,181)(23,182)(24,183)(25,184)(26,185)(27,186)(28,187)(29,147)(30,148)(31,149)(32,150)(33,151)(34,152)(35,153)(36,154)(37,155)(38,156)(39,157)(40,158)(41,159)(42,160)(43,161)(44,162)(45,163)(46,164)(47,165)(48,166)(49,167)(50,168)(51,141)(52,142)(53,143)(54,144)(55,145)(56,146)(57,224)(58,197)(59,198)(60,199)(61,200)(62,201)(63,202)(64,203)(65,204)(66,205)(67,206)(68,207)(69,208)(70,209)(71,210)(72,211)(73,212)(74,213)(75,214)(76,215)(77,216)(78,217)(79,218)(80,219)(81,220)(82,221)(83,222)(84,223)(85,116)(86,117)(87,118)(88,119)(89,120)(90,121)(91,122)(92,123)(93,124)(94,125)(95,126)(96,127)(97,128)(98,129)(99,130)(100,131)(101,132)(102,133)(103,134)(104,135)(105,136)(106,137)(107,138)(108,139)(109,140)(110,113)(111,114)(112,115), (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), (1,60,150,107)(2,59,151,106)(3,58,152,105)(4,57,153,104)(5,84,154,103)(6,83,155,102)(7,82,156,101)(8,81,157,100)(9,80,158,99)(10,79,159,98)(11,78,160,97)(12,77,161,96)(13,76,162,95)(14,75,163,94)(15,74,164,93)(16,73,165,92)(17,72,166,91)(18,71,167,90)(19,70,168,89)(20,69,141,88)(21,68,142,87)(22,67,143,86)(23,66,144,85)(24,65,145,112)(25,64,146,111)(26,63,147,110)(27,62,148,109)(28,61,149,108)(29,113,185,202)(30,140,186,201)(31,139,187,200)(32,138,188,199)(33,137,189,198)(34,136,190,197)(35,135,191,224)(36,134,192,223)(37,133,193,222)(38,132,194,221)(39,131,195,220)(40,130,196,219)(41,129,169,218)(42,128,170,217)(43,127,171,216)(44,126,172,215)(45,125,173,214)(46,124,174,213)(47,123,175,212)(48,122,176,211)(49,121,177,210)(50,120,178,209)(51,119,179,208)(52,118,180,207)(53,117,181,206)(54,116,182,205)(55,115,183,204)(56,114,184,203), (1,188)(2,173)(3,186)(4,171)(5,184)(6,169)(7,182)(8,195)(9,180)(10,193)(11,178)(12,191)(13,176)(14,189)(15,174)(16,187)(17,172)(18,185)(19,170)(20,183)(21,196)(22,181)(23,194)(24,179)(25,192)(26,177)(27,190)(28,175)(29,167)(30,152)(31,165)(32,150)(33,163)(34,148)(35,161)(36,146)(37,159)(38,144)(39,157)(40,142)(41,155)(42,168)(43,153)(44,166)(45,151)(46,164)(47,149)(48,162)(49,147)(50,160)(51,145)(52,158)(53,143)(54,156)(55,141)(56,154)(57,127)(58,140)(59,125)(60,138)(61,123)(62,136)(63,121)(64,134)(65,119)(66,132)(67,117)(68,130)(69,115)(70,128)(71,113)(72,126)(73,139)(74,124)(75,137)(76,122)(77,135)(78,120)(79,133)(80,118)(81,131)(82,116)(83,129)(84,114)(85,221)(86,206)(87,219)(88,204)(89,217)(90,202)(91,215)(92,200)(93,213)(94,198)(95,211)(96,224)(97,209)(98,222)(99,207)(100,220)(101,205)(102,218)(103,203)(104,216)(105,201)(106,214)(107,199)(108,212)(109,197)(110,210)(111,223)(112,208)>;
G:=Group( (1,188)(2,189)(3,190)(4,191)(5,192)(6,193)(7,194)(8,195)(9,196)(10,169)(11,170)(12,171)(13,172)(14,173)(15,174)(16,175)(17,176)(18,177)(19,178)(20,179)(21,180)(22,181)(23,182)(24,183)(25,184)(26,185)(27,186)(28,187)(29,147)(30,148)(31,149)(32,150)(33,151)(34,152)(35,153)(36,154)(37,155)(38,156)(39,157)(40,158)(41,159)(42,160)(43,161)(44,162)(45,163)(46,164)(47,165)(48,166)(49,167)(50,168)(51,141)(52,142)(53,143)(54,144)(55,145)(56,146)(57,224)(58,197)(59,198)(60,199)(61,200)(62,201)(63,202)(64,203)(65,204)(66,205)(67,206)(68,207)(69,208)(70,209)(71,210)(72,211)(73,212)(74,213)(75,214)(76,215)(77,216)(78,217)(79,218)(80,219)(81,220)(82,221)(83,222)(84,223)(85,116)(86,117)(87,118)(88,119)(89,120)(90,121)(91,122)(92,123)(93,124)(94,125)(95,126)(96,127)(97,128)(98,129)(99,130)(100,131)(101,132)(102,133)(103,134)(104,135)(