metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4○D28⋊3C4, D28⋊20(C2×C4), (C2×C4).43D28, C4.60(C2×D28), C4⋊C4.226D14, (C2×C28).134D4, C28.140(C2×D4), C14.D8⋊24C2, C4.37(D14⋊C4), Dic14⋊18(C2×C4), C14.Q16⋊24C2, C28.60(C22×C4), (C22×C4).93D14, C14.83(C8⋊C22), C28.20(C22⋊C4), (C2×C28).319C23, C22.4(D14⋊C4), (C22×C14).184D4, C23.76(C7⋊D4), C7⋊3(C23.36D4), C2.2(D4.D14), C2.2(C28.C23), (C2×D28).233C22, C14.83(C8.C22), (C22×C28).134C22, (C2×Dic14).260C22, (C2×C4⋊C4)⋊2D7, (C14×C4⋊C4)⋊2C2, C4.49(C2×C4×D7), (C2×C4).39(C4×D7), (C2×C28).78(C2×C4), C2.12(C2×D14⋊C4), (C2×C4○D28).6C2, (C2×C7⋊C8).80C22, (C2×C4.Dic7)⋊8C2, (C2×C14).439(C2×D4), C14.39(C2×C22⋊C4), C22.58(C2×C7⋊D4), (C2×C4).182(C7⋊D4), (C7×C4⋊C4).257C22, (C2×C4).419(C22×D7), (C2×C14).58(C22⋊C4), SmallGroup(448,500)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4○D28⋊C4
G = < a,b,c,d | a4=c2=d4=1, b14=a2, ab=ba, ac=ca, dad-1=a-1, cbc=a2b13, dbd-1=a2b, dcd-1=b7c >
Subgroups: 772 in 162 conjugacy classes, 63 normal (29 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C4⋊C4, C4⋊C4, C2×C8, M4(2), C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, C28, D14, C2×C14, C2×C14, C2×C14, D4⋊C4, Q8⋊C4, C2×C4⋊C4, C2×M4(2), C2×C4○D4, C7⋊C8, Dic14, Dic14, C4×D7, D28, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C23.36D4, C2×C7⋊C8, C4.Dic7, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C4○D28, C2×C7⋊D4, C22×C28, C22×C28, C14.D8, C14.Q16, C2×C4.Dic7, C14×C4⋊C4, C2×C4○D28, C4○D28⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, D14, C2×C22⋊C4, C8⋊C22, C8.C22, C4×D7, D28, C7⋊D4, C22×D7, C23.36D4, D14⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, C2×D14⋊C4, D4.D14, C28.C23, C4○D28⋊C4
►On 224 points
Generators in S224
(1 8 15 22)(2 9 16 23)(3 10 17 24)(4 11 18 25)(5 12 19 26)(6 13 20 27)(7 14 21 28)(29 36 43 50)(30 37 44 51)(31 38 45 52)(32 39 46 53)(33 40 47 54)(34 41 48 55)(35 42 49 56)(57 64 71 78)(58 65 72 79)(59 66 73 80)(60 67 74 81)(61 68 75 82)(62 69 76 83)(63 70 77 84)(85 92 99 106)(86 93 100 107)(87 94 101 108)(88 95 102 109)(89 96 103 110)(90 97 104 111)(91 98 105 112)(113 134 127 120)(114 135 128 121)(115 136 129 122)(116 137 130 123)(117 138 131 124)(118 139 132 125)(119 140 133 126)(141 162 155 148)(142 163 156 149)(143 164 157 150)(144 165 158 151)(145 166 159 152)(146 167 160 153)(147 168 161 154)(169 190 183 176)(170 191 184 177)(171 192 185 178)(172 193 186 179)(173 194 187 180)(174 195 188 181)(175 196 189 182)(197 218 211 204)(198 219 212 205)(199 220 213 206)(200 221 214 207)(201 222 215 208)(202 223 216 209)(203 224 217 210)
(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)
