G = C4.(C2×D28) order 448 = 26·7
14th non-split extension by C4 of C2×D28 acting via C2×D28/C22×D7=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4○D28⋊4C4, C4.63(C2×D28), C4⋊C4.235D14, D28.26(C2×C4), (C2×C28).496D4, C28.143(C2×D4), (C2×C4).146D28, C42⋊C2⋊2D7, C14.D8⋊43C2, C4.52(D14⋊C4), C14.85(C4○D8), C14.Q16⋊43C2, C28.65(C22×C4), (C22×C14).75D4, C28.64(C22⋊C4), (C2×C28).329C23, C22.1(D14⋊C4), Dic14.26(C2×C4), (C22×C4).339D14, C23.38(C7⋊D4), C7⋊3(C23.24D4), C2.2(D4.8D14), (C2×D28).235C22, (C22×C28).151C22, (C2×Dic14).262C22, C4.52(C2×C4×D7), (C22×C7⋊C8)⋊2C2, (C2×C4).81(C4×D7), (C2×C28).92(C2×C4), C2.18(C2×D14⋊C4), (C2×C4○D28).7C2, (C7×C42⋊C2)⋊2C2, (C2×C14).458(C2×D4), (C2×C7⋊C8).243C22, C14.45(C2×C22⋊C4), C22.73(C2×C7⋊D4), (C2×C4).274(C7⋊D4), (C7×C4⋊C4).266C22, (C2×C4).429(C22×D7), (C2×C14).15(C22⋊C4), SmallGroup(448,536)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4.(C2×D28)
G = < a,b,c,d | a4=b2=c28=1, d2=a, ab=ba, cac-1=a-1, ad=da, cbc-1=a2b, bd=db, dcd-1=ac-1 >
Subgroups: 756 in 158 conjugacy classes, 63 normal (25 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, 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, C42⋊C2, C22×C8, 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, C23.24D4, C2×C7⋊C8, C2×C7⋊C8, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C4○D28, C2×C7⋊D4, C22×C28, C14.D8, C14.Q16, C22×C7⋊C8, C7×C42⋊C2, C2×C4○D28, C4.(C2×D28)
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, D14, C2×C22⋊C4, C4○D8, C4×D7, D28, C7⋊D4, C22×D7, C23.24D4, D14⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, C2×D14⋊C4, D4.8D14, C4.(C2×D28)
►On 224 points
Generators in S224
(1 216 43 95)(2 96 44 217)(3 218 45 97)(4 98 46 219)(5 220 47 99)(6 100 48 221)(7 222 49 101)(8 102 50 223)(9 224 51 103)(10 104 52 197)(11 198 53 105)(12 106 54 199)(13 200 55 107)(14 108 56 201)(15 202 29 109)(16 110 30 203)(17 204 31 111)(18 112 32 205)(19 206 33 85)(20 86 34 207)(21 208 35 87)(22 88 36 209)(23 210 37 89)(24 90 38 211)(25 212 39 91)(26 92 40 213)(27 214 41 93)(28 94 42 215)(57 177 138 151)(58 152 139 178)(59 179 140 153)(60 154 113 180)(61 181 114 155)(62 156 115 182)(63 183 116 157)(64 158 117 184)(65 185 118 159)(66 160 119 186)(67 187 120 161)(68 162 121 188)(69 189 122 163)(70 164 123 190)(71 191 124 165)(72 166 125 192)(73 193 126 167)(74 168 127 194)(75 195 128 141)(76 142 129 196)(77 169 130 143)(78 144 131 170)(79 171 132 145)(80 146 133 172)(81 173 134 147)(82 148 135 174)(83 175 136 149)(84 150 137 176)