105,136)(106,137)(107,138)(108,139)(109,140)(110,113)(111,114)(112,115), (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), (1,60,150,107)(2,59,151,106)(3,58,152,105)(4,57,153,104)(5,84,154,103)(6,83,155,102)(7,82,156,101)(8,81,157,100)(9,80,158,99)(10,79,159,98)(11,78,160,97)(12,77,161,96)(13,76,162,95)(14,75,163,94)(15,74,164,93)(16,73,165,92)(17,72,166,91)(18,71,167,90)(19,70,168,89)(20,69,141,88)(21,68,142,87)(22,67,143,86)(23,66,144,85)(24,65,145,112)(25,64,146,111)(26,63,147,110)(27,62,148,109)(28,61,149,108)(29,113,185,202)(30,140,186,201)(31,139,187,200)(32,138,188,199)(33,137,189,198)(34,136,190,197)(35,135,191,224)(36,134,192,223)(37,133,193,222)(38,132,194,221)(39,131,195,220)(40,130,196,219)(41,129,169,218)(42,128,170,217)(43,127,171,216)(44,126,172,215)(45,125,173,214)(46,124,174,213)(47,123,175,212)(48,122,176,211)(49,121,177,210)(50,120,178,209)(51,119,179,208)(52,118,180,207)(53,117,181,206)(54,116,182,205)(55,115,183,204)(56,114,184,203), (1,188)(2,173)(3,186)(4,171)(5,184)(6,169)(7,182)(8,195)(9,180)(10,193)(11,178)(12,191)(13,176)(14,189)(15,174)(16,187)(17,172)(18,185)(19,170)(20,183)(21,196)(22,181)(23,194)(24,179)(25,192)(26,177)(27,190)(28,175)(29,167)(30,152)(31,165)(32,150)(33,163)(34,148)(35,161)(36,146)(37,159)(38,144)(39,157)(40,142)(41,155)(42,168)(43,153)(44,166)(45,151)(46,164)(47,149)(48,162)(49,147)(50,160)(51,145)(52,158)(53,143)(54,156)(55,141)(56,154)(57,127)(58,140)(59,125)(60,138)(61,123)(62,136)(63,121)(64,134)(65,119)(66,132)(67,117)(68,130)(69,115)(70,128)(71,113)(72,126)(73,139)(74,124)(75,137)(76,122)(77,135)(78,120)(79,133)(80,118)(81,131)(82,116)(83,129)(84,114)(85,221)(86,206)(87,219)(88,204)(89,217)(90,202)(91,215)(92,200)(93,213)(94,198)(95,211)(96,224)(97,209)(98,222)(99,207)(100,220)(101,205)(102,218)(103,203)(104,216)(105,201)(106,214)(107,199)(108,212)(109,197)(110,210)(111,223)(112,208) );
G=PermutationGroup([(1,188),(2,189),(3,190),(4,191),(5,192),(6,193),(7,194),(8,195),(9,196),(10,169),(11,170),(12,171),(13,172),(14,173),(15,174),(16,175),(17,176),(18,177),(19,178),(20,179),(21,180),(22,181),(23,182),(24,183),(25,184),(26,185),(27,186),(28,187),(29,147),(30,148),(31,149),(32,150),(33,151),(34,152),(35,153),(36,154),(37,155),(38,156),(39,157),(40,158),(41,159),(42,160),(43,161),(44,162),(45,163),(46,164),(47,165),(48,166),(49,167),(50,168),(51,141),(52,142),(53,143),(54,144),(55,145),(56,146),(57,224),(58,197),(59,198),(60,199),(61,200),(62,201),(63,202),(64,203),(65,204),(66,205),(67,206),(68,207),(69,208),(70,209),(71,210),(72,211),(73,212),(74,213),(75,214),(76,215),(77,216),(78,217),(79,218),(80,219),(81,220),(82,221),(83,222),(84,223),(85,116),(86,117),(87,118),(88,119),(89,120),(90,121),(91,122),(92,123),(93,124),(94,125),(95,126),(96,127),(97,128),(98,129),(99,130),(100,131),(101,132),(102,133),(103,134),(104,135),(105,136),(106,137),(107,138),(108,139),(109,140),(110,113),(111,114),(112,115)], [(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)], [(1,60,150,107),(2,59,151,106),(3,58,152,105),(4,57,153,104),(5,84,154,103),(6,83,155,102),(7,82,156,101),(8,81,157,100),(9,80,158,99),(10,79,159,98),(11,78,160,97),(12,77,161,96),(13,76,162,95),(14,75,163,94),(15,74,164,93),(16,73,165,92),(17,72,166,91),(18,71,167,90),(19,70,168,89),(20,69,141,88),(21,68,142,87),(22,67,143,86),(23,66,144,85),(24,65,145,112),(25,64,146,111),(26,63,147,110),(27,62,148,109),(28