C2xC28:4D4 - GroupNames

G = C₂×C₂₈⋊₄D₄ order 448 = 2⁶·7

Direct product of C₂ and C₂₈⋊₄D₄

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C₂×C₂₈⋊₄D₄, C₄²⋊₃₉D₁₄, (C₂×C₄)⋊₇D₂₈, C₄⋊₂(C₂×D₂₈), (C₂×C₂₈)⋊₃₀D₄, C₂₈⋊₁₀(C₂×D₄), (C₂×C₄²)⋊₉D₇, C₁₄⋊₁(C₄⋊₁D₄), (C₄×C₂₈)⋊₅₀C₂², (C₂²×D₂₈)⋊₄C₂, C₂.₅(C₂²×D₂₈), C₁₄.₃(C₂²×D₄), (C₂×D₂₈)⋊₄₂C₂², (C₂×C₁₄).₁₉C₂⁴, C₂².₆₄(C₂×D₂₈), (C₂×C₂₈).₇₈₀C₂³, (C₂²×C₄).₄₃₈D₁₄, (C₂²×D₇).₁C₂³, C₂².₆₂(C₂³×D₇), (C₂³×D₇).₂₇C₂², C₂³.₃₁₅(C₂²×D₇), (C₂²×C₂₈).₅₂₃C₂², (C₂²×C₁₄).₃₈₁C₂³, (C₂×C₄×C₂₈)⋊₈C₂, C₇⋊₁(C₂×C₄⋊₁D₄), (C₂×C₁₄).₁₇₀(C₂×D₄), (C₂×C₄).₇₂₉(C₂²×D₇), SmallGroup(448,928)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂×C₁₄ — C₂×C₂₈⋊₄D₄

Chief series

C₁ — C₇ — C₁₄ — C₂×C₁₄ — C₂²×D₇ — C₂³×D₇ — C₂²×D₂₈ — C₂×C₂₈⋊₄D₄

Lower central

C₇ — C₂×C₁₄ — C₂×C₂₈⋊₄D₄

Upper central

C₁ — C₂³ — C₂×C₄²

Generators and relations for C₂×C₂₈⋊₄D₄
G = < a,b,c,d | a²=b⁴=c²⁸=d²=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b^-1, dcd=c^-1 >

Subgroups: 3204 in 498 conjugacy classes, 159 normal (9 characteristic)
C₁, C₂, C₂, C₄, C₂², C₂², C₂², C₇, C₂×C₄, D₄, C₂³, C₂³, D₇, C₁₄, C₄², C₂²×C₄, C₂×D₄, C₂⁴, C₂₈, D₁₄, C₂×C₁₄, C₂×C₁₄, C₂×C₄², C₄⋊₁D₄, C₂²×D₄, D₂₈, C₂×C₂₈, C₂²×D₇, C₂²×D₇, C₂²×C₁₄, C₂×C₄⋊₁D₄, C₄×C₂₈, C₂×D₂₈, C₂×D₂₈, C₂²×C₂₈, C₂³×D₇, C₂₈⋊₄D₄, C₂×C₄×C₂₈, C₂²×D₂₈, C₂×C₂₈⋊₄D₄
Quotients: C₁, C₂, C₂², D₄, C₂³, D₇, C₂×D₄, C₂⁴, D₁₄, C₄⋊₁D₄, C₂²×D₄, D₂₈, C₂²×D₇, C₂×C₄⋊₁D₄, C₂×D₂₈, C₂³×D₇, C₂₈⋊₄D₄, C₂²×D₂₈, C₂×C₂₈⋊₄D₄

Smallest permutation representation of C₂×C₂₈⋊₄D₄
►On 224 points

Generators in S₂₂₄

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

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

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

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

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

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

124 conjugacy classes

class	1	2A	···	2G	2H	···	2O	4A	···	4L	7A	7B	7C	14A	···	14U	28A	···	28BT
order	1	2	···	2	2	···	2	4	···	4	7	7	7	14	···	14	28	···	28
size	1	1	···	1	28	···	28	2	···	2	2	2	2	2	···	2	2	···	2

124 irreducible representations

dim	1	1	1	1	2	2	2	2	2
type	+	+	+	+	+	+	+	+	+
image	C₁	C₂	C₂	C₂	D₄	D₇	D₁₄	D₁₄	D₂₈
kernel	C₂×C₂₈⋊₄D₄	C₂₈⋊₄D₄	C₂×C₄×C₂₈	C₂²×D₂₈	C₂×C₂₈	C₂×C₄²	C₄²	C₂²×C₄	C₂×C₄
# reps	1	8	1	6	12	3	12	9	72

Matrix representation of C₂×C₂₈⋊₄D₄ ►in GL₆(𝔽₂₉)

28	0	0	0	0	0
0	28	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

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	27	18
0	0	0	0	11	2

16	7	0	0	0	0
22	26	0	0	0	0
0	0	3	4	0	0
0	0	21	9	0	0
0	0	0	0	8	3
0	0	0	0	26	28

16	7	0	0	0	0
5	13	0	0	0	0
0	0	11	21	0	0
0	0	15	18	0	0
0	0	0	0	26	21
0	0	0	0	1	3

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,27,11,0,0,0,0,18,2],[16,22,0,0,0,0,7,26,0,0,0,0,0,0,3,21,0,0,0,0,4,9,0,0,0,0,0,0,8,26,0,0,0,0,3,28],[16,5,0,0,0,0,7,13,0,0,0,0,0,0,11,15,0,0,0,0,21,18,0,0,0,0,0,0,26,1,0,0,0,0,21,3] >;

C₂×C₂₈⋊₄D₄ in GAP, Magma, Sage, TeX

C_2\times C_{28}\rtimes_4D_4

% in TeX

G:=Group("C2xC28:4D4");

// GroupNames label

G:=SmallGroup(448,928);

// by ID

G=gap.SmallGroup(448,928);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,675,80,18822]);

// Polycyclic

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

// generators/relations

G = C2×C28⋊4D4 order 448 = 26·7

Direct product of C2 and C28⋊4D4

G = C₂×C₂₈⋊₄D₄ order 448 = 2⁶·7

Direct product of C₂ and C₂₈⋊₄D₄