(1 15)(2 30)(3 17)(4 32)(5 19)(6 34)(7 21)(8 36)(9 23)(10 38)(11 25)(12 40)(13 27)(14 42)(16 44)(18 46)(20 48)(22 50)(24 52)(26 54)(28 56)(29 43)(31 45)(33 47)(35 49)(37 51)(39 53)(41 55)(57 124)(58 72)(59 126)(60 74)(61 128)(62 76)(63 130)(64 78)(65 132)(66 80)(67 134)(68 82)(69 136)(70 84)(71 138)(73 140)(75 114)(77 116)(79 118)(81 120)(83 122)(85 99)(86 221)(87 101)(88 223)(89 103)(90 197)(91 105)(92 199)(93 107)(94 201)(95 109)(96 203)(97 111)(98 205)(100 207)(102 209)(104 211)(106 213)(108 215)(110 217)(112 219)(113 127)(115 129)(117 131)(119 133)(121 135)(123 137)(125 139)(141 181)(142 156)(143 183)(144 158)(145 185)(146 160)(147 187)(148 162)(149 189)(150 164)(151 191)(152 166)(153 193)(154 168)(155 195)(157 169)(159 171)(161 173)(163 175)(165 177)(167 179)(170 184)(172 186)(174 188)(176 190)(178 192)(180 194)(182 196)(198 212)(200 214)(202 216)(204 218)(206 220)(208 222)(210 224)
(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)
(1 186 216 66 43 160 95 119)(2 118 96 159 44 65 217 185)(3 184 218 64 45 158 97 117)(4 116 98 157 46 63 219 183)(5 182 220 62 47 156 99 115)(6 114 100 155 48 61 221 181)(7 180 222 60 49 154 101 113)(8 140 102 153 50 59 223 179)(9 178 224 58 51 152 103 139)(10 138 104 151 52 57 197 177)(11 176 198 84 53 150 105 137)(12 136 106 149 54 83 199 175)(13 174 200 82 55 148 107 135)(14 134 108 147 56 81 201 173)(15 172 202 80 29 146 109 133)(16 132 110 145 30 79 203 171)(17 170 204 78 31 144 111 131)(18 130 112 143 32 77 205 169)(19 196 206 76 33 142 85 129)(20 128 86 141 34 75 207 195)(21 194 208 74 35 168 87 127)(22 126 88 167 36 73 209 193)(23 192 210 72 37 166 89 125)(24 124 90 165 38 71 211 191)(25 190 212 70 39 164 91 123)(26 122 92 163 40 69 213 189)(27 188 214 68 41 162 93 121)(28 120 94 161 42 67 215 187)
G:=sub<Sym(224)| (1,216,43,95)(2,96,44,217)(3,218,45,97)(4,98,46,219)(5,220,47,99)(6,100,48,221)(7,222,49,101)(8,102,50,223)(9,224,51,103)(10,104,52,197)(11,198,53,105)(12,106,54,199)(13,200,55,107)(14,108,56,201)(15,202,29,109)(16,110,30,203)(17,204,31,111)(18,112,32,205)(19,206,33,85)(20,86,34,207)(21,208,35,87)(22,88,36,209)(23,210,37,89)(24,90,38,211)(25,212,39,91)(26,92,40,213)(27,214,41,93)(28,94,42,215)(57,177,138,151)(58,152,139,178)(59,179,140,153)(60,154,113,180)(61,181,114,155)(62,156,115,182)(63,183,116,157)(64,158,117,184)(65,185,118,159)(66,160,119,186)(67,187,120,161)(68,162,121,188)(69,189,122,163)(70,164,123,190)(71,191,124,165)(72,166,125,192)(73,193,126,167)(74,168,127,194)(75,195,128,141)(76,142,129,196)(77,169,130,143)(78,144,131,170)(79,171,132,145)(80,146,133,172)(81,173,134,147)(82,148,135,174)(83,175,136,149)(84,150,137,176), (1,15)(2,30)(3,17)(4,32)(5,19)(6,34)(7,21)(8,36)(9,23)(10,38)(11,25)(12,40)(13,27)(14,42)(16,44)(18,46)(20,48)(22,50)(24,52)(26,54)(28,56)(29,43)(31,45)(33,47)(35,49)(37,51)(39,53)(41,55)(57,124)(58,72)(59,126)(60,74)(61,128)(62,76)(63,130)(64,78)(65,132)(66,80)(67,134)(68,82)(69,136)(70,84)(71,138)(73,140)(75,114)(77,116)(79,118)(81,120)(83,122)(85,99)(86,221)(87,101)(88,223)(89,103