(1 133)(2 132)(3 131)(4 130)(5 129)(6 128)(7 127)(8 126)(9 125)(10 124)(11 123)(12 122)(13 121)(14 120)(15 119)(16 118)(17 117)(18 116)(19 115)(20 114)(21 113)(22 140)(23 139)(24 138)(25 137)(26 136)(27 135)(28 134)(29 163)(30 162)(31 161)(32 160)(33 159)(34 158)(35 157)(36 156)(37 155)(38 154)(39 153)(40 152)(41 151)(42 150)(43 149)(44 148)(45 147)(46 146)(47 145)(48 144)(49 143)(50 142)(51 141)(52 168)(53 167)(54 166)(55 165)(56 164)(57 175)(58 174)(59 173)(60 172)(61 171)(62 170)(63 169)(64 196)(65 195)(66 194)(67 193)(68 192)(69 191)(70 190)(71 189)(72 188)(73 187)(74 186)(75 185)(76 184)(77 183)(78 182)(79 181)(80 180)(81 179)(82 178)(83 177)(84 176)(85 207)(86 206)(87 205)(88 204)(89 203)(90 202)(91 201)(92 200)(93 199)(94 198)(95 197)(96 224)(97 223)(98 222)(99 221)(100 220)(101 219)(102 218)(103 217)(104 216)(105 215)(106 214)(107 213)(108 212)(109 211)(110 210)(111 209)(112 208)
(1 103 52 71)(2 90 53 58)(3 105 54 73)(4 92 55 60)(5 107 56 75)(6 94 29 62)(7 109 30 77)(8 96 31 64)(9 111 32 79)(10 98 33 66)(11 85 34 81)(12 100 35 68)(13 87 36 83)(14 102 37 70)(15 89 38 57)(16 104 39 72)(17 91 40 59)(18 106 41 74)(19 93 42 61)(20 108 43 76)(21 95 44 63)(22 110 45 78)(23 97 46 65)(24 112 47 80)(25 99 48 67)(26 86 49 82)(27 101 50 69)(28 88 51 84)(113 218 148 190)(114 205 149 177)(115 220 150 192)(116 207 151 179)(117 222 152 194)(118 209 153 181)(119 224 154 196)(120 211 155 183)(121 198 156 170)(122 213 157 185)(123 200 158 172)(124 215 159 187)(125 202 160 174)(126 217 161 189)(127 204 162 176)(128 219 163 191)(129 206 164 178)(130 221 165 193)(131 208 166 180)(132 223 167 195)(133 210 168 182)(134 197 141 169)(135 212 142 184)(136 199 143 171)(137 214 144 186)(138 201 145 173)(139 216 146 188)(140 203 147 175)
G:=sub<Sym(224)| (1,8,15,22)(2,9,16,23)(3,10,17,24)(4,11,18,25)(5,12,19,26)(6,13,20,27)(7,14,21,28)(29,36,43,50)(30,37,44,51)(31,38,45,52)(32,39,46,53)(33,40,47,54)(34,41,48,55)(35,42,49,56)(57,64,71,78)(58,65,72,79)(59,66,73,80)(60,67,74,81)(61,68,75,82)(62,69,76,83)(63,70,77,84)(85,92,99,106)(86,93,100,107)(87,94,101,108)(88,95,102,109)(89,96,103,110)(90,97,104,111)(91,98,105,112)(113,134,127,120)(114,135,128,121)(115,136,129,122)(116,137,130,123)(117,138,131,124)(118,139,132,125)(119,140,133,126)(141,162,155,148)(142,163,156,149)(143,164,157,150)(144,165,158,151)(145,166,159,152)(146,167,160,153)(147,168,161,154)(169,190,183,176)(170,191,184,177)(171,192,185,178)(172,193,186,179)(173,194,187,180)(174,195,188,181)(175,196,189,182)(197,218,211,204)(198,219,212,205)(199,220,213,206)(200,221,214,207)(201,222,215,208)(202,223,216,209)(203,224,217,210), (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), (1,133)(2,132)(3,131)(4,130)(5,129)(6,128)(7,127)(8,126)(9,125)(10,124)(11,123)(12,122)(13,121)(14,120)(15,119)(16,118)(17,117)(18,116)(19,115)(20,114)(21,113)(22,140)(23,139)(24,138)(25,137)(26,136)(27,135)(28,134)(29,163)(30,162)(31,161)(32,160)(33,159)(34,158)(35,157)(36,156)(37,155)(38,154)(39,153)(40,152)(41,151)(42,150)(43,149)(44,148)(45,147)(46,146)(47,145)(48,144)(49,143)(50,142)(51,141)(52,168)(53,167)(54,166)(55,165)(56,164)(57,175)(58,174