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×C28).542C23, (C2×C14).295C24, (C22×C4).379D14, C14.142(C22×D4), C23.D7⋊61C22, (C23×C14).76C22, C23.337(C22×D7), C22.308(C23×D7), C22.79(D4⋊2D7), (C22×C28).275C22, (C22×C14).419C23, (C2×Dic7).152C23, (C23×D7).113C22, (C22×D7).239C23, (C22×Dic7).163C22, (D4×C2×C14)⋊4C2, C4⋊3(C2×C7⋊D4), C7⋊5(C2×C4⋊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
Generators and relations for C2×C28⋊2D4
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 >
Subgroups: 1876 in 426 conjugacy classes, 135 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, C23, D7, C14, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, C24, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C2×C4⋊C4, C4⋊D4, C23×C4, C22×D4, C22×D4, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C7×D4, C22×D7, C22×D7, C22×C14, C22×C14, C22×C14, C2×C4⋊D4, C4⋊Dic7, C23.D7, C2×C4×D7, C2×C4×D7, C22×Dic7, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, C23×D7, C23×C14, C2×C4⋊Dic7, C28⋊2D4, C2×C23.D7, D7×C22×C4, C22×C7⋊D4, D4×C2×C14, C2×C28⋊2D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C4⋊D4, C22×D4, C2×C4○D4, C7⋊D4, C22×D7, C2×C4⋊D4, D4×D7, D4⋊2D7, C2×C7⋊D4, C23×D7, C28⋊2D4, C2×D4×D7, C2×D4⋊2D7, C22×C7⋊D4, C2×C28⋊2D4
►On 224 points
Generators in S224
(1 103)(2 104)(3 105)(4 106)(5 107)(6 108)(7 109)(8 110)(9 111)(10 112)(11 85)(12 86)(13 87)(14 88)(15 89)(16 90)(17 91)(18 92)(19 93)(20 94)(21 95)(22 96)(23 97)(24 98)(25 99)(26 100)(27 101)(28 102)(29 167)(30 168)(31 141)(32 142)(33 143)(34 144)(35 145)(36 146)(37 147)(38 148)(39 149)(40 150)(41 151)(42 152)(43 153)(44 154)(45 155)(46 156)(47 157)(48 158)(49 159)(50 160)(51 161)(52 162)(53 163)(54 164)(55 165)(56 166)(57 133)(58 134)(59 135)(60 136)(61 137)(62 138)(63 139)(64 140)(65 113)(66 114)(67 115)(68 116)(69 117)(70 118)(71 119)(72 120)(73 121)(74 122)(75 123)(76 124)(77 125)(78 126)(79 127)(80 128)(81 129)(82 130)(83 131)(84 132)(169 217)(170 218)(171 219)(172 220)(173 221)(174 222)(175 223)(176 224)(177 197)(178 198)(179 199)(180 200)(181 201)(182 202)(183 203)(184 204)(185 205)(186 206)(187 207)(188 208)(189 209)(190 210)(191 211)(192 212)(193 213)(194 214)(195 215)(196 216)
(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)
(1 130 56 224)(2 129 29 223)(3 128 30 222)(4 127 31 221)(5 126 32 220)(6 125 33 219)(7 124 34 218)(8 123 35 217)(9 122 36 216)(10 121 37 215)(11 120 38 214)(12 119 39 213)(13 118 40 212)(14 117 41 211)(15 116 42 210)(16 115 43 209)(17 114 44 208)(18 113 45 207)(19 140 46 206)(20 139 47 205)(21 138 48 204)(22 137 49 203)(23 136 50 202)(24 135 51 201)(25 134 52 200)(26 133 53 199)(27 132 54 198)(28 131 55 197)(57 163 179 100)(58 162 180 99)(59 161 181 98)(60 160 182 97)(61 159 183 96)(62 158 184 95)(63 157 185 94)(64 156 186 93)(65 155 187 92)(66 154 188 91)(67 153 189 90)(68 152 190 89)(69 151 191 88)(70 150 192 87)(71 149 193 86)(72 148 194 85)(73 147 195 112)(74 146 196 111)(75 145 169 110)(76 144 170 109)(77 143 171 108)(78 142 172 107)(79 141 173 106)(80 168 174 105)(81 167 175 104)(82 166 176 103)(83 165 177 102)(84 164 178 101)