)(90,197)(91,105)(92,199)(93,107)(94,201)(95,109)(96,203)(97,111)(98,205)(100,207)(102,209)(104,211)(106,213)(108,215)(110,217)(112,219)(113,127)(115,129)(117,131)(119,133)(121,135)(123,137)(125,139)(141,181)(142,156)(143,183)(144,158)(145,185)(146,160)(147,187)(148,162)(149,189)(150,164)(151,191)(152,166)(153,193)(154,168)(155,195)(157,169)(159,171)(161,173)(163,175)(165,177)(167,179)(170,184)(172,186)(174,188)(176,190)(178,192)(180,194)(182,196)(198,212)(200,214)(202,216)(204,218)(206,220)(208,222)(210,224), (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), (1,186,216,66,43,160,95,119)(2,118,96,159,44,65,217,185)(3,184,218,64,45,158,97,117)(4,116,98,157,46,63,219,183)(5,182,220,62,47,156,99,115)(6,114,100,155,48,61,221,181)(7,180,222,60,49,154,101,113)(8,140,102,153,50,59,223,179)(9,178,224,58,51,152,103,139)(10,138,104,151,52,57,197,177)(11,176,198,84,53,150,105,137)(12,136,106,149,54,83,199,175)(13,174,200,82,55,148,107,135)(14,134,108,147,56,81,201,173)(15,172,202,80,29,146,109,133)(16,132,110,145,30,79,203,171)(17,170,204,78,31,144,111,131)(18,130,112,143,32,77,205,169)(19,196,206,76,33,142,85,129)(20,128,86,141,34,75,207,195)(21,194,208,74,35,168,87,127)(22,126,88,167,36,73,209,193)(23,192,210,72,37,166,89,125)(24,124,90,165,38,71,211,191)(25,190,212,70,39,164,91,123)(26,122,92,163,40,69,213,189)(27,188,214,68,41,162,93,121)(28,120,94,161,42,67,215,187)>;
G:=Group( (1,216,43,95)(2,96,44,217)(3,218,45,97)(4,98,46,219)(5,220,47,99)(6,100,48,221)(7,222,49,101)(8,102,50,223)(9,224,51,103)(10,104,52,197)(11,198,53,105)(12,106,54,199)(13,200,55,107)(14,108,56,201)(15,202,29,109)(16,110,30,203)(17,204,31,111)(18,112,32,205)(19,206,33,85)(20,86,34,207)(21,208,35,87)(22,88,36,209)(23,210,37,89)(24,90,38,211)(25,212,39,91)(26,92,40,213)(27,214,41,93)(28,94,42,215)(57,177,138,151)(58,152,139,178)(59,179,140,153)(60,154,113,180)(61,181,114,155)(62,156,115,182)(63,183,116,157)(64,158,117,184)(65,185,118,159)(66,160,119,186)(67,187,120,161)(68,162,121,188)(69,189,122,163)(70,164,123,190)(71,191,124,165)(72,166,125,192)(73,193,126,167)(74,168,127,194)(75,195,128,141)(76,142,129,196)(77,169,130,143)(78,144,131,170)(79,171,132,145)(80,146,133,172)(81,173,134,147)(82,148,135,174)(83,175,136,149)(84,150,137,176), (1,15)(2,30)(3,17)(4,32)(5,19)(6,34)(7,21)(8,36)(9,23)(10,38)(11,25)(12,40)(13,27)(14,42)(16,44)(18,46)(20,48)(22,50)(24,52)(26,54)(28,56)(29,43)(31,45)(33,47)(35,49)(37,51)(39,53)(41,55)(57,124)(58,72)(59,126)(60,74)(61,128)(62,76)(63,130)(64,78)(65,132)(66,80)(67,134)(68,82)(69,136)(70,84)(71,138)(73,140)(75,114)(77,116)(79,118)(81,120)(83,122)(85,99)(86,221)(87,101)(88,223)(89,103)(90,197)(91,105)(92,199)(93,107)(94,201)(95,109)(96,203)(97,111)(98,205)(100,207)(102,209)(104,211)(106,213)(108,215)(110