)(59,173)(60,172)(61,171)(62,170)(63,169)(64,196)(65,195)(66,194)(67,193)(68,192)(69,191)(70,190)(71,189)(72,188)(73,187)(74,186)(75,185)(76,184)(77,183)(78,182)(79,181)(80,180)(81,179)(82,178)(83,177)(84,176)(85,207)(86,206)(87,205)(88,204)(89,203)(90,202)(91,201)(92,200)(93,199)(94,198)(95,197)(96,224)(97,223)(98,222)(99,221)(100,220)(101,219)(102,218)(103,217)(104,216)(105,215)(106,214)(107,213)(108,212)(109,211)(110,210)(111,209)(112,208), (1,103,52,71)(2,90,53,58)(3,105,54,73)(4,92,55,60)(5,107,56,75)(6,94,29,62)(7,109,30,77)(8,96,31,64)(9,111,32,79)(10,98,33,66)(11,85,34,81)(12,100,35,68)(13,87,36,83)(14,102,37,70)(15,89,38,57)(16,104,39,72)(17,91,40,59)(18,106,41,74)(19,93,42,61)(20,108,43,76)(21,95,44,63)(22,110,45,78)(23,97,46,65)(24,112,47,80)(25,99,48,67)(26,86,49,82)(27,101,50,69)(28,88,51,84)(113,218,148,190)(114,205,149,177)(115,220,150,192)(116,207,151,179)(117,222,152,194)(118,209,153,181)(119,224,154,196)(120,211,155,183)(121,198,156,170)(122,213,157,185)(123,200,158,172)(124,215,159,187)(125,202,160,174)(126,217,161,189)(127,204,162,176)(128,219,163,191)(129,206,164,178)(130,221,165,193)(131,208,166,180)(132,223,167,195)(133,210,168,182)(134,197,141,169)(135,212,142,184)(136,199,143,171)(137,214,144,186)(138,201,145,173)(139,216,146,188)(140,203,147,175)>;
G:=Group( (1,8,15,22)(2,9,16,23)(3,10,17,24)(4,11,18,25)(5,12,19,26)(6,13,20,27)(7,14,21,28)(29,36,43,50)(30,37,44,51)(31,38,45,52)(32,39,46,53)(33,40,47,54)(34,41,48,55)(35,42,49,56)(57,64,71,78)(58,65,72,79)(59,66,73,80)(60,67,74,81)(61,68,75,82)(62,69,76,83)(63,70,77,84)(85,92,99,106)(86,93,100,107)(87,94,101,108)(88,95,102,109)(89,96,103,110)(90,97,104,111)(91,98,105,112)(113,134,127,120)(114,135,128,121)(115,136,129,122)(116,137,130,123)(117,138,131,124)(118,139,132,125)(119,140,133,126)(141,162,155,148)(142,163,156,149)(143,164,157,150)(144,165,158,151)(145,166,159,152)(146,167,160,153)(147,168,161,154)(169,190,183,176)(170,191,184,177)(171,192,185,178)(172,193,186,179)(173,194,187,180)(174,195,188,181)(175,196,189,182)(197,218,211,204)(198,219,212,205)(199,220,213,206)(200,221,214,207)(201,222,215,208)(202,223,216,209)(203,224,217,210), (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), (1,133)(2,132)(3,131)(4,130)(5,129)(6,128)(7,127)(8,126)(9,125)(10,124)(11,123)(12,122)(13,121)(14,120)(15,119)(16,118)(17,117)(18,116)(19,115)(20,114)(21,113)(22,140)(23,139)(24,138)(25,137)(26,136)(27,135)(28,134)(29,163)(30,162)(31,161)(32,160)(33,159)(34,158)(35,157)(36,156)(37,155)(38,154)(39,153)(40,152)(41,151)(42,150)(43,149)(44,148)(45,147)(46,146)(47,145)(48,144)(49,143)(50,142)(51,141)(52,168)(53,167)(54,166)(55,165)(56,164)(57,175)(58,174)(59,173)(60,172)(61,171)(62,170)(63,169)(64,196)(65,195)(66,194)(67,193)(68,192)(69,191)(70,190)(71,189)(72,188)(73,187)(74,186)(75,185)(76,184)(77,183)(78,182)(79,181)(80,180)(81,179)(82,178)(83,177)(84,176