metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4).45D28, (C2×C28).56D4, (C22×D7).5Q8, C22.51(Q8×D7), (C2×Dic7).62D4, C22.250(D4×D7), C14.63(C4⋊D4), C2.26(C4⋊D28), C2.11(C28⋊7D4), C7⋊3(C23.Q8), C2.9(D14⋊3Q8), C22.130(C2×D28), (C22×C4).106D14, C14.51(C22⋊Q8), C14.C42⋊21C2, C2.23(D14⋊Q8), C2.17(D14⋊2Q8), (C22×C28).69C22, (C23×D7).23C22, C23.383(C22×D7), C14.30(C42⋊2C2), C2.13(Dic7⋊D4), C22.111(C4○D28), (C22×C14).358C23, C22.54(Q8⋊2D7), C22.105(D4⋊2D7), (C22×Dic7).63C22, (C2×C4⋊C4)⋊12D7, (C14×C4⋊C4)⋊23C2, (C2×C4⋊Dic7)⋊14C2, (C2×C14).86(C2×Q8), (C2×Dic7⋊C4)⋊42C2, (C2×D14⋊C4).24C2, (C2×C14).338(C2×D4), (C2×C4).44(C7⋊D4), C2.15(C4⋊C4⋊D7), (C2×C14).87(C4○D4), C22.143(C2×C7⋊D4), SmallGroup(448,528)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4).45D28
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd=ab-1, dcd=ac-1 >
Subgroups: 996 in 186 conjugacy classes, 63 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, D14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.Q8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C22×Dic7, C22×C28, C23×D7, C14.C42, C2×Dic7⋊C4, C2×C4⋊Dic7, C2×D14⋊C4, C14×C4⋊C4, (C2×C4).45D28
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C4⋊D4, C22⋊Q8, C42⋊2C2, D28, C7⋊D4, C22×D7, C23.Q8, C2×D28, C4○D28, D4×D7, D4⋊2D7, Q8×D7, Q8⋊2D7, C2×C7⋊D4, C4⋊D28, D14⋊Q8, D14⋊2Q8, C4⋊C4⋊D7, C28⋊7D4, Dic7⋊D4, D14⋊3Q8, (C2×C4).45D28
►On 224 points
Generators in S224
(1 49)(2 50)(3 51)(4 52)(5 53)(6 54)(7 55)(8 56)(9 29)(10 30)(11 31)(12 32)(13 33)(14 34)(15 35)(16 36)(17 37)(18 38)(19 39)(20 40)(21 41)(22 42)(23 43)(24 44)(25 45)(26 46)(27 47)(28 48)(57 113)(58 114)(59 115)(60 116)(61 117)(62 118)(63 119)(64 120)(65 121)(66 122)(67 123)(68 124)(69 125)(70 126)(71 127)(72 128)(73 129)(74 130)(75 131)(76 132)(77 133)(78 134)(79 135)(80 136)(81 137)(82 138)(83 139)(84 140)(85 205)(86 206)(87 207)(88 208)(89 209)(90 210)(91 211)(92 212)(93 213)(94 214)(95 215)(96 216)(97 217)(98 218)(99 219)(100 220)(101 221)(102 222)(103 223)(104 224)(105 197)(106 198)(107 199)(108 200)(109 201)(110 202)(111 203)(112 204)(141 177)(142 178)(143 179)(144 180)(145 181)(146 182)(147 183)(148 184)(149 185)(150 186)(151 187)(152 188)(153 189)(154 190)(155 191)(156 192)(157 193)(158 194)(159 195)(160 196)(161 169)(162 170)(163 171)(164 172)(165 173)(166 174)(167 175)(168 176)
(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)
(1 111 133 189)(2 110 134 188)(3 109 135 187)(4 108 136 186)(5 107 137 185)(6 106 138 184)(7 105 139 183)(8 104 140 182)(9 103 113 181)(10 102 114 180)(11 101 115 179)(12 100 116 178)(13 99 117 177)(14 98 118 176)(15 97 119 175)(16 96 120 174)(17 95 121 173)(18 94 122 172)(19 93 123 171)(20 92 124 170)(21 91 125 169)(22 90 126 196)(23 89 127 195)(24 88 128 194)(25 87 129 193)(26 86 130 192)(27 85 131 191)(28 112 132 190)(29 223 57 145)(30 222 58 144)(31 221 59 143)(32 220 60 142)(33 219 61 141)(34 218 62 168)(35 217 63 167)(36 216 64 166)(37 215 65 165)(38 214 66 164)(39 213 67 163)(40 212 68 162)(41 211 69 161)(42 210 70 160)(43 209 71 159)(44 208 72 158)(45 207 73 157)(46 206 74 156)(47 205 75 155)(48 204 76 154)(49 203 77 153)(50 202 78 152)(51 201 79 151)(52 200 80 150)(53 199 81 149)(54 198 82 148)(55 197 83 147)(56 224 84 146)
