metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4)⋊2D28, (C2×C28)⋊5D4, (C22×D7)⋊3D4, C14.4C22≀C2, (C22×D28)⋊1C2, C7⋊1(C23⋊2D4), C14.1(C4⋊1D4), C2.7(C28⋊1D4), C2.3(C4⋊D28), C22.155(D4×D7), C22.80(C2×D28), (C22×C4).70D14, C2.7(C22⋊D28), C14.35(C4⋊D4), C2.C42⋊10D7, (C23×D7).3C22, (C22×C28).46C22, C23.359(C22×D7), (C22×C14).296C23, C22.44(Q8⋊2D7), (C22×Dic7).18C22, (C2×D14⋊C4)⋊15C2, (C2×C14).96(C2×D4), (C7×C2.C42)⋊8C2, (C2×C14).184(C4○D4), SmallGroup(448,205)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4)⋊2D28
G = < a,b,c,d | a2=b4=c28=d2=1, cbc-1=ab=ba, ac=ca, ad=da, dbd=ab-1, dcd=c-1 >
Subgroups: 2236 in 322 conjugacy classes, 69 normal (12 characteristic)
C1, C2, C2 [×6], C2 [×6], C4 [×7], C22, C22 [×6], C22 [×30], C7, C2×C4 [×6], C2×C4 [×9], D4 [×24], C23, C23 [×24], D7 [×6], C14, C14 [×6], C22⋊C4 [×6], C22×C4 [×3], C22×C4, C2×D4 [×18], C24 [×3], Dic7, C28 [×6], D14 [×30], C2×C14, C2×C14 [×6], C2.C42, C2×C22⋊C4 [×3], C22×D4 [×3], D28 [×24], C2×Dic7 [×3], C2×C28 [×6], C2×C28 [×6], C22×D7 [×6], C22×D7 [×18], C22×C14, C23⋊2D4, D14⋊C4 [×6], C2×D28 [×18], C22×Dic7, C22×C28 [×3], C23×D7 [×3], C7×C2.C42, C2×D14⋊C4 [×3], C22×D28 [×3], (C2×C4)⋊2D28
Quotients: C1, C2 [×7], C22 [×7], D4 [×12], C23, D7, C2×D4 [×6], C4○D4, D14 [×3], C22≀C2 [×3], C4⋊D4 [×3], C4⋊1D4, D28 [×6], C22×D7, C23⋊2D4, C2×D28 [×3], D4×D7 [×3], Q8⋊2D7, C4⋊D28, C22⋊D28 [×3], C28⋊1D4 [×3], (C2×C4)⋊2D28
►On 224 points
Generators in S224
(1 179)(2 180)(3 181)(4 182)(5 183)(6 184)(7 185)(8 186)(9 187)(10 188)(11 189)(12 190)(13 191)(14 192)(15 193)(16 194)(17 195)(18 196)(19 169)(20 170)(21 171)(22 172)(23 173)(24 174)(25 175)(26 176)(27 177)(28 178)(29 203)(30 204)(31 205)(32 206)(33 207)(34 208)(35 209)(36 210)(37 211)(38 212)(39 213)(40 214)(41 215)(42 216)(43 217)(44 218)(45 219)(46 220)(47 221)(48 222)(49 223)(50 224)(51 197)(52 198)(53 199)(54 200)(55 201)(56 202)(57 104)(58 105)(59 106)(60 107)(61 108)(62 109)(63 110)(64 111)(65 112)(66 85)(67 86)(68 87)(69 88)(70 89)(71 90)(72 91)(73 92)(74 93)(75 94)(76 95)(77 96)(78 97)(79 98)(80 99)(81 100)(82 101)(83 102)(84 103)(113 153)(114 154)(115 155)(116 156)(117 157)(118 158)(119 159)(120 160)(121 161)(122 162)(123 163)(124 164)(125 165)(126 166)(127 167)(128 168)(129 141)(130 142)(131 143)(132 144)(133 145)(134 146)(135 147)(136 148)(137 149)(138 150)(139 151)(140 152)
(1 73 115 41)(2 93 116 216)(3 75 117 43)(4 95 118 218)(5 77 119 45)(6 97 120 220)(7 79 121 47)(8 99 122 222)(9 81 123 49)(10 101 124 224)(11 83 125 51)(12 103 126 198)(13 57 127 53)(14 105 128 200)(15 59 129 55)(16 107 130 202)(17 61 131 29)(18 109 132 204)(19 63 133 31)(20 111 134 206)(21 65 135 33)(22 85 136 208)(23 67 137 35)(24 87 138 210)(25 69 139 37)(26 89 140 212)(27 71 113 39)(28 91 114 214)(30 196 62 144)(32 170 64 146)(34 172 66 148)(36 174 68 150)(38 176 70 152)(40 178 72 154)(42 180 74 156)(44 182 76 158)(46 184 78 160)(48 186 80 162)(50 188 82 164)(52 190 84 166)(54 192 58 168)(56 194 60 142)(86 149 209 173)(88 151 211 175)(90 153 213 177)(92 155 215 179)(94 157 217 181)(96 159 219 183)(98 161 221 185)(100 163 223 187)(102 165 197 189)(104 167 199 191)(106 141 201 193)(108 143 203 195)(110 145 205 169)(112 147 207 171)