,217)(112,219)(113,127)(115,129)(117,131)(119,133)(121,135)(123,137)(125,139)(141,181)(142,156)(143,183)(144,158)(145,185)(146,160)(147,187)(148,162)(149,189)(150,164)(151,191)(152,166)(153,193)(154,168)(155,195)(157,169)(159,171)(161,173)(163,175)(165,177)(167,179)(170,184)(172,186)(174,188)(176,190)(178,192)(180,194)(182,196)(198,212)(200,214)(202,216)(204,218)(206,220)(208,222)(210,224), (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), (1,186,216,66,43,160,95,119)(2,118,96,159,44,65,217,185)(3,184,218,64,45,158,97,117)(4,116,98,157,46,63,219,183)(5,182,220,62,47,156,99,115)(6,114,100,155,48,61,221,181)(7,180,222,60,49,154,101,113)(8,140,102,153,50,59,223,179)(9,178,224,58,51,152,103,139)(10,138,104,151,52,57,197,177)(11,176,198,84,53,150,105,137)(12,136,106,149,54,83,199,175)(13,174,200,82,55,148,107,135)(14,134,108,147,56,81,201,173)(15,172,202,80,29,146,109,133)(16,132,110,145,30,79,203,171)(17,170,204,78,31,144,111,131)(18,130,112,143,32,77,205,169)(19,196,206,76,33,142,85,129)(20,128,86,141,34,75,207,195)(21,194,208,74,35,168,87,127)(22,126,88,167,36,73,209,193)(23,192,210,72,37,166,89,125)(24,124,90,165,38,71,211,191)(25,190,212,70,39,164,91,123)(26,122,92,163,40,69,213,189)(27,188,214,68,41,162,93,121)(28,120,94,161,42,67,215,187) );
G=PermutationGroup([[(1,216,43,95),(2,96,44,217),(3,218,45,97),(4,98,46,219),(5,220,47,99),(6,100,48,221),(7,222,49,101),(8,102,50,223),(9,224,51,103),(10,104,52,197),(11,198,53,105),(12,106,54,199),(13,200,55,107),(14,108,56,201),(15,202,29,109),(16,110,30,203),(17,204,31,111),(18,112,32,205),(19,206,33,85),(20,86,34,207),(21,208,35,87),(22,88,36,209),(23,210,37,89),(24,90,38,211),(25,212,39,91),(26,92,40,213),(27,214,41,93),(28,94,42,215),(57,177,138,151),(58,152,139,178),(59,179,140,153),(60,154,113,180),(61,181,114,155),(62,156,115,182),(63,183,116,157),(64,158,117,184),(65,185,118,159),(66,160,119,186),(67,187,120,161),(68,162,121,188),(69,189,122,163),(70,164,123,190),(71,191,124,165),(72,166,125,192),(73,193,126,167),(74,168,127,194),(75,195,128,141),(76,142,129,196),(77,169,130,143),(78,144,131,170),(79,171,132,145),(80,146,133,172),(81,173,134,147),(82,148,135,174),(83,175,136,149),(84,150,137,176)], [(1,15),(2,30),(3,17),(4,32),(5,19),(6,34),(7,21),(8,36),(9,23),(10,38),(11,25),(12,40),(13,27),(14,42),(16,44),(18,46),(20,48),(22,50),(24,52),(26,54),(28,56),(29,43),(31,45),(33,47),(35,49),(37,51),(39,53),(41,55),(57,124),(58,72),(59,126),(60,74),(61,128),(62,76),(63,130),(64,78),(65,132),(66,80),(67,134),(68,82),(69,136),(70,84),(71,138),(73,140),(75,114),(77,116),(79,118),(81,120),(83,122),(85,99),(86,221),(87,101),(88,223),(89,103),(90,197),(91,105),(92,199),(93,107),(94,201),(95,109),(96,203),(97,111),(98,205),(100,207),(102,209),(104,211),(106,213