direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C28.23D4, (C2×Q8)⋊29D14, (C22×Q8)⋊6D7, (C2×C28).215D4, C28.259(C2×D4), D14⋊C4⋊74C22, C14⋊4(C4.4D4), (Q8×C14)⋊36C22, (C2×C28).646C23, (C2×C14).306C24, (C4×Dic7)⋊69C22, (C22×D28).19C2, C14.154(C22×D4), (C22×C4).385D14, (C2×D28).278C22, (C23×D7).78C22, C23.342(C22×D7), C22.317(C23×D7), (C22×C14).424C23, (C22×C28).439C22, C22.40(Q8⋊2D7), (C2×Dic7).289C23, (C22×D7).133C23, (C22×Dic7).234C22, (Q8×C2×C14)⋊5C2, C7⋊5(C2×C4.4D4), (C2×C4×Dic7)⋊13C2, C4.28(C2×C7⋊D4), (C2×D14⋊C4)⋊43C2, C14.128(C2×C4○D4), (C2×C14).589(C2×D4), C2.35(C2×Q8⋊2D7), C2.27(C22×C7⋊D4), (C2×C4).157(C7⋊D4), (C2×C4).243(C22×D7), C22.117(C2×C7⋊D4), (C2×C14).201(C4○D4), SmallGroup(448,1267)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C28.23D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b13, dbd=b-1, dcd=b14c-1 >
Subgroups: 1652 in 330 conjugacy classes, 127 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, C24, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C4.4D4, C22×D4, C22×Q8, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C22×C14, C2×C4.4D4, C4×Dic7, D14⋊C4, C2×D28, C2×D28, C22×Dic7, C22×C28, C22×C28, Q8×C14, Q8×C14, C23×D7, C2×C4×Dic7, C2×D14⋊C4, C28.23D4, C22×D28, Q8×C2×C14, C2×C28.23D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C4.4D4, C22×D4, C2×C4○D4, C7⋊D4, C22×D7, C2×C4.4D4, Q8⋊2D7, C2×C7⋊D4, C23×D7, C28.23D4, C2×Q8⋊2D7, C22×C7⋊D4, C2×C28.23D4
►On 224 points
Generators in S224
(1 182)(2 183)(3 184)(4 185)(5 186)(6 187)(7 188)(8 189)(9 190)(10 191)(11 192)(12 193)(13 194)(14 195)(15 196)(16 169)(17 170)(18 171)(19 172)(20 173)(21 174)(22 175)(23 176)(24 177)(25 178)(26 179)(27 180)(28 181)(29 127)(30 128)(31 129)(32 130)(33 131)(34 132)(35 133)(36 134)(37 135)(38 136)(39 137)(40 138)(41 139)(42 140)(43 113)(44 114)(45 115)(46 116)(47 117)(48 118)(49 119)(50 120)(51 121)(52 122)(53 123)(54 124)(55 125)(56 126)(57 201)(58 202)(59 203)(60 204)(61 205)(62 206)(63 207)(64 208)(65 209)(66 210)(67 211)(68 212)(69 213)(70 214)(71 215)(72 216)(73 217)(74 218)(75 219)(76 220)(77 221)(78 222)(79 223)(80 224)(81 197)(82 198)(83 199)(84 200)(85 143)(86 144)(87 145)(88 146)(89 147)(90 148)(91 149)(92 150)(93 151)(94 152)(95 153)(96 154)(97 155)(98 156)(99 157)(100 158)(101 159)(102 160)(103 161)(104 162)(105 163)(106 164)(107 165)(108 166)(109 167)(110 168)(111 141)(112 142)
(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)