(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)
(1 185)(2 184)(3 183)(4 182)(5 181)(6 180)(7 179)(8 178)(9 177)(10 176)(11 175)(12 174)(13 173)(14 172)(15 171)(16 170)(17 169)(18 196)(19 195)(20 194)(21 193)(22 192)(23 191)(24 190)(25 189)(26 188)(27 187)(28 186)(29 63)(30 62)(31 61)(32 60)(33 59)(34 58)(35 57)(36 84)(37 83)(38 82)(39 81)(40 80)(41 79)(42 78)(43 77)(44 76)(45 75)(46 74)(47 73)(48 72)(49 71)(50 70)(51 69)(52 68)(53 67)(54 66)(55 65)(56 64)(85 200)(86 199)(87 198)(88 197)(89 224)(90 223)(91 222)(92 221)(93 220)(94 219)(95 218)(96 217)(97 216)(98 215)(99 214)(100 213)(101 212)(102 211)(103 210)(104 209)(105 208)(106 207)(107 206)(108 205)(109 204)(110 203)(111 202)(112 201)(113 163)(114 162)(115 161)(116 160)(117 159)(118 158)(119 157)(120 156)(121 155)(122 154)(123 153)(124 152)(125 151)(126 150)(127 149)(128 148)(129 147)(130 146)(131 145)(132 144)(133 143)(134 142)(135 141)(136 168)(137 167)(138 166)(139 165)(140 164)
G:=sub<Sym(224)| (1,179)(2,180)(3,181)(4,182)(5,183)(6,184)(7,185)(8,186)(9,187)(10,188)(11,189)(12,190)(13,191)(14,192)(15,193)(16,194)(17,195)(18,196)(19,169)(20,170)(21,171)(22,172)(23,173)(24,174)(25,175)(26,176)(27,177)(28,178)(29,203)(30,204)(31,205)(32,206)(33,207)(34,208)(35,209)(36,210)(37,211)(38,212)(39,213)(40,214)(41,215)(42,216)(43,217)(44,218)(45,219)(46,220)(47,221)(48,222)(49,223)(50,224)(51,197)(52,198)(53,199)(54,200)(55,201)(56,202)(57,104)(58,105)(59,106)(60,107)(61,108)(62,109)(63,110)(64,111)(65,112)(66,85)(67,86)(68,87)(69,88)(70,89)(71,90)(72,91)(73,92)(74,93)(75,94)(76,95)(77,96)(78,97)(79,98)(80,99)(81,100)(82,101)(83,102)(84,103)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160)(121,161)(122,162)(123,163)(124,164)(125,165)(126,166)(127,167)(128,168)(129,141)(130,142)(131,143)(132,144)(133,145)(134,146)(135,147)(136,148)(137,149)(138,150)(139,151)(140,152), (1,73,115,41)(2,93,116,216)(3,75,117,43)(4,95,118,218)(5,77,119,45)(6,97,120,220)(7,79,121,47)(8,99,122,222)(9,81,123,49)(10,101,124,224)(11,83,125,51)(12,103,126,198)(13,57,127,53)(14,105,128,200)(15,59,129,55)(16,107,130,202)(17,61,131,29)(18,109,132,204)(19,63,133,31)(20,111,134,206)(21,65,135,33)(22,85,136,208)(23,67,137,35)(24,87,138,210)(25,69,139,37)(26,89,140,212)(27,71,113,39)(28,91,114,214)(30,196,62,144)(32,170,64,146)(34,172,66,148)(36,174,68,150)(38,176,70,152)(40,178,72,154)(42,180,74,156)(44,182,76,158)(46,184,78,160)(48,186,80,162)(50,188,82,164)(52,190,84,166)(54,192,58,168)(56,194,60