(1 49)(2 28)(3 47)(4 26)(5 45)(6 24)(7 43)(8 22)(9 41)(10 20)(11 39)(12 18)(13 37)(14 16)(15 35)(17 33)(19 31)(21 29)(23 55)(25 53)(27 51)(30 40)(32 38)(34 36)(42 56)(44 54)(46 52)(48 50)(57 125)(58 68)(59 123)(60 66)(61 121)(62 64)(63 119)(65 117)(67 115)(69 113)(70 84)(71 139)(72 82)(73 137)(74 80)(75 135)(76 78)(77 133)(79 131)(81 129)(83 127)(85 187)(86 150)(87 185)(88 148)(89 183)(90 146)(91 181)(92 144)(93 179)(94 142)(95 177)(96 168)(97 175)(98 166)(99 173)(100 164)(101 171)(102 162)(103 169)(104 160)(105 195)(106 158)(107 193)(108 156)(109 191)(110 154)(111 189)(112 152)(114 124)(116 122)(118 120)(126 140)(128 138)(130 136)(132 134)(141 215)(143 213)(145 211)(147 209)(149 207)(151 205)(153 203)(155 201)(157 199)(159 197)(161 223)(163 221)(165 219)(167 217)(170 222)(172 220)(174 218)(176 216)(178 214)(180 212)(182 210)(184 208)(186 206)(188 204)(190 202)(192 200)(194 198)(196 224)
G:=sub<Sym(224)| (1,49)(2,50)(3,51)(4,52)(5,53)(6,54)(7,55)(8,56)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(57,113)(58,114)(59,115)(60,116)(61,117)(62,118)(63,119)(64,120)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,129)(74,130)(75,131)(76,132)(77,133)(78,134)(79,135)(80,136)(81,137)(82,138)(83,139)(84,140)(85,205)(86,206)(87,207)(88,208)(89,209)(90,210)(91,211)(92,212)(93,213)(94,214)(95,215)(96,216)(97,217)(98,218)(99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,197)(106,198)(107,199)(108,200)(109,201)(110,202)(111,203)(112,204)(141,177)(142,178)(143,179)(144,180)(145,181)(146,182)(147,183)(148,184)(149,185)(150,186)(151,187)(152,188)(153,189)(154,190)(155,191)(156,192)(157,193)(158,194)(159,195)(160,196)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176), (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), (1,111,133,189)(2,110,134,188)(3,109,135,187)(4,108,136,186)(5,107,137,185)(6,106,138,184)(7,105,139,183)(8,104,140,182)(9,103,113,181)(10,102,114,180)(11,101,115,179)(12,100,116,178)(13,99,117,177)(14,98,118,176)(15,97,119,175)(16,96,120,174)(17,95,121,173)(18,94,122,172)(19,93,123,171)(20,92,124,170)(21,91,125,169)(22,90,126,196)(23,89,127,195)(24,88,128,194)(25,87,129,193)(26,86,130,192)(27,85,131,191)(28,112,132,190)(29,223,57,145)(30,222,58,144)(31,221,59,143)(32,220,60,142)(33,219,61,141)(34,218,62,168)(35,217,63,167)(36,216,64,166)(37,215,65,165)(38,214,66,164)(39,213,67,163)(40,212,68,162)(41,211,69,161)(42,210,70,160)(43,209,71,159)(44,208,72,158)(45,207,73,157)(46,206,74