(1 161 80 53)(2 146 81 38)(3 159 82 51)(4 144 83 36)(5 157 84 49)(6 142 57 34)(7 155 58 47)(8 168 59 32)(9 153 60 45)(10 166 61 30)(11 151 62 43)(12 164 63 56)(13 149 64 41)(14 162 65 54)(15 147 66 39)(16 160 67 52)(17 145 68 37)(18 158 69 50)(19 143 70 35)(20 156 71 48)(21 141 72 33)(22 154 73 46)(23 167 74 31)(24 152 75 44)(25 165 76 29)(26 150 77 42)(27 163 78 55)(28 148 79 40)(85 214 133 172)(86 199 134 185)(87 212 135 170)(88 197 136 183)(89 210 137 196)(90 223 138 181)(91 208 139 194)(92 221 140 179)(93 206 113 192)(94 219 114 177)(95 204 115 190)(96 217 116 175)(97 202 117 188)(98 215 118 173)(99 200 119 186)(100 213 120 171)(101 198 121 184)(102 211 122 169)(103 224 123 182)(104 209 124 195)(105 222 125 180)(106 207 126 193)(107 220 127 178)(108 205 128 191)(109 218 129 176)(110 203 130 189)(111 216 131 174)(112 201 132 187)
(1 203)(2 202)(3 201)(4 200)(5 199)(6 198)(7 197)(8 224)(9 223)(10 222)(11 221)(12 220)(13 219)(14 218)(15 217)(16 216)(17 215)(18 214)(19 213)(20 212)(21 211)(22 210)(23 209)(24 208)(25 207)(26 206)(27 205)(28 204)(29 140)(30 139)(31 138)(32 137)(33 136)(34 135)(35 134)(36 133)(37 132)(38 131)(39 130)(40 129)(41 128)(42 127)(43 126)(44 125)(45 124)(46 123)(47 122)(48 121)(49 120)(50 119)(51 118)(52 117)(53 116)(54 115)(55 114)(56 113)(57 184)(58 183)(59 182)(60 181)(61 180)(62 179)(63 178)(64 177)(65 176)(66 175)(67 174)(68 173)(69 172)(70 171)(71 170)(72 169)(73 196)(74 195)(75 194)(76 193)(77 192)(78 191)(79 190)(80 189)(81 188)(82 187)(83 186)(84 185)(85 144)(86 143)(87 142)(88 141)(89 168)(90 167)(91 166)(92 165)(93 164)(94 163)(95 162)(96 161)(97 160)(98 159)(99 158)(100 157)(101 156)(102 155)(103 154)(104 153)(105 152)(106 151)(107 150)(108 149)(109 148)(110 147)(111 146)(112 145)
G:=sub<Sym(224)| (1,182)(2,183)(3,184)(4,185)(5,186)(6,187)(7,188)(8,189)(9,190)(10,191)(11,192)(12,193)(13,194)(14,195)(15,196)(16,169)(17,170)(18,171)(19,172)(20,173)(21,174)(22,175)(23,176)(24,177)(25,178)(26,179)(27,180)(28,181)(29,127)(30,128)(31,129)(32,130)(33,131)(34,132)(35,133)(36,134)(37,135)(38,136)(39,137)(40,138)(41,139)(42,140)(43,113)(44,114)(45,115)(46,116)(47,117)(48,118)(49,119)(50,120)(51,121)(52,122)(53,123)(54,124)(55,125)(56,126)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,207)(64,208)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,217)(74,218)(75,219)(76,220)(77,221)(78,222)(79,223)(80,224)(81,197)(82,198)(83,199)(84,200)(85,143)(86,144)(87,145)(88,146)(89,147)(90,148)(91,149)(92,150)(93,151)(94,152)(95,153)(96,154)(97,155)(98,156)(99,157)(100,158)(101,159)(102,160)(103,161)(104,162)(105,163)(106,164)(107,165)(108,166)(109,167)(110,168)(111,141)(112,142), (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), (1,161,80,53)(2,146,81,38)(3,159,82,51)(4,144,83,36)(5,157,84,49)(6,142,57,34)(7,155,58,47)(8,168,59,32)(9,153,60,45)(10,166,61,30)(11,151,62,43)(12,164,63,56)(13,149,64,41)(14,162,65,54)(15,147,66,39)(16,160,67,52)(17,145,68,37)(18,158,69,50)(19,143,70,35)(20,156,71,48)(21,141,72,33)(22,154,73,46)(23,167,74,31)(24,152,75,44)(25,165,76,29)(26,150,77,42)(27,163,78,55)(28,148,79,40)(85,214,133,172)(86,199,134,185)(87,212,135,170)(88,197,136,183)(89,210,137,196)(90,223,138,181)(91,208,139,194)(92,221,