,142)(86,149,209,173)(88,151,211,175)(90,153,213,177)(92,155,215,179)(94,157,217,181)(96,159,219,183)(98,161,221,185)(100,163,223,187)(102,165,197,189)(104,167,199,191)(106,141,201,193)(108,143,203,195)(110,145,205,169)(112,147,207,171), (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), (1,185)(2,184)(3,183)(4,182)(5,181)(6,180)(7,179)(8,178)(9,177)(10,176)(11,175)(12,174)(13,173)(14,172)(15,171)(16,170)(17,169)(18,196)(19,195)(20,194)(21,193)(22,192)(23,191)(24,190)(25,189)(26,188)(27,187)(28,186)(29,63)(30,62)(31,61)(32,60)(33,59)(34,58)(35,57)(36,84)(37,83)(38,82)(39,81)(40,80)(41,79)(42,78)(43,77)(44,76)(45,75)(46,74)(47,73)(48,72)(49,71)(50,70)(51,69)(52,68)(53,67)(54,66)(55,65)(56,64)(85,200)(86,199)(87,198)(88,197)(89,224)(90,223)(91,222)(92,221)(93,220)(94,219)(95,218)(96,217)(97,216)(98,215)(99,214)(100,213)(101,212)(102,211)(103,210)(104,209)(105,208)(106,207)(107,206)(108,205)(109,204)(110,203)(111,202)(112,201)(113,163)(114,162)(115,161)(116,160)(117,159)(118,158)(119,157)(120,156)(121,155)(122,154)(123,153)(124,152)(125,151)(126,150)(127,149)(128,148)(129,147)(130,146)(131,145)(132,144)(133,143)(134,142)(135,141)(136,168)(137,167)(138,166)(139,165)(140,164)>;
G:=Group( (1,179)(2,180)(3,181)(4,182)(5,183)(6,184)(7,185)(8,186)(9,187)(10,188)(11,189)(12,190)(13,191)(14,192)(15,193)(16,194)(17,195)(18,196)(19,169)(20,170)(21,171)(22,172)(23,173)(24,174)(25,175)(26,176)(27,177)(28,178)(29,203)(30,204)(31,205)(32,206)(33,207)(34,208)(35,209)(36,210)(37,211)(38,212)(39,213)(40,214)(41,215)(42,216)(43,217)(44,218)(45,219)(46,220)(47,221)(48,222)(49,223)(50,224)(51,197)(52,198)(53,199)(54,200)(55,201)(56,202)(57,104)(58,105)(59,106)(60,107)(61,108)(62,109)(63,110)(64,111)(65,112)(66,85)(67,86)(68,87)(69,88)(70,89)(71,90)(72,91)(73,92)(74,93)(75,94)(76,95)(77,96)(78,97)(79,98)(80,99)(81,100)(82,101)(83,102)(84,103)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160)(121,161)(122,162)(123,163)(124,164)(125,165)(126,166)(127,167)(128,168)(129,141)(130,142)(131,143)(132,144)(133,145)(134,146)(135,147)(136,148)(137,149)(138,150)(139,151)(140,152), (1,73,115,41)(2,93,116,216)(3,75,117,43)(4,95,118,218)(5,77,119,45)(6,97,120,220)(7,79,121,47)(8,99,122,222)(9,81,123,49)(10,101,124,224)(11,83,125,51)(12,103,126,198)(13,57,127,53)(14,105,128,200)(15,59,129,55)(16,107,130,202)(17,61,131,29)(18,109,132,204)(19,63,133,31)(20,111,134,206)(21,65,135,33)(22,85,136,208)(23,67,137,35)(24,87,138,210)(25,69,139,37)(26,89,140,212)(27,71,113,39)(28,91,114,214)(30,196,62,144)(32,170,64,146)(34,172,66,148)(36,174,68,150)(38,176,70,152)(40,178,72,154)(42,180,74,156)(44,182,76,158)(46,184,78,160)(48,186,80,162)(50,188,82,164)(52,190,84,166)(54,192,58,168)(56,194,60,142)(86,149,209,173)(88,151,211,175)(90,153,213,177)(92,155,215,179)(94,157,217,181)(96,159,219,183)(98,161,221,185)(100