),(108,215),(110,217),(112,219),(113,127),(115,129),(117,131),(119,133),(121,135),(123,137),(125,139),(141,181),(142,156),(143,183),(144,158),(145,185),(146,160),(147,187),(148,162),(149,189),(150,164),(151,191),(152,166),(153,193),(154,168),(155,195),(157,169),(159,171),(161,173),(163,175),(165,177),(167,179),(170,184),(172,186),(174,188),(176,190),(178,192),(180,194),(182,196),(198,212),(200,214),(202,216),(204,218),(206,220),(208,222),(210,224)], [(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)], [(1,186,216,66,43,160,95,119),(2,118,96,159,44,65,217,185),(3,184,218,64,45,158,97,117),(4,116,98,157,46,63,219,183),(5,182,220,62,47,156,99,115),(6,114,100,155,48,61,221,181),(7,180,222,60,49,154,101,113),(8,140,102,153,50,59,223,179),(9,178,224,58,51,152,103,139),(10,138,104,151,52,57,197,177),(11,176,198,84,53,150,105,137),(12,136,106,149,54,83,199,175),(13,174,200,82,55,148,107,135),(14,134,108,147,56,81,201,173),(15,172,202,80,29,146,109,133),(16,132,110,145,30,79,203,171),(17,170,204,78,31,144,111,131),(18,130,112,143,32,77,205,169),(19,196,206,76,33,142,85,129),(20,128,86,141,34,75,207,195),(21,194,208,74,35,168,87,127),(22,126,88,167,36,73,209,193),(23,192,210,72,37,166,89,125),(24,124,90,165,38,71,211,191),(25,190,212,70,39,164,91,123),(26,122,92,163,40,69,213,189),(27,188,214,68,41,162,93,121),(28,120,94,161,42,67,215,187)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | D14 | D14 | C4○D8 | C4×D7 | D28 | C7⋊D4 | C7⋊D4 | D4.8D14 |
| kernel | C4.(C2×D28) | C14.D8 | C14.Q16 | C22×C7⋊C8 | C7×C42⋊C2 | C2×C4○D28 | C4○D28 | C2×C28 | C22×C14 | C42⋊C2 | C4⋊C4 | C22×C4 | C14 | C2×C4 | C2×C4 | C2×C4 | C23 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 3 | 1 | 3 | 6 | 3 | 8 | 12 | 12 | 6 | 6 | 12 |
Matrix representation of C4.(C2×D28) ►in GL4(𝔽113) generated by
| 98 | 0 | 0 | 0 |
| 46 | 15 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 112 | 0 | 0 | 0 |
| 101 | 1 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 10 | 36 | 0 | 0 |
| 38 | 103 | 0 | 0 |
| 0 | 0 | 94 | 32 |
| 0 | 0 | 49 | 78 |
| 95 | 0 | 0 | 0 |
| 80 | 44 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 56 | 112 |
G:=sub<GL(4,GF(113))| [98,46,0,0,0,15,0,0,0,0,1,0,0,0,0,1],[112,101,0,0,0,1,0,0,0,0,112,0,0,0,0,112],[10,38,0,0,36,103,0,0,0,0,94,49,0,0,32,78],[95,80,0,0,0,44,0,0,0,0,1,56,0,0,0,112] >;
C4.(C2×D28) in GAP, Magma, Sage, TeX
C_4.(C_2\times D_{28}) % in TeX
G:=Group("C4.(C2xD28)"); // GroupNames label
G:=SmallGroup(448,536);
// by ID
G=gap.SmallGroup(448,536);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,422,58,1684,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^2=c^28=1,d^2=a,a*b=b*a,c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^2*b,b*d=d*b,d*c*d^-1=a*c^-1>;
// generators/relations