140,179)(93,206,113,192)(94,219,114,177)(95,204,115,190)(96,217,116,175)(97,202,117,188)(98,215,118,173)(99,200,119,186)(100,213,120,171)(101,198,121,184)(102,211,122,169)(103,224,123,182)(104,209,124,195)(105,222,125,180)(106,207,126,193)(107,220,127,178)(108,205,128,191)(109,218,129,176)(110,203,130,189)(111,216,131,174)(112,201,132,187), (1,203)(2,202)(3,201)(4,200)(5,199)(6,198)(7,197)(8,224)(9,223)(10,222)(11,221)(12,220)(13,219)(14,218)(15,217)(16,216)(17,215)(18,214)(19,213)(20,212)(21,211)(22,210)(23,209)(24,208)(25,207)(26,206)(27,205)(28,204)(29,140)(30,139)(31,138)(32,137)(33,136)(34,135)(35,134)(36,133)(37,132)(38,131)(39,130)(40,129)(41,128)(42,127)(43,126)(44,125)(45,124)(46,123)(47,122)(48,121)(49,120)(50,119)(51,118)(52,117)(53,116)(54,115)(55,114)(56,113)(57,184)(58,183)(59,182)(60,181)(61,180)(62,179)(63,178)(64,177)(65,176)(66,175)(67,174)(68,173)(69,172)(70,171)(71,170)(72,169)(73,196)(74,195)(75,194)(76,193)(77,192)(78,191)(79,190)(80,189)(81,188)(82,187)(83,186)(84,185)(85,144)(86,143)(87,142)(88,141)(89,168)(90,167)(91,166)(92,165)(93,164)(94,163)(95,162)(96,161)(97,160)(98,159)(99,158)(100,157)(101,156)(102,155)(103,154)(104,153)(105,152)(106,151)(107,150)(108,149)(109,148)(110,147)(111,146)(112,145)>;
G:=Group( (1,182)(2,183)(3,184)(4,185)(5,186)(6,187)(7,188)(8,189)(9,190)(10,191)(11,192)(12,193)(13,194)(14,195)(15,196)(16,169)(17,170)(18,171)(19,172)(20,173)(21,174)(22,175)(23,176)(24,177)(25,178)(26,179)(27,180)(28,181)(29,127)(30,128)(31,129)(32,130)(33,131)(34,132)(35,133)(36,134)(37,135)(38,136)(39,137)(40,138)(41,139)(42,140)(43,113)(44,114)(45,115)(46,116)(47,117)(48,118)(49,119)(50,120)(51,121)(52,122)(53,123)(54,124)(55,125)(56,126)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,207)(64,208)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,217)(74,218)(75,219)(76,220)(77,221)(78,222)(79,223)(80,224)(81,197)(82,198)(83,199)(84,200)(85,143)(86,144)(87,145)(88,146)(89,147)(90,148)(91,149)(92,150)(93,151)(94,152)(95,153)(96,154)(97,155)(98,156)(99,157)(100,158)(101,159)(102,160)(103,161)(104,162)(105,163)(106,164)(107,165)(108,166)(109,167)(110,168)(111,141)(112,142), (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), (1,161,80,53)(2,146,81,38)(3,159,82,51)(4,144,83,36)(5,157,84,49)(6,142,57,34)(7,155,58,47)(8,168,59,32)(9,153,60,45)(10,166,61,30)(11,151,62,43)(12,164,63,56)(13,149,64,41)(14,162,65,54)(15,147,66,39)(16,160,67,52)(17,145,68,37)(18,158,69,50)(19,143,70,35)(20,156,71,48)(21,141,72,33)(22,154,73,46)(23,167,74,31)(24,152,75,44)(25,165,76,29)(26,150,77,42)(27,163,78,55)(28,148,79,40)(85,214,133,172)(86,199,134,185)(87,212,135,170)(88,197,136,183)(89,210,137,196)(90,223,138,181)(91,208,139,194)(92,221,140,179)(93,206,113,192)(94,219,114,177)(95,204,115,190)(96,217,116,175)(97,202,117,188)(98,215,118,173)(99,200