,163,223,187)(102,165,197,189)(104,167,199,191)(106,141,201,193)(108,143,203,195)(110,145,205,169)(112,147,207,171), (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), (1,185)(2,184)(3,183)(4,182)(5,181)(6,180)(7,179)(8,178)(9,177)(10,176)(11,175)(12,174)(13,173)(14,172)(15,171)(16,170)(17,169)(18,196)(19,195)(20,194)(21,193)(22,192)(23,191)(24,190)(25,189)(26,188)(27,187)(28,186)(29,63)(30,62)(31,61)(32,60)(33,59)(34,58)(35,57)(36,84)(37,83)(38,82)(39,81)(40,80)(41,79)(42,78)(43,77)(44,76)(45,75)(46,74)(47,73)(48,72)(49,71)(50,70)(51,69)(52,68)(53,67)(54,66)(55,65)(56,64)(85,200)(86,199)(87,198)(88,197)(89,224)(90,223)(91,222)(92,221)(93,220)(94,219)(95,218)(96,217)(97,216)(98,215)(99,214)(100,213)(101,212)(102,211)(103,210)(104,209)(105,208)(106,207)(107,206)(108,205)(109,204)(110,203)(111,202)(112,201)(113,163)(114,162)(115,161)(116,160)(117,159)(118,158)(119,157)(120,156)(121,155)(122,154)(123,153)(124,152)(125,151)(126,150)(127,149)(128,148)(129,147)(130,146)(131,145)(132,144)(133,143)(134,142)(135,141)(136,168)(137,167)(138,166)(139,165)(140,164) );
G=PermutationGroup([(1,179),(2,180),(3,181),(4,182),(5,183),(6,184),(7,185),(8,186),(9,187),(10,188),(11,189),(12,190),(13,191),(14,192),(15,193),(16,194),(17,195),(18,196),(19,169),(20,170),(21,171),(22,172),(23,173),(24,174),(25,175),(26,176),(27,177),(28,178),(29,203),(30,204),(31,205),(32,206),(33,207),(34,208),(35,209),(36,210),(37,211),(38,212),(39,213),(40,214),(41,215),(42,216),(43,217),(44,218),(45,219),(46,220),(47,221),(48,222),(49,223),(50,224),(51,197),(52,198),(53,199),(54,200),(55,201),(56,202),(57,104),(58,105),(59,106),(60,107),(61,108),(62,109),(63,110),(64,111),(65,112),(66,85),(67,86),(68,87),(69,88),(70,89),(71,90),(72,91),(73,92),(74,93),(75,94),(76,95),(77,96),(78,97),(79,98),(80,99),(81,100),(82,101),(83,102),(84,103),(113,153),(114,154),(115,155),(116,156),(117,157),(118,158),(119,159),(120,160),(121,161),(122,162),(123,163),(124,164),(125,165),(126,166),(127,167),(128,168),(129,141),(130,142),(131,143),(132,144),(133,145),(134,146),(135,147),(136,148),(137,149),(138,150),(139,151),(140,152)], [(1,73,115,41),(2,93,116,216),(3,75,117,43),(4,95,118,218),(5,77,119,45),(6,97,120,220),(7,79,121,47),(8,99,122,222),(9,81,123,49),(10,101,124,224),(11,83,125,51),(12,103,126,198),(13,57,127,53),(14,105,128,200),(15,59,129,55),(16,107,130,202),(17,61,131,29),(18,109,132,204),(19,63,133,31),(20,111,134,206),(21,65,135,33),(22,85,136,208),(23,67,137,35),(24,87,138,210),(25,69,139,37),(26,89,140,212),(27,71,113,39),(28,91,114,214),(30,196,62,144),(32,170,64,146),(34,172,66,148),(36,174,68,150),(38,176,70,152),(40,178,72,154),(42,180,74,156),(44,182,76,158),(46,184,78,160),(48,186,80,162),(50,188,82,164),(52,190,84,166),(54,192,58,168),(56,194,60,142),(86,149,209,173),(88,151,211,175),(90,153,213,177),(92