)(85,207)(86,206)(87,205)(88,204)(89,203)(90,202)(91,201)(92,200)(93,199)(94,198)(95,197)(96,224)(97,223)(98,222)(99,221)(100,220)(101,219)(102,218)(103,217)(104,216)(105,215)(106,214)(107,213)(108,212)(109,211)(110,210)(111,209)(112,208), (1,103,52,71)(2,90,53,58)(3,105,54,73)(4,92,55,60)(5,107,56,75)(6,94,29,62)(7,109,30,77)(8,96,31,64)(9,111,32,79)(10,98,33,66)(11,85,34,81)(12,100,35,68)(13,87,36,83)(14,102,37,70)(15,89,38,57)(16,104,39,72)(17,91,40,59)(18,106,41,74)(19,93,42,61)(20,108,43,76)(21,95,44,63)(22,110,45,78)(23,97,46,65)(24,112,47,80)(25,99,48,67)(26,86,49,82)(27,101,50,69)(28,88,51,84)(113,218,148,190)(114,205,149,177)(115,220,150,192)(116,207,151,179)(117,222,152,194)(118,209,153,181)(119,224,154,196)(120,211,155,183)(121,198,156,170)(122,213,157,185)(123,200,158,172)(124,215,159,187)(125,202,160,174)(126,217,161,189)(127,204,162,176)(128,219,163,191)(129,206,164,178)(130,221,165,193)(131,208,166,180)(132,223,167,195)(133,210,168,182)(134,197,141,169)(135,212,142,184)(136,199,143,171)(137,214,144,186)(138,201,145,173)(139,216,146,188)(140,203,147,175) );
G=PermutationGroup([[(1,8,15,22),(2,9,16,23),(3,10,17,24),(4,11,18,25),(5,12,19,26),(6,13,20,27),(7,14,21,28),(29,36,43,50),(30,37,44,51),(31,38,45,52),(32,39,46,53),(33,40,47,54),(34,41,48,55),(35,42,49,56),(57,64,71,78),(58,65,72,79),(59,66,73,80),(60,67,74,81),(61,68,75,82),(62,69,76,83),(63,70,77,84),(85,92,99,106),(86,93,100,107),(87,94,101,108),(88,95,102,109),(89,96,103,110),(90,97,104,111),(91,98,105,112),(113,134,127,120),(114,135,128,121),(115,136,129,122),(116,137,130,123),(117,138,131,124),(118,139,132,125),(119,140,133,126),(141,162,155,148),(142,163,156,149),(143,164,157,150),(144,165,158,151),(145,166,159,152),(146,167,160,153),(147,168,161,154),(169,190,183,176),(170,191,184,177),(171,192,185,178),(172,193,186,179),(173,194,187,180),(174,195,188,181),(175,196,189,182),(197,218,211,204),(198,219,212,205),(199,220,213,206),(200,221,214,207),(201,222,215,208),(202,223,216,209),(203,224,217,210)], [(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)], [(1,133),(2,132),(3,131),(4,130),(5,129),(6,128),(7,127),(8,126),(9,125),(10,124),(11,123),(12,122),(13,121),(14,120),(15,119),(16,118),(17,117),(18,116),(19,115),(20,114),(21,113),(22,140),(23,139),(24,138),(25,137),(26,136),(27,135),(28,134),(29,163),(30,162),(31,161),(32,160),(33,159),(34,158),(35,157),(36,156),(37,155),(38,154),(39,153),(40,152),(41,151),(42,150),(43,149),(44,148),(45,147),(46,146),(47,145),(48,144),(49,143),(50,142),(51,141),(52,168),(53,167),(54,166),(55,165),(56,164),(57,175),(58,174),(59,173),(60,172),(61,171),(62,170),(63,169),(64,196),(65,195),(66,194),(67,193),(68,192),(69,191),(70,190),(71,189),(72,188),(73,187),(74,186),(75,185),(76,184),(77,183),(78,182),(79,181),(80,180),(81,179),(82,178),(83,177),(84,176),(85,207),(86,206),(87,205),(88,204),(89,203),(90,