direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C22⋊C4×C28, C22⋊(C4×C28), C2.1(D4×C28), (C22×C4)⋊6C28, (C2×C42)⋊1C14, (C2×C14)⋊2C42, (C22×C28)⋊12C4, (C2×C28).533D4, C14.103(C4×D4), (C23×C28).5C2, (C23×C4).4C14, C23.14(C2×C28), C14.31(C2×C42), C24.25(C2×C14), C22.27(D4×C14), C2.C42⋊13C14, C22.14(C22×C28), (C23×C14).82C22, C23.50(C22×C14), C14.51(C42⋊C2), (C22×C28).488C22, (C22×C14).441C23, (C2×C4×C28)⋊2C2, C2.3(C2×C4×C28), (C2×C4)⋊6(C2×C28), (C2×C28)⋊28(C2×C4), (C2×C4).143(C7×D4), C2.2(C14×C22⋊C4), (C2×C14).594(C2×D4), C14.90(C2×C22⋊C4), C2.2(C7×C42⋊C2), C22.13(C7×C4○D4), (C14×C22⋊C4).34C2, (C2×C22⋊C4).14C14, (C22×C4).82(C2×C14), (C2×C14).203(C4○D4), (C2×C14).213(C22×C4), (C7×C2.C42)⋊29C2, (C22×C14).109(C2×C4), SmallGroup(448,785)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22⋊C4×C28
G = < a,b,c,d | a28=b2=c2=d4=1, ab=ba, ac=ca, ad=da, dbd-1=bc=cb, cd=dc >
Subgroups: 370 in 258 conjugacy classes, 146 normal (22 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, C23, C14, C14, C14, C42, C22⋊C4, C22×C4, C22×C4, C22×C4, C24, C28, C28, C2×C14, C2×C14, C2×C14, C2.C42, C2×C42, C2×C22⋊C4, C23×C4, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C4×C22⋊C4, C4×C28, C7×C22⋊C4, C22×C28, C22×C28, C22×C28, C23×C14, C7×C2.C42, C2×C4×C28, C14×C22⋊C4, C23×C28, C22⋊C4×C28
Quotients: C1, C2, C4, C22, C7, C2×C4, D4, C23, C14, C42, C22⋊C4, C22×C4, C2×D4, C4○D4, C28, C2×C14, C2×C42, C2×C22⋊C4, C42⋊C2, C4×D4, C2×C28, C7×D4, C22×C14, C4×C22⋊C4, C4×C28, C7×C22⋊C4, C22×C28, D4×C14, C7×C4○D4, C2×C4×C28, C14×C22⋊C4, C7×C42⋊C2, D4×C28, C22⋊C4×C28
►On 224 points
Generators in S224
(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)
(1 110)(2 111)(3 112)(4 85)(5 86)(6 87)(7 88)(8 89)(9 90)(10 91)(11 92)(12 93)(13 94)(14 95)(15 96)(16 97)(17 98)(18 99)(19 100)(20 101)(21 102)(22 103)(23 104)(24 105)(25 106)(26 107)(27 108)(28 109)(29 82)(30 83)(31 84)(32 57)(33 58)(34 59)(35 60)(36 61)(37 62)(38 63)(39 64)(40 65)(41 66)(42 67)(43 68)(44 69)(45 70)(46 71)(47 72)(48 73)(49 74)(50 75)(51 76)(52 77)(53 78)(54 79)(55 80)(56 81)(113 177)(114 178)(115 179)(116 180)(117 181)(118 182)(119 183)(120 184)(121 185)(122 186)(123 187)(124 188)(125 189)(126 190)(127 191)(128 192)(129 193)(130 194)(131 195)(132 196)(133 169)(134 170)(135 171)(136 172)(137 173)(138 174)(139 175)(140 176)(141 220)(142 221)(143 222)(144 223)(145 224)(146 197)(147 198)(148 199)(149 200)(150 201)(151 202)(152 203)(153 204)(154 205)(155 206)(156 207)(157 208)(158 209)(159 210)(160 211)(161 212)(162 213)(163 214)(164 215)(165 216)(166 217)(167 218)(168 219)
(1 202)(2 203)(3 204)(4 205)(5 206)(6 207)(7 208)(8 209)(9 210)(10 211)(11 212)(12 213)(13 214)(14 215)(15 216)(16 217)(17 218)(18 219)(19 220)(20 221)(21 222)(22 223)(23 224)(24 197)(25 198)(26 199)(27 200)(28 201)(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)(57 114)(58 115)(59 116)(60 117)(61 118)(62 119)(63 120)(64 121)(65 122)(66 123)(67 124)(68 125)(69 126)(70 127)(71 128)(72 129)(73 130)(74 131)(75 132)(76 133)(77 134)(78 135)(79 136)(80 137)(81 138)(82 139)(83 140)(84 113)(85 154)(86 155)(87 156)(88 157)(89 158)(90 159)(91 160)(92 161)(93 162)(94 163)(95 164)(96 165)(97 166)(98 167)(99 168)(100 141)(101 142)(102 143)(103 144)(104 145)(105 146)(106 147)(107 148)(108 149)(109 150)(110 151)(111 152)(112 153)