,155,215,179),(94,157,217,181),(96,159,219,183),(98,161,221,185),(100,163,223,187),(102,165,197,189),(104,167,199,191),(106,141,201,193),(108,143,203,195),(110,145,205,169),(112,147,207,171)], [(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)], [(1,185),(2,184),(3,183),(4,182),(5,181),(6,180),(7,179),(8,178),(9,177),(10,176),(11,175),(12,174),(13,173),(14,172),(15,171),(16,170),(17,169),(18,196),(19,195),(20,194),(21,193),(22,192),(23,191),(24,190),(25,189),(26,188),(27,187),(28,186),(29,63),(30,62),(31,61),(32,60),(33,59),(34,58),(35,57),(36,84),(37,83),(38,82),(39,81),(40,80),(41,79),(42,78),(43,77),(44,76),(45,75),(46,74),(47,73),(48,72),(49,71),(50,70),(51,69),(52,68),(53,67),(54,66),(55,65),(56,64),(85,200),(86,199),(87,198),(88,197),(89,224),(90,223),(91,222),(92,221),(93,220),(94,219),(95,218),(96,217),(97,216),(98,215),(99,214),(100,213),(101,212),(102,211),(103,210),(104,209),(105,208),(106,207),(107,206),(108,205),(109,204),(110,203),(111,202),(112,201),(113,163),(114,162),(115,161),(116,160),(117,159),(118,158),(119,157),(120,156),(121,155),(122,154),(123,153),(124,152),(125,151),(126,150),(127,149),(128,148),(129,147),(130,146),(131,145),(132,144),(133,143),(134,142),(135,141),(136,168),(137,167),(138,166),(139,165),(140,164)])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2M | 4A | ··· | 4F | 4G | 4H | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | ··· | 28 | 4 | ··· | 4 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D28 | D4×D7 | Q8⋊2D7 |
| kernel | (C2×C4)⋊2D28 | C7×C2.C42 | C2×D14⋊C4 | C22×D28 | C2×C28 | C22×D7 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 1 | 3 | 3 | 6 | 6 | 3 | 2 | 9 | 36 | 9 | 3 |
Matrix representation of (C2×C4)⋊2D28 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 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 | 21 | 23 | 0 | 0 |
| 0 | 0 | 6 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 20 | 25 | 0 | 0 | 0 | 0 |
| 4 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 4 | 0 | 0 |
| 0 | 0 | 25 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 16 |
| 0 | 0 | 0 | 0 | 16 | 8 |
| 10 | 7 | 0 | 0 | 0 | 0 |
| 19 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,21,6,0,0,0,0,23,8,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[20,4,0,0,0,0,25,21,0,0,0,0,0,0,9,25,0,0,0,0,4,8,0,0,0,0,0,0,21,16,0,0,0,0,16,8],[10,19,0,0,0,0,7,19,0,0,0,0,0,0,19,10,0,0,0,0,22,10,0,0,0,0,0,0,28,0,0,0,0,0,0,28] >;
(C2×C4)⋊2D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)\rtimes_2D_{28} % in TeX
G:=Group("(C2xC4):2D28"); // GroupNames label
G:=SmallGroup(448,205);
// by ID
G=gap.SmallGroup(448,205);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,254,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=d^2=1,c*b*c^-1=a*b=b*a,a*c=c*a,a*d=d*a,d*b*d=a*b^-1,d*c*d=c^-1>;
// generators/relations