,156)(47,205,75,155)(48,204,76,154)(49,203,77,153)(50,202,78,152)(51,201,79,151)(52,200,80,150)(53,199,81,149)(54,198,82,148)(55,197,83,147)(56,224,84,146), (1,49)(2,28)(3,47)(4,26)(5,45)(6,24)(7,43)(8,22)(9,41)(10,20)(11,39)(12,18)(13,37)(14,16)(15,35)(17,33)(19,31)(21,29)(23,55)(25,53)(27,51)(30,40)(32,38)(34,36)(42,56)(44,54)(46,52)(48,50)(57,125)(58,68)(59,123)(60,66)(61,121)(62,64)(63,119)(65,117)(67,115)(69,113)(70,84)(71,139)(72,82)(73,137)(74,80)(75,135)(76,78)(77,133)(79,131)(81,129)(83,127)(85,187)(86,150)(87,185)(88,148)(89,183)(90,146)(91,181)(92,144)(93,179)(94,142)(95,177)(96,168)(97,175)(98,166)(99,173)(100,164)(101,171)(102,162)(103,169)(104,160)(105,195)(106,158)(107,193)(108,156)(109,191)(110,154)(111,189)(112,152)(114,124)(116,122)(118,120)(126,140)(128,138)(130,136)(132,134)(141,215)(143,213)(145,211)(147,209)(149,207)(151,205)(153,203)(155,201)(157,199)(159,197)(161,223)(163,221)(165,219)(167,217)(170,222)(172,220)(174,218)(176,216)(178,214)(180,212)(182,210)(184,208)(186,206)(188,204)(190,202)(192,200)(194,198)(196,224)>;
G:=Group( (1,49)(2,50)(3,51)(4,52)(5,53)(6,54)(7,55)(8,56)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(57,113)(58,114)(59,115)(60,116)(61,117)(62,118)(63,119)(64,120)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,129)(74,130)(75,131)(76,132)(77,133)(78,134)(79,135)(80,136)(81,137)(82,138)(83,139)(84,140)(85,205)(86,206)(87,207)(88,208)(89,209)(90,210)(91,211)(92,212)(93,213)(94,214)(95,215)(96,216)(97,217)(98,218)(99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,197)(106,198)(107,199)(108,200)(109,201)(110,202)(111,203)(112,204)(141,177)(142,178)(143,179)(144,180)(145,181)(146,182)(147,183)(148,184)(149,185)(150,186)(151,187)(152,188)(153,189)(154,190)(155,191)(156,192)(157,193)(158,194)(159,195)(160,196)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176), (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), (1,111,133,189)(2,110,134,188)(3,109,135,187)(4,108,136,186)(5,107,137,185)(6,106,138,184)(7,105,139,183)(8,104,140,182)(9,103,113,181)(10,102,114,180)(11,101,115,179)(12,100,116,178)(13,99,117,177)(14,98,118,176)(15,97,119,175)(16,96,120,174)(17,95,121,173)(18,94,122,172)(19,93,123,171)(20,92,124,170)(21,91,125,169)(22,90,126,196)(23,89,127,195)(24,88,128,194)(25,87,129,193)(26,86,130,192)(27,85,131,191)(28,112,132,190)(29,223,57,145)(30,222,58,144)(31,221,59,143)(32,220,60,142)(33,219,61,141)(34,218,62,168)(35,217,63,167)(36,216,64,166)(37,215,65,165)(38,214,66,164)(39,213,67,163)(40,212,68,162)(41,211,69,161)(42,210,70,160)(43,209,71,159)(44,208,72,158)(45,207,73,157)(46,206,74,156)(47,205,75,155)(48,204,76,154)(49,203,77,153)(50,202,78,152)(51,201,79,151)(52,200,80,150)(53,199,81,149)(54,198,82,148)(55,197,83,147)(56,224,84,146), (1,49)(2,28)(3,47)(4,26)(5,45)(6,24)(7,43)(8,22)(9,41)(10,20)(11,39)(12,18)