(1 114 96 46)(2 115 97 47)(3 116 98 48)(4 117 99 49)(5 118 100 50)(6 119 101 51)(7 120 102 52)(8 121 103 53)(9 122 104 54)(10 123 105 55)(11 124 106 56)(12 125 107 29)(13 126 108 30)(14 127 109 31)(15 128 110 32)(16 129 111 33)(17 130 112 34)(18 131 85 35)(19 132 86 36)(20 133 87 37)(21 134 88 38)(22 135 89 39)(23 136 90 40)(24 137 91 41)(25 138 92 42)(26 139 93 43)(27 140 94 44)(28 113 95 45)(57 165 192 202)(58 166 193 203)(59 167 194 204)(60 168 195 205)(61 141 196 206)(62 142 169 207)(63 143 170 208)(64 144 171 209)(65 145 172 210)(66 146 173 211)(67 147 174 212)(68 148 175 213)(69 149 176 214)(70 150 177 215)(71 151 178 216)(72 152 179 217)(73 153 180 218)(74 154 181 219)(75 155 182 220)(76 156 183 221)(77 157 184 222)(78 158 185 223)(79 159 186 224)(80 160 187 197)(81 161 188 198)(82 162 189 199)(83 163 190 200)(84 164 191 201)
G:=sub<Sym(224)| (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), (1,110)(2,111)(3,112)(4,85)(5,86)(6,87)(7,88)(8,89)(9,90)(10,91)(11,92)(12,93)(13,94)(14,95)(15,96)(16,97)(17,98)(18,99)(19,100)(20,101)(21,102)(22,103)(23,104)(24,105)(25,106)(26,107)(27,108)(28,109)(29,82)(30,83)(31,84)(32,57)(33,58)(34,59)(35,60)(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,73)(49,74)(50,75)(51,76)(52,77)(53,78)(54,79)(55,80)(56,81)(113,177)(114,178)(115,179)(116,180)(117,181)(118,182)(119,183)(120,184)(121,185)(122,186)(123,187)(124,188)(125,189)(126,190)(127,191)(128,192)(129,193)(130,194)(131,195)(132,196)(133,169)(134,170)(135,171)(136,172)(137,173)(138,174)(139,175)(140,176)(141,220)(142,221)(143,222)(144,223)(145,224)(146,197)(147,198)(148,199)(149,200)(150,201)(151,202)(152,203)(153,204)(154,205)(155,206)(156,207)(157,208)(158,209)(159,210)(160,211)(161,212)(162,213)(163,214)(164,215)(165,216)(166,217)(167,218)(168,219), (1,202)(2,203)(3,204)(4,205)(5,206)(6,207)(7,208)(8,209)(9,210)(10,211)(11,212)(12,213)(13,214)(14,215)(15,216)(16,217)(17,218)(18,219)(19,220)(20,221)(21,222)(22,223)(23,224)(24,197)(25,198)(26,199)(27,200)(28,201)(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)(57,114)(58,115)(59,116)(60,117)(61,118)(62,119)(63,120)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,127)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,113)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159)(91,160)(92,161)(93,162)(94,163)(95,164)(96,165)(97,166)(98,167)(99,168)(100,141)(101,142)(102,143)(103,144)(104,145)(105,146)(106,147)(107,148)(108,149)(109,150)(110,151)(111,152)(112,153), (1,114,96,46)(2,115,97,47)(3,116,98,48)(4,117,99,49)(5,118,100,50)(6,119,101,51)(7,120,102,52)(8,121,103,53)(9,122,104,54)(10,123,105,55)(11,124,106,56)(12,125,107,29)(13,126,108,30)(14,127,109,31)(15,128,110,32)(16,129,111,33)(17,130,112,34)(18,131,85,35)(19,132,86,36)(20,133,87,37)(21,134,88,38)(22,135,89,39)(23,136,90,40)(24,137,91,41)(25,138,92,42)(26,139,93,43)(27,140,94,44)(28,113,95,45)(57,165,192,202)(58,166,193,203)(59,167,194,204)(60,168,195,205)(61,141,196,206)(62,142,169,207)(63,143,170,208)(64,144,171,209)(65,145,172,210)(66,146,173,211)(67,147,174,212)(68,148,175,213)(69,149,176,214)(70,150,177,215)(71,151,178,216)(72,152,179,217)(73,153,180,218)(74,154,181,219)(75,155,182,220)(76,156,183,221)(77,157,184,222)(78,158,185,223)(79,159,186,224)(80,160,187,197)(81,161,188,198)(82,162,189,199)(83,163,190,200)(84,164,191,201)>;