,119,186)(100,213,120,171)(101,198,121,184)(102,211,122,169)(103,224,123,182)(104,209,124,195)(105,222,125,180)(106,207,126,193)(107,220,127,178)(108,205,128,191)(109,218,129,176)(110,203,130,189)(111,216,131,174)(112,201,132,187), (1,203)(2,202)(3,201)(4,200)(5,199)(6,198)(7,197)(8,224)(9,223)(10,222)(11,221)(12,220)(13,219)(14,218)(15,217)(16,216)(17,215)(18,214)(19,213)(20,212)(21,211)(22,210)(23,209)(24,208)(25,207)(26,206)(27,205)(28,204)(29,140)(30,139)(31,138)(32,137)(33,136)(34,135)(35,134)(36,133)(37,132)(38,131)(39,130)(40,129)(41,128)(42,127)(43,126)(44,125)(45,124)(46,123)(47,122)(48,121)(49,120)(50,119)(51,118)(52,117)(53,116)(54,115)(55,114)(56,113)(57,184)(58,183)(59,182)(60,181)(61,180)(62,179)(63,178)(64,177)(65,176)(66,175)(67,174)(68,173)(69,172)(70,171)(71,170)(72,169)(73,196)(74,195)(75,194)(76,193)(77,192)(78,191)(79,190)(80,189)(81,188)(82,187)(83,186)(84,185)(85,144)(86,143)(87,142)(88,141)(89,168)(90,167)(91,166)(92,165)(93,164)(94,163)(95,162)(96,161)(97,160)(98,159)(99,158)(100,157)(101,156)(102,155)(103,154)(104,153)(105,152)(106,151)(107,150)(108,149)(109,148)(110,147)(111,146)(112,145) );
G=PermutationGroup([[(1,182),(2,183),(3,184),(4,185),(5,186),(6,187),(7,188),(8,189),(9,190),(10,191),(11,192),(12,193),(13,194),(14,195),(15,196),(16,169),(17,170),(18,171),(19,172),(20,173),(21,174),(22,175),(23,176),(24,177),(25,178),(26,179),(27,180),(28,181),(29,127),(30,128),(31,129),(32,130),(33,131),(34,132),(35,133),(36,134),(37,135),(38,136),(39,137),(40,138),(41,139),(42,140),(43,113),(44,114),(45,115),(46,116),(47,117),(48,118),(49,119),(50,120),(51,121),(52,122),(53,123),(54,124),(55,125),(56,126),(57,201),(58,202),(59,203),(60,204),(61,205),(62,206),(63,207),(64,208),(65,209),(66,210),(67,211),(68,212),(69,213),(70,214),(71,215),(72,216),(73,217),(74,218),(75,219),(76,220),(77,221),(78,222),(79,223),(80,224),(81,197),(82,198),(83,199),(84,200),(85,143),(86,144),(87,145),(88,146),(89,147),(90,148),(91,149),(92,150),(93,151),(94,152),(95,153),(96,154),(97,155),(98,156),(99,157),(100,158),(101,159),(102,160),(103,161),(104,162),(105,163),(106,164),(107,165),(108,166),(109,167),(110,168),(111,141),(112,142)], [(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)], [(1,161,80,53),(2,146,81,38),(3,159,82,51),(4,144,83,36),(5,157,84,49),(6,142,57,34),(7,155,58,47),(8,168,59,32),(9,153,60,45),(10,166,61,30),(11,151,62,43),(12,164,63,56),(13,149,64,41),(14,162,65,54),(15,147,66,39),(16,160,67,52),(17,145,68,37),(18,158,69,50),(19,143,70,35),(20,156,71,48),(21,141,72,33),(22,154,73,46),(23,167,74,31),(24,152,75,44),(25,165,76,29),(26,150,77,42),(27,163,78,55),(28,148,79,40),(85,214,133,172),(86,199,134,185),(87,212,135,170),(88,197,136,183),(89,210,137,196),(90,223,138,181),(91,208,139,194),(92,221,140,179),(93,206,113,192),(94,219,114,177),(95,