202),(91,201),(92,200),(93,199),(94,198),(95,197),(96,224),(97,223),(98,222),(99,221),(100,220),(101,219),(102,218),(103,217),(104,216),(105,215),(106,214),(107,213),(108,212),(109,211),(110,210),(111,209),(112,208)], [(1,103,52,71),(2,90,53,58),(3,105,54,73),(4,92,55,60),(5,107,56,75),(6,94,29,62),(7,109,30,77),(8,96,31,64),(9,111,32,79),(10,98,33,66),(11,85,34,81),(12,100,35,68),(13,87,36,83),(14,102,37,70),(15,89,38,57),(16,104,39,72),(17,91,40,59),(18,106,41,74),(19,93,42,61),(20,108,43,76),(21,95,44,63),(22,110,45,78),(23,97,46,65),(24,112,47,80),(25,99,48,67),(26,86,49,82),(27,101,50,69),(28,88,51,84),(113,218,148,190),(114,205,149,177),(115,220,150,192),(116,207,151,179),(117,222,152,194),(118,209,153,181),(119,224,154,196),(120,211,155,183),(121,198,156,170),(122,213,157,185),(123,200,158,172),(124,215,159,187),(125,202,160,174),(126,217,161,189),(127,204,162,176),(128,219,163,191),(129,206,164,178),(130,221,165,193),(131,208,166,180),(132,223,167,195),(133,210,168,182),(134,197,141,169),(135,212,142,184),(136,199,143,171),(137,214,144,186),(138,201,145,173),(139,216,146,188),(140,203,147,175)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | D14 | D14 | C4×D7 | D28 | C7⋊D4 | C7⋊D4 | C8⋊C22 | C8.C22 | D4.D14 | C28.C23 |
| kernel | C4○D28⋊C4 | C14.D8 | C14.Q16 | C2×C4.Dic7 | C14×C4⋊C4 | C2×C4○D28 | C4○D28 | C2×C28 | C22×C14 | C2×C4⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C23 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 3 | 1 | 3 | 6 | 3 | 12 | 12 | 6 | 6 | 1 | 1 | 6 | 6 |
Matrix representation of C4○D28⋊C4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 106 | 0 | 0 |
| 0 | 0 | 7 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 97 |
| 0 | 0 | 0 | 0 | 16 | 0 |
| 52 | 16 | 0 | 0 | 0 | 0 |
| 50 | 61 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 97 |
| 0 | 0 | 0 | 0 | 16 | 0 |
| 0 | 0 | 0 | 106 | 0 | 0 |
| 0 | 0 | 7 | 0 | 0 | 0 |
| 70 | 34 | 0 | 0 | 0 | 0 |
| 32 | 43 | 0 | 0 | 0 | 0 |
| 0 | 0 | 66 | 74 | 0 | 0 |
| 0 | 0 | 74 | 47 | 0 | 0 |
| 0 | 0 | 0 | 0 | 74 | 47 |
| 0 | 0 | 0 | 0 | 47 | 39 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,112,0,0,0,0,0,0,0,0,1,0,0,0,0,112,0],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,7,0,0,0,0,106,0,0,0,0,0,0,0,0,16,0,0,0,0,97,0],[52,50,0,0,0,0,16,61,0,0,0,0,0,0,0,0,0,7,0,0,0,0,106,0,0,0,0,16,0,0,0,0,97,0,0,0],[70,32,0,0,0,0,34,43,0,0,0,0,0,0,66,74,0,0,0,0,74,47,0,0,0,0,0,0,74,47,0,0,0,0,47,39] >;
C4○D28⋊C4 in GAP, Magma, Sage, TeX
C_4\circ D_{28}\rtimes C_4 % in TeX
G:=Group("C4oD28:C4"); // GroupNames label
G:=SmallGroup(448,500);
// by ID
G=gap.SmallGroup(448,500);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,422,387,58,1684,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=c^2=d^4=1,b^14=a^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c=a^2*b^13,d*b*d^-1=a^2*b,d*c*d^-1=b^7*c>;
// generators/relations