(1 103)(2 88)(3 101)(4 86)(5 99)(6 112)(7 97)(8 110)(9 95)(10 108)(11 93)(12 106)(13 91)(14 104)(15 89)(16 102)(17 87)(18 100)(19 85)(20 98)(21 111)(22 96)(23 109)(24 94)(25 107)(26 92)(27 105)(28 90)(29 151)(30 164)(31 149)(32 162)(33 147)(34 160)(35 145)(36 158)(37 143)(38 156)(39 141)(40 154)(41 167)(42 152)(43 165)(44 150)(45 163)(46 148)(47 161)(48 146)(49 159)(50 144)(51 157)(52 142)(53 155)(54 168)(55 153)(56 166)(57 207)(58 220)(59 205)(60 218)(61 203)(62 216)(63 201)(64 214)(65 199)(66 212)(67 197)(68 210)(69 223)(70 208)(71 221)(72 206)(73 219)(74 204)(75 217)(76 202)(77 215)(78 200)(79 213)(80 198)(81 211)(82 224)(83 209)(84 222)(113 179)(114 192)(115 177)(116 190)(117 175)(118 188)(119 173)(120 186)(121 171)(122 184)(123 169)(124 182)(125 195)(126 180)(127 193)(128 178)(129 191)(130 176)(131 189)(132 174)(133 187)(134 172)(135 185)(136 170)(137 183)(138 196)(139 181)(140 194)
G:=sub<Sym(224)| (1,103)(2,104)(3,105)(4,106)(5,107)(6,108)(7,109)(8,110)(9,111)(10,112)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,91)(18,92)(19,93)(20,94)(21,95)(22,96)(23,97)(24,98)(25,99)(26,100)(27,101)(28,102)(29,167)(30,168)(31,141)(32,142)(33,143)(34,144)(35,145)(36,146)(37,147)(38,148)(39,149)(40,150)(41,151)(42,152)(43,153)(44,154)(45,155)(46,156)(47,157)(48,158)(49,159)(50,160)(51,161)(52,162)(53,163)(54,164)(55,165)(56,166)(57,133)(58,134)(59,135)(60,136)(61,137)(62,138)(63,139)(64,140)(65,113)(66,114)(67,115)(68,116)(69,117)(70,118)(71,119)(72,120)(73,121)(74,122)(75,123)(76,124)(77,125)(78,126)(79,127)(80,128)(81,129)(82,130)(83,131)(84,132)(169,217)(170,218)(171,219)(172,220)(173,221)(174,222)(175,223)(176,224)(177,197)(178,198)(179,199)(180,200)(181,201)(182,202)(183,203)(184,204)(185,205)(186,206)(187,207)(188,208)(189,209)(190,210)(191,211)(192,212)(193,213)(194,214)(195,215)(196,216), (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), (1,130,56,224)(2,129,29,223)(3,128,30,222)(4,127,31,221)(5,126,32,220)(6,125,33,219)(7,124,34,218)(8,123,35,217)(9,122,36,216)(10,121,37,215)(11,120,38,214)(12,119,39,213)(13,118,40,212)(14,117,41,211)(15,116,42,210)(16,115,43,209)(17,114,44,208)(18,113,45,207)(19,140,46,206)(20,139,47,205)(21,138,48,204)(22,137,49,203)(23,136,50,202)(24,135,51,201)(25,134,52,200)(26,133,53,199)(27,132,54,198)(28,131,55,197)(57,163,179,100)(58,162,180,99)(59,161,181,98)(60,160,182,97)(61,159,183,96)(62,158,184,95)(63,157,185,94)(64,156,186,93)(65,155,187,92)(66,154,188,91)(67,153,189,90)(68,152,190,89)(69,151,191,88)(70,150,192,87)(71,149,193,86)(72,148,194,85)(73,147,195,112)(74,146,196,111)(75,145,169,110)(76,144,170,109)(77,143,171,108)(78,142,172,107)(79,141,173,106)(80,168,174,105)(81,167,175,104)(82,166,176,103)(83,165,177,102)(84,164,178,101), (1,103)(2,88)(3,101)(4,86)(5,99)(6,112)(7,97)(8,110)(9,95)(10,108)(11,93)(12,106)(13,91)(14,104)(15,89)(16,102)(17,87)(18,100)(19,85)(20,98)(21,111)(22,96)(23,109)(24,94)(25,107)(26,92)(27,105)(28,90)(29,151)(30,164)(31,149)(32,162)(33,147)(34,160)(35,145)(36,158)(37,143)(38,156)(39,141)(40,154)(41,167)(42,152)(43,165)(44,150)(45,163)(46,148)(47,161)(48,146)(49,159)(50,144)(51,157)(52,142)(53,155)(54,168)(55,153)(56,166)(57,207)(58,220)(59,205)(60,218)(61,203)(62,216)(63,201)(64,214)(65,199)(66,212)(67,197)(68,210)(69,223)(70,208)(71,221)(72,206)(73,219)(74,204)(75,217)(76,202)(77,215)(78,200)(79,213)(80,198)(81,211)(82,224)(83,209)(84,222)(113,179)(114,192)(115,177)(116,190)(117,175)(118,188)(119,173)(120,186)(121,171)(122,184)(123,169)(124,182)(125,195)(126,180)(127,193)(128,178)(129,191)(130,176)(131,189)(132,174)(133,187)(134,172)(135,185)(136,170)(137,183)(138,196)(139,181)(140,194)>;