(13,37)(14,16)(15,35)(17,33)(19,31)(21,29)(23,55)(25,53)(27,51)(30,40)(32,38)(34,36)(42,56)(44,54)(46,52)(48,50)(57,125)(58,68)(59,123)(60,66)(61,121)(62,64)(63,119)(65,117)(67,115)(69,113)(70,84)(71,139)(72,82)(73,137)(74,80)(75,135)(76,78)(77,133)(79,131)(81,129)(83,127)(85,187)(86,150)(87,185)(88,148)(89,183)(90,146)(91,181)(92,144)(93,179)(94,142)(95,177)(96,168)(97,175)(98,166)(99,173)(100,164)(101,171)(102,162)(103,169)(104,160)(105,195)(106,158)(107,193)(108,156)(109,191)(110,154)(111,189)(112,152)(114,124)(116,122)(118,120)(126,140)(128,138)(130,136)(132,134)(141,215)(143,213)(145,211)(147,209)(149,207)(151,205)(153,203)(155,201)(157,199)(159,197)(161,223)(163,221)(165,219)(167,217)(170,222)(172,220)(174,218)(176,216)(178,214)(180,212)(182,210)(184,208)(186,206)(188,204)(190,202)(192,200)(194,198)(196,224) );
G=PermutationGroup([[(1,49),(2,50),(3,51),(4,52),(5,53),(6,54),(7,55),(8,56),(9,29),(10,30),(11,31),(12,32),(13,33),(14,34),(15,35),(16,36),(17,37),(18,38),(19,39),(20,40),(21,41),(22,42),(23,43),(24,44),(25,45),(26,46),(27,47),(28,48),(57,113),(58,114),(59,115),(60,116),(61,117),(62,118),(63,119),(64,120),(65,121),(66,122),(67,123),(68,124),(69,125),(70,126),(71,127),(72,128),(73,129),(74,130),(75,131),(76,132),(77,133),(78,134),(79,135),(80,136),(81,137),(82,138),(83,139),(84,140),(85,205),(86,206),(87,207),(88,208),(89,209),(90,210),(91,211),(92,212),(93,213),(94,214),(95,215),(96,216),(97,217),(98,218),(99,219),(100,220),(101,221),(102,222),(103,223),(104,224),(105,197),(106,198),(107,199),(108,200),(109,201),(110,202),(111,203),(112,204),(141,177),(142,178),(143,179),(144,180),(145,181),(146,182),(147,183),(148,184),(149,185),(150,186),(151,187),(152,188),(153,189),(154,190),(155,191),(156,192),(157,193),(158,194),(159,195),(160,196),(161,169),(162,170),(163,171),(164,172),(165,173),(166,174),(167,175),(168,176)], [(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)], [(1,111,133,189),(2,110,134,188),(3,109,135,187),(4,108,136,186),(5,107,137,185),(6,106,138,184),(7,105,139,183),(8,104,140,182),(9,103,113,181),(10,102,114,180),(11,101,115,179),(12,100,116,178),(13,99,117,177),(14,98,118,176),(15,97,119,175),(16,96,120,174),(17,95,121,173),(18,94,122,172),(19,93,123,171),(20,92,124,170),(21,91,125,169),(22,90,126,196),(23,89,127,195),(24,88,128,194),(25,87,129,193),(26,86,130,192),(27,85,131,191),(28,112,132,190),(29,223,57,145),(30,222,58,144),(31,221,59,143),(32,220,60,142),(33,219,61,141),(34,218,62,168),(35,217,63,167),(36,216,64,166),(37,215,65,165),(38,214,66,164),(39,213,67,163),(40,212,68,162),(41,211,69,161),(42,210,70,160),(43,209,71,159),(44,208,72,158),(45,207,73,157),(46,206,74,156),(47,205,75,155),(48,204,76,154),(49,203,77,153),(50,202,78,152),(51,201,79,151),(52,200,80,150),(53,199,81,149),(54,198,82,148),(55,197,83,147),(56,224,84,146)], [(1,49),(