204,115,190),(96,217,116,175),(97,202,117,188),(98,215,118,173),(99,200,119,186),(100,213,120,171),(101,198,121,184),(102,211,122,169),(103,224,123,182),(104,209,124,195),(105,222,125,180),(106,207,126,193),(107,220,127,178),(108,205,128,191),(109,218,129,176),(110,203,130,189),(111,216,131,174),(112,201,132,187)], [(1,203),(2,202),(3,201),(4,200),(5,199),(6,198),(7,197),(8,224),(9,223),(10,222),(11,221),(12,220),(13,219),(14,218),(15,217),(16,216),(17,215),(18,214),(19,213),(20,212),(21,211),(22,210),(23,209),(24,208),(25,207),(26,206),(27,205),(28,204),(29,140),(30,139),(31,138),(32,137),(33,136),(34,135),(35,134),(36,133),(37,132),(38,131),(39,130),(40,129),(41,128),(42,127),(43,126),(44,125),(45,124),(46,123),(47,122),(48,121),(49,120),(50,119),(51,118),(52,117),(53,116),(54,115),(55,114),(56,113),(57,184),(58,183),(59,182),(60,181),(61,180),(62,179),(63,178),(64,177),(65,176),(66,175),(67,174),(68,173),(69,172),(70,171),(71,170),(72,169),(73,196),(74,195),(75,194),(76,193),(77,192),(78,191),(79,190),(80,189),(81,188),(82,187),(83,186),(84,185),(85,144),(86,143),(87,142),(88,141),(89,168),(90,167),(91,166),(92,165),(93,164),(94,163),(95,162),(96,161),(97,160),(98,159),(99,158),(100,157),(101,156),(102,155),(103,154),(104,153),(105,152),(106,151),(107,150),(108,149),(109,148),(110,147),(111,146),(112,145)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | C7⋊D4 | Q8⋊2D7 |
| kernel | C2×C28.23D4 | C2×C4×Dic7 | C2×D14⋊C4 | C28.23D4 | C22×D28 | Q8×C2×C14 | C2×C28 | C22×Q8 | C2×C14 | C22×C4 | C2×Q8 | C2×C4 | C22 |
| # reps | 1 | 1 | 4 | 8 | 1 | 1 | 4 | 3 | 8 | 9 | 12 | 24 | 12 |
Matrix representation of C2×C28.23D4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 7 | 0 | 0 | 0 | 0 |
| 4 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 27 | 0 | 0 |
| 0 | 0 | 4 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 3 |
| 0 | 0 | 0 | 0 | 19 | 0 |
| 0 | 7 | 0 | 0 | 0 | 0 |
| 25 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 28 |
| 0 | 0 | 0 | 0 | 24 | 9 |
| 0 | 22 | 0 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 27 | 0 | 0 |
| 0 | 0 | 3 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 8 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,4,0,0,0,0,7,11,0,0,0,0,0,0,23,4,0,0,0,0,27,6,0,0,0,0,0,0,22,19,0,0,0,0,3,0],[0,25,0,0,0,0,7,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,20,24,0,0,0,0,28,9],[0,4,0,0,0,0,22,0,0,0,0,0,0,0,23,3,0,0,0,0,27,6,0,0,0,0,0,0,1,0,0,0,0,0,8,28] >;
C2×C28.23D4 in GAP, Magma, Sage, TeX
C_2\times C_{28}._{23}D_4 % in TeX
G:=Group("C2xC28.23D4"); // GroupNames label
G:=SmallGroup(448,1267);
// by ID
G=gap.SmallGroup(448,1267);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,675,297,136,18822]);
// 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^13,d*b*d=b^-1,d*c*d=b^14*c^-1>;
// generators/relations