G:=Group( (1,103)(2,104)(3,105)(4,106)(5,107)(6,108)(7,109)(8,110)(9,111)(10,112)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,91)(18,92)(19,93)(20,94)(21,95)(22,96)(23,97)(24,98)(25,99)(26,100)(27,101)(28,102)(29,167)(30,168)(31,141)(32,142)(33,143)(34,144)(35,145)(36,146)(37,147)(38,148)(39,149)(40,150)(41,151)(42,152)(43,153)(44,154)(45,155)(46,156)(47,157)(48,158)(49,159)(50,160)(51,161)(52,162)(53,163)(54,164)(55,165)(56,166)(57,133)(58,134)(59,135)(60,136)(61,137)(62,138)(63,139)(64,140)(65,113)(66,114)(67,115)(68,116)(69,117)(70,118)(71,119)(72,120)(73,121)(74,122)(75,123)(76,124)(77,125)(78,126)(79,127)(80,128)(81,129)(82,130)(83,131)(84,132)(169,217)(170,218)(171,219)(172,220)(173,221)(174,222)(175,223)(176,224)(177,197)(178,198)(179,199)(180,200)(181,201)(182,202)(183,203)(184,204)(185,205)(186,206)(187,207)(188,208)(189,209)(190,210)(191,211)(192,212)(193,213)(194,214)(195,215)(196,216), (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), (1,130,56,224)(2,129,29,223)(3,128,30,222)(4,127,31,221)(5,126,32,220)(6,125,33,219)(7,124,34,218)(8,123,35,217)(9,122,36,216)(10,121,37,215)(11,120,38,214)(12,119,39,213)(13,118,40,212)(14,117,41,211)(15,116,42,210)(16,115,43,209)(17,114,44,208)(18,113,45,207)(19,140,46,206)(20,139,47,205)(21,138,48,204)(22,137,49,203)(23,136,50,202)(24,135,51,201)(25,134,52,200)(26,133,53,199)(27,132,54,198)(28,131,55,197)(57,163,179,100)(58,162,180,99)(59,161,181,98)(60,160,182,97)(61,159,183,96)(62,158,184,95)(63,157,185,94)(64,156,186,93)(65,155,187,92)(66,154,188,91)(67,153,189,90)(68,152,190,89)(69,151,191,88)(70,150,192,87)(71,149,193,86)(72,148,194,85)(73,147,195,112)(74,146,196,111)(75,145,169,110)(76,144,170,109)(77,143,171,108)(78,142,172,107)(79,141,173,106)(80,168,174,105)(81,167,175,104)(82,166,176,103)(83,165,177,102)(84,164,178,101), (1,103)(2,88)(3,101)(4,86)(5,99)(6,112)(7,97)(8,110)(9,95)(10,108)(11,93)(12,106)(13,91)(14,104)(15,89)(16,102)(17,87)(18,100)(19,85)(20,98)(21,111)(22,96)(23,109)(24,94)(25,107)(26,92)(27,105)(28,90)(29,151)(30,164)(31,149)(32,162)(33,147)(34,160)(35,145)(36,158)(37,143)(38,156)(39,141)(40,154)(41,167)(42,152)(43,165)(44,150)(45,163)(46,148)(47,161)(48,146)(49,159)(50,144)(51,157)(52,142)(53,155)(54,168)(55,153)(56,166)(57,207)(58,220)(59,205)(60,218)(61,203)(62,216)(63,201)(64,214)(65,199)(66,212)(67,197)(68,210)(69,223)(70,208)(71,221)(72,206)(73,219)(74,204)(75,217)(76,202)(77,215)(78,200)(79,213)(80,198)(81,211)(82,224)(83,209)(84,222)(113,179)(114,192)(115,177)(116,190)(117,175)(118,188)(119,173)(120,186)(121,171)(122,184)(123,169)(124,182)(125,195)(126,180)(127,193)(128,178)(129,191)(130,176)(131,189)(132,174)(133,187)(134,172)(135,185)(136,170)(137,183)(138,196)(139,181)(140,194) );