G:=Group( (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), (1,110)(2,111)(3,112)(4,85)(5,86)(6,87)(7,88)(8,89)(9,90)(10,91)(11,92)(12,93)(13,94)(14,95)(15,96)(16,97)(17,98)(18,99)(19,100)(20,101)(21,102)(22,103)(23,104)(24,105)(25,106)(26,107)(27,108)(28,109)(29,82)(30,83)(31,84)(32,57)(33,58)(34,59)(35,60)(36,61)(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,73)(49,74)(50,75)(51,76)(52,77)(53,78)(54,79)(55,80)(56,81)(113,177)(114,178)(115,179)(116,180)(117,181)(118,182)(119,183)(120,184)(121,185)(122,186)(123,187)(124,188)(125,189)(126,190)(127,191)(128,192)(129,193)(130,194)(131,195)(132,196)(133,169)(134,170)(135,171)(136,172)(137,173)(138,174)(139,175)(140,176)(141,220)(142,221)(143,222)(144,223)(145,224)(146,197)(147,198)(148,199)(149,200)(150,201)(151,202)(152,203)(153,204)(154,205)(155,206)(156,207)(157,208)(158,209)(159,210)(160,211)(161,212)(162,213)(163,214)(164,215)(165,216)(166,217)(167,218)(168,219), (1,202)(2,203)(3,204)(4,205)(5,206)(6,207)(7,208)(8,209)(9,210)(10,211)(11,212)(12,213)(13,214)(14,215)(15,216)(16,217)(17,218)(18,219)(19,220)(20,221)(21,222)(22,223)(23,224)(24,197)(25,198)(26,199)(27,200)(28,201)(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)(57,114)(58,115)(59,116)(60,117)(61,118)(62,119)(63,120)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,127)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,113)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159)(91,160)(92,161)(93,162)(94,163)(95,164)(96,165)(97,166)(98,167)(99,168)(100,141)(101,142)(102,143)(103,144)(104,145)(105,146)(106,147)(107,148)(108,149)(109,150)(110,151)(111,152)(112,153), (1,114,96,46)(2,115,97,47)(3,116,98,48)(4,117,99,49)(5,118,100,50)(6,119,101,51)(7,120,102,52)(8,121,103,53)(9,122,104,54)(10,123,105,55)(11,124,106,56)(12,125,107,29)(13,126,108,30)(14,127,109,31)(15,128,110,32)(16,129,111,33)(17,130,112,34)(18,131,85,35)(19,132,86,36)(20,133,87,37)(21,134,88,38)(22,135,89,39)(23,136,90,40)(24,137,91,41)(25,138,92,42)(26,139,93,43)(27,140,94,44)(28,113,95,45)(57,165,192,202)(58,166,193,203)(59,167,194,204)(60,168,195,205)(61,141,196,206)(62,142,169,207)(63,143,170,208)(64,144,171,209)(65,145,172,210)(66,146,173,211)(67,147,174,212)(68,148,175,213)(69,149,176,214)(70,150,177,215)(71,151,178,216)(72,152,179,217)(73,153,180,218)(74,154,181,219)(75,155,182,220)(76,156,183,221)(77,157,184,222)(78,158,185,223)(79,159,186,224)(80,160,187,197)(81,161,188,198)(82,162,189,199)(83,163,190,200)(84,164,191,201) );
G=PermutationGroup([[(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)], [(1,110),(2,111),(3,112),(4,85),(5,86),(6,87),(7,88),(8,89),(9,90),(10,91),(11,92),(12,93),(13,94),(14,95),(15,96),(16,97),(17,98),(18,99),(19,100),(20,101),(21,102),(22,103),(23,104),(24,105),(25,106),(26,107),(27,108),(28,109),(29,82),(30,83),(31,84),(32,57),(33,58),(34,59),(35,60),(36,61),(37,62),(38,63),(39,64),(40,65),(41,66),(42,67),(43,68),(44,69),(45,70),(46,71),(47,72),(48,73),(49,74),(50,75),(51,76),(52,77),(53,78),(54,79),(55,80),(56,81),(113,177),(114,178),(115,179),(116,180),(117,181),(118,182),(119,183),(120,184),(121,185),(122,186),(123,187),(124,188),(125,189),(126,190),(127,191),(128,192),(129,193),(130,194),(131,195),(132,196),(133,169),(134,170),(135,171),(136,172),(137,173),(138,174),(139,175),(140,176),(141,220),(142,221),(143,222),(144,223),(145,224),(146,197),(147,198),(148,199),(149,200),(150,201),(151,202),(152,203),(153,204),(154,205),(155,206),(156,207),(157,208),(158,209),(