,61,149,108),(29,113,185,202),(30,140,186,201),(31,139,187,200),(32,138,188,199),(33,137,189,198),(34,136,190,197),(35,135,191,224),(36,134,192,223),(37,133,193,222),(38,132,194,221),(39,131,195,220),(40,130,196,219),(41,129,169,218),(42,128,170,217),(43,127,171,216),(44,126,172,215),(45,125,173,214),(46,124,174,213),(47,123,175,212),(48,122,176,211),(49,121,177,210),(50,120,178,209),(51,119,179,208),(52,118,180,207),(53,117,181,206),(54,116,182,205),(55,115,183,204),(56,114,184,203)], [(1,188),(2,173),(3,186),(4,171),(5,184),(6,169),(7,182),(8,195),(9,180),(10,193),(11,178),(12,191),(13,176),(14,189),(15,174),(16,187),(17,172),(18,185),(19,170),(20,183),(21,196),(22,181),(23,194),(24,179),(25,192),(26,177),(27,190),(28,175),(29,167),(30,152),(31,165),(32,150),(33,163),(34,148),(35,161),(36,146),(37,159),(38,144),(39,157),(40,142),(41,155),(42,168),(43,153),(44,166),(45,151),(46,164),(47,149),(48,162),(49,147),(50,160),(51,145),(52,158),(53,143),(54,156),(55,141),(56,154),(57,127),(58,140),(59,125),(60,138),(61,123),(62,136),(63,121),(64,134),(65,119),(66,132),(67,117),(68,130),(69,115),(70,128),(71,113),(72,126),(73,139),(74,124),(75,137),(76,122),(77,135),(78,120),(79,133),(80,118),(81,131),(82,116),(83,129),(84,114),(85,221),(86,206),(87,219),(88,204),(89,217),(90,202),(91,215),(92,200),(93,213),(94,198),(95,211),(96,224),(97,209),(98,222),(99,207),(100,220),(101,205),(102,218),(103,203),(104,216),(105,201),(106,214),(107,199),(108,212),(109,197),(110,210),(111,223),(112,208)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 21 | 22 | 0 | 0 | 0 | 0 |
| 5 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 23 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 17 |
| 0 | 0 | 0 | 0 | 27 | 27 |
| 0 | 19 | 0 | 0 | 0 | 0 |
| 26 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 2 | 0 | 0 |
| 0 | 0 | 11 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 10 | 0 | 0 | 0 | 0 |
| 3 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 24 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[21,5,0,0,0,0,22,26,0,0,0,0,0,0,25,23,0,0,0,0,3,26,0,0,0,0,0,0,2,27,0,0,0,0,17,27],[0,26,0,0,0,0,19,0,0,0,0,0,0,0,21,11,0,0,0,0,2,8,0,0,0,0,0,0,1,0,0,0,0,0,2,28],[0,3,0,0,0,0,10,0,0,0,0,0,0,0,25,24,0,0,0,0,3,4,0,0,0,0,0,0,28,0,0,0,0,0,0,28] >;
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 14A | ··· | 14U | 14V | ··· | 14AS | 28A | ··· | 28L |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 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 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | 14 | 14 | 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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | D4×D7 | D4⋊2D7 |
| kernel | C2×C28⋊2D4 | C2×C4⋊Dic7 | C28⋊2D4 | C2×C23.D7 | D7×C22×C4 | C22×C7⋊D4 | D4×C2×C14 | C2×C28 | C22×D7 | C22×D4 | C2×C14 | C22×C4 | C2×D4 | C24 | C2×C4 | C22 | C22 |
| # reps | 1 | 1 | 8 | 2 | 1 | 2 | 1 | 4 | 4 | 3 | 4 | 3 | 12 | 6 | 24 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_2\times C_{28}\rtimes_2D_4 % in TeX
G:=Group("C2xC28:2D4"); // GroupNames label
G:=SmallGroup(448,1253);
// by ID
G=gap.SmallGroup(448,1253);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,184,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d=b^13,d*c*d=c^-1>;
// generators/relations
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ℤ
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