G=PermutationGroup([[(1,103),(2,104),(3,105),(4,106),(5,107),(6,108),(7,109),(8,110),(9,111),(10,112),(11,85),(12,86),(13,87),(14,88),(15,89),(16,90),(17,91),(18,92),(19,93),(20,94),(21,95),(22,96),(23,97),(24,98),(25,99),(26,100),(27,101),(28,102),(29,167),(30,168),(31,141),(32,142),(33,143),(34,144),(35,145),(36,146),(37,147),(38,148),(39,149),(40,150),(41,151),(42,152),(43,153),(44,154),(45,155),(46,156),(47,157),(48,158),(49,159),(50,160),(51,161),(52,162),(53,163),(54,164),(55,165),(56,166),(57,133),(58,134),(59,135),(60,136),(61,137),(62,138),(63,139),(64,140),(65,113),(66,114),(67,115),(68,116),(69,117),(70,118),(71,119),(72,120),(73,121),(74,122),(75,123),(76,124),(77,125),(78,126),(79,127),(80,128),(81,129),(82,130),(83,131),(84,132),(169,217),(170,218),(171,219),(172,220),(173,221),(174,222),(175,223),(176,224),(177,197),(178,198),(179,199),(180,200),(181,201),(182,202),(183,203),(184,204),(185,205),(186,206),(187,207),(188,208),(189,209),(190,210),(191,211),(192,212),(193,213),(194,214),(195,215),(196,216)], [(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)], [(1,130,56,224),(2,129,29,223),(3,128,30,222),(4,127,31,221),(5,126,32,220),(6,125,33,219),(7,124,34,218),(8,123,35,217),(9,122,36,216),(10,121,37,215),(11,120,38,214),(12,119,39,213),(13,118,40,212),(14,117,41,211),(15,116,42,210),(16,115,43,209),(17,114,44,208),(18,113,45,207),(19,140,46,206),(20,139,47,205),(21,138,48,204),(22,137,49,203),(23,136,50,202),(24,135,51,201),(25,134,52,200),(26,133,53,199),(27,132,54,198),(28,131,55,197),(57,163,179,100),(58,162,180,99),(59,161,181,98),(60,160,182,97),(61,159,183,96),(62,158,184,95),(63,157,185,94),(64,156,186,93),(65,155,187,92),(66,154,188,91),(67,153,189,90),(68,152,190,89),(69,151,191,88),(70,150,192,87),(71,149,193,86),(72,148,194,85),(73,147,195,112),(74,146,196,111),(75,145,169,110),(76,144,170,109),(77,143,171,108),(78,142,172,107),(79,141,173,106),(80,168,174,105),(81,167,175,104),(82,166,176,103),(83,165,177,102),(84,164,178,101)], [(1,103),(2,88),(3,101),(4,86),(5,99),(6,112),(7,97),(8,110),(9,95),(10,108),(11,93),(12,106),(13,91),(14,104),(15,89),(16,102),(17,87),(18,100),(19,85),(20,98),(21,111),(22,96),(23,109),(24,94),(25,107),(26,92),(27,105),(28,90),(29,151),(30,164),(31,149),(32,162),(33,147),(34,160),(35,145),(36,158),(37,143),(38,156),(39,141),(40,154),(41,167),(42,152),(43,165),(44,150),(45,163),(46,148),(47,161),(48,146),(49,159),(50,144),(51,157),(52,142),(53,155),(54,168),(55,153),(56,166),(57,207),(58,220),(59,205),(60,218),(61,203),(62,216),(63,201),(64,214),(65,199),(66,212),(67,197),(68,210),(69,223),(70,208),(71,221),(72,206),(73,219),(74,204),(75,217),(76,202),(77,215),(78,200),(79,213),(80,198),(81,211),(82,224),(83,209),(84,222),(113,179),(114,192),(115,177),(116,190),(117,175),(118,188),(119,173),(120,186),(121,171),(122,184),(123,169),(124,182),(125,195),(126,180),(127,193),(128,178),(129,191),(130,176),(131,189),(132,174),(133,187),(134,172),(135,185),(136,170),(137,183),(138,196),(139,181),(140,194)]])
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 |
Matrix representation of C2×C28⋊2D4 ►in 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] >;
C2×C28⋊2D4 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