159,210),(160,211),(161,212),(162,213),(163,214),(164,215),(165,216),(166,217),(167,218),(168,219)], [(1,202),(2,203),(3,204),(4,205),(5,206),(6,207),(7,208),(8,209),(9,210),(10,211),(11,212),(12,213),(13,214),(14,215),(15,216),(16,217),(17,218),(18,219),(19,220),(20,221),(21,222),(22,223),(23,224),(24,197),(25,198),(26,199),(27,200),(28,201),(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),(57,114),(58,115),(59,116),(60,117),(61,118),(62,119),(63,120),(64,121),(65,122),(66,123),(67,124),(68,125),(69,126),(70,127),(71,128),(72,129),(73,130),(74,131),(75,132),(76,133),(77,134),(78,135),(79,136),(80,137),(81,138),(82,139),(83,140),(84,113),(85,154),(86,155),(87,156),(88,157),(89,158),(90,159),(91,160),(92,161),(93,162),(94,163),(95,164),(96,165),(97,166),(98,167),(99,168),(100,141),(101,142),(102,143),(103,144),(104,145),(105,146),(106,147),(107,148),(108,149),(109,150),(110,151),(111,152),(112,153)], [(1,114,96,46),(2,115,97,47),(3,116,98,48),(4,117,99,49),(5,118,100,50),(6,119,101,51),(7,120,102,52),(8,121,103,53),(9,122,104,54),(10,123,105,55),(11,124,106,56),(12,125,107,29),(13,126,108,30),(14,127,109,31),(15,128,110,32),(16,129,111,33),(17,130,112,34),(18,131,85,35),(19,132,86,36),(20,133,87,37),(21,134,88,38),(22,135,89,39),(23,136,90,40),(24,137,91,41),(25,138,92,42),(26,139,93,43),(27,140,94,44),(28,113,95,45),(57,165,192,202),(58,166,193,203),(59,167,194,204),(60,168,195,205),(61,141,196,206),(62,142,169,207),(63,143,170,208),(64,144,171,209),(65,145,172,210),(66,146,173,211),(67,147,174,212),(68,148,175,213),(69,149,176,214),(70,150,177,215),(71,151,178,216),(72,152,179,217),(73,153,180,218),(74,154,181,219),(75,155,182,220),(76,156,183,221),(77,157,184,222),(78,158,185,223),(79,159,186,224),(80,160,187,197),(81,161,188,198),(82,162,189,199),(83,163,190,200),(84,164,191,201)]])
280 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 4I | ··· | 4AB | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 28A | ··· | 28AV | 28AW | ··· | 28FL |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 |
280 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | ||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | C7 | C14 | C14 | C14 | C14 | C28 | C28 | D4 | C4○D4 | C7×D4 | C7×C4○D4 |
| kernel | C22⋊C4×C28 | C7×C2.C42 | C2×C4×C28 | C14×C22⋊C4 | C23×C28 | C7×C22⋊C4 | C22×C28 | C4×C22⋊C4 | C2.C42 | C2×C42 | C2×C22⋊C4 | C23×C4 | C22⋊C4 | C22×C4 | C2×C28 | C2×C14 | C2×C4 | C22 |
| # reps | 1 | 2 | 2 | 2 | 1 | 16 | 8 | 6 | 12 | 12 | 12 | 6 | 96 | 48 | 4 | 4 | 24 | 24 |
Matrix representation of C22⋊C4×C28 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 26 | 0 |
| 0 | 0 | 0 | 26 |
| 1 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 28 | 28 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 17 | 5 |
| 0 | 0 | 0 | 12 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,17,0,0,0,0,26,0,0,0,0,26],[1,0,0,0,0,28,0,0,0,0,1,28,0,0,0,28],[1,0,0,0,0,1,0,0,0,0,28,0,0,0,0,28],[12,0,0,0,0,12,0,0,0,0,17,0,0,0,5,12] >;
C22⋊C4×C28 in GAP, Magma, Sage, TeX
C_2^2\rtimes C_4\times C_{28} % in TeX
G:=Group("C2^2:C4xC28"); // GroupNames label
G:=SmallGroup(448,785);
// by ID
G=gap.SmallGroup(448,785);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,784,813,1576,604]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^2=d^4=1,a*b=b*a,a*c=c*a,a*d=d*a,d*b*d^-1=b*c=c*b,c*d=d*c>;
// generators/relations