2,28),(3,47),(4,26),(5,45),(6,24),(7,43),(8,22),(9,41),(10,20),(11,39),(12,18),(13,37),(14,16),(15,35),(17,33),(19,31),(21,29),(23,55),(25,53),(27,51),(30,40),(32,38),(34,36),(42,56),(44,54),(46,52),(48,50),(57,125),(58,68),(59,123),(60,66),(61,121),(62,64),(63,119),(65,117),(67,115),(69,113),(70,84),(71,139),(72,82),(73,137),(74,80),(75,135),(76,78),(77,133),(79,131),(81,129),(83,127),(85,187),(86,150),(87,185),(88,148),(89,183),(90,146),(91,181),(92,144),(93,179),(94,142),(95,177),(96,168),(97,175),(98,166),(99,173),(100,164),(101,171),(102,162),(103,169),(104,160),(105,195),(106,158),(107,193),(108,156),(109,191),(110,154),(111,189),(112,152),(114,124),(116,122),(118,120),(126,140),(128,138),(130,136),(132,134),(141,215),(143,213),(145,211),(147,209),(149,207),(151,205),(153,203),(155,201),(157,199),(159,197),(161,223),(163,221),(165,219),(167,217),(170,222),(172,220),(174,218),(176,216),(178,214),(180,212),(182,210),(184,208),(186,206),(188,204),(190,202),(192,200),(194,198),(196,224)]])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | ··· | 4F | 4G | ··· | 4L | 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 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | + | - | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | Q8 | D7 | C4○D4 | D14 | D28 | C7⋊D4 | C4○D28 | D4×D7 | D4⋊2D7 | Q8×D7 | Q8⋊2D7 |
| kernel | (C2×C4).45D28 | C14.C42 | C2×Dic7⋊C4 | C2×C4⋊Dic7 | C2×D14⋊C4 | C14×C4⋊C4 | C2×Dic7 | C2×C28 | C22×D7 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 1 | 3 | 1 | 2 | 4 | 2 | 3 | 6 | 9 | 12 | 12 | 12 | 3 | 3 | 3 | 3 |
Matrix representation of (C2×C4).45D28 ►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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 14 | 8 | 0 | 0 | 0 | 0 |
| 8 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 24 | 0 | 0 |
| 0 | 0 | 5 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 5 |
| 0 | 0 | 0 | 0 | 24 | 17 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 3 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 13 |
| 0 | 0 | 0 | 0 | 27 | 5 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 3 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 3 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[14,8,0,0,0,0,8,15,0,0,0,0,0,0,27,5,0,0,0,0,24,12,0,0,0,0,0,0,2,24,0,0,0,0,5,17],[0,1,0,0,0,0,28,0,0,0,0,0,0,0,1,3,0,0,0,0,0,28,0,0,0,0,0,0,24,27,0,0,0,0,13,5],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,3,0,0,0,0,0,28,0,0,0,0,0,0,1,3,0,0,0,0,0,28] >;
(C2×C4).45D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)._{45}D_{28} % in TeX
G:=Group("(C2xC4).45D28"); // GroupNames label
G:=SmallGroup(448,528);
// by ID
G=gap.SmallGroup(448,528);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,387,184,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d=a*b^-1,d*c*d=a*c^-1>;
// generators/relations