metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4)⋊6D28, (C2×D28)⋊7C4, (C2×C28)⋊28D4, (C2×C42)⋊6D7, C4⋊2(D14⋊C4), C2.19(C4×D28), C14.18(C4×D4), C28⋊4(C22⋊C4), C2.2(C28⋊7D4), C2.2(C28⋊4D4), (C22×D28).4C2, C22.39(C2×D28), C14.10(C4⋊1D4), C14.56(C4⋊D4), C2.3(C4.D28), (C22×C4).399D14, C14.12(C4.4D4), C22.48(C4○D28), C7⋊1(C24.3C22), (C23×D7).11C22, C23.272(C22×D7), (C22×C28).478C22, (C22×C14).314C23, (C22×Dic7).32C22, (C2×C4×C28)⋊7C2, (C2×D14⋊C4)⋊2C2, (C2×C4⋊Dic7)⋊7C2, C2.6(C2×D14⋊C4), (C2×C4).111(C4×D7), C22.119(C2×C4×D7), (C2×C28).225(C2×C4), (C2×C14).428(C2×D4), C14.33(C2×C22⋊C4), C22.43(C2×C7⋊D4), (C2×C14).73(C4○D4), (C2×C4).239(C7⋊D4), (C22×D7).18(C2×C4), (C2×C14).100(C22×C4), SmallGroup(448,473)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4)⋊6D28
G = < a,b,c,d | a2=b4=c28=d2=1, dbd=ab=ba, ac=ca, ad=da, bc=cb, dcd=c-1 >
Subgroups: 1540 in 258 conjugacy classes, 87 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C22×D4, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C24.3C22, C4⋊Dic7, D14⋊C4, C4×C28, C2×D28, C2×D28, C22×Dic7, C22×C28, C22×C28, C23×D7, C2×C4⋊Dic7, C2×D14⋊C4, C2×C4×C28, C22×D28, (C2×C4)⋊6D28
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C4○D4, D14, C2×C22⋊C4, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4×D7, D28, C7⋊D4, C22×D7, C24.3C22, D14⋊C4, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C4×D28, C28⋊4D4, C4.D28, C2×D14⋊C4, C28⋊7D4, (C2×C4)⋊6D28
►On 224 points
Generators in S224
(1 96)(2 97)(3 98)(4 99)(5 100)(6 101)(7 102)(8 103)(9 104)(10 105)(11 106)(12 107)(13 108)(14 109)(15 110)(16 111)(17 112)(18 85)(19 86)(20 87)(21 88)(22 89)(23 90)(24 91)(25 92)(26 93)(27 94)(28 95)(29 192)(30 193)(31 194)(32 195)(33 196)(34 169)(35 170)(36 171)(37 172)(38 173)(39 174)(40 175)(41 176)(42 177)(43 178)(44 179)(45 180)(46 181)(47 182)(48 183)(49 184)(50 185)(51 186)(52 187)(53 188)(54 189)(55 190)(56 191)(57 153)(58 154)(59 155)(60 156)(61 157)(62 158)(63 159)(64 160)(65 161)(66 162)(67 163)(68 164)(69 165)(70 166)(71 167)(72 168)(73 141)(74 142)(75 143)(76 144)(77 145)(78 146)(79 147)(80 148)(81 149)(82 150)(83 151)(84 152)(113 199)(114 200)(115 201)(116 202)(117 203)(118 204)(119 205)(120 206)(121 207)(122 208)(123 209)(124 210)(125 211)(126 212)(127 213)(128 214)(129 215)(130 216)(131 217)(132 218)(133 219)(134 220)(135 221)(136 222)(137 223)(138 224)(139 197)(140 198)
(1 66 223 193)(2 67 224 194)(3 68 197 195)(4 69 198 196)(5 70 199 169)(6 71 200 170)(7 72 201 171)(8 73 202 172)(9 74 203 173)(10 75 204 174)(11 76 205 175)(12 77 206 176)(13 78 207 177)(14 79 208 178)(15 80 209 179)(16 81 210 180)(17 82 211 181)(18 83 212 182)(19 84 213 183)(20 57 214 184)(21 58 215 185)(22 59 216 186)(23 60 217 187)(24 61 218 188)(25 62 219 189)(26 63 220 190)(27 64 221 191)(28 65 222 192)(29 95 161 136)(30 96 162 137)(31 97 163 138)(32 98 164 139)(33 99 165 140)(34 100 166 113)(35 101 167 114)(36 102 168 115)(37 103 141 116)(38 104 142 117)(39 105 143 118)(40 106 144 119)(41 107 145 120)(42 108 146 121)(43 109 147 122)(44 110 148 123)(45 111 149 124)(46 112 150 125)(47 85 151 126)(48 86 152 127)(49 87 153 128)(50 88 154 129)(51 89 155 130)(52 90 156 131)(53 91 157 132)(54 92 158 133)(55 93 159 134)(56 94 160 135)
(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)
(1 115)(2 114)(3 113)(4 140)(5 139)(6 138)(7 137)(8 136)(9 135)(10 134)(11 133)(12 132)(13 131)(14 130)(15 129)(16 128)(17 127)(18 126)(19 125)(20 124)(21 123)(22 122)(23 121)(24 120)(25 119)(26 118)(27 117)(28 116)(29 141)(30 168)(31 167)(32 166)(33 165)(34 164)(35 163)(36 162)(37 161)(38 160)(39 159)(40 158)(41 157)(42 156)(43 155)(44 154)(45 153)(46 152)(47 151)(48 150)(49 149)(50 148)(51 147)(52 146)(53 145)(54 144)(55 143)(56 142)(57 180)(58 179)(59 178)(60 177)(61 176)(62 175)(63 174)(64 173)(65 172)(66 171)(67 170)(68 169)(69 196)(70 195)(71 194)(72 193)(73 192)(74 191)(75 190)(76 189)(77 188)(78 187)(79 186)(80 185)(81 184)(82 183)(83 182)(84 181)(85 212)(86 211)(87 210)(88 209)(89 208)(90 207)(91 206)(92 205)(93 204)(94 203)(95 202)(96 201)(97 200)(98 199)(99 198)(100 197)(101 224)(102 223)(103 222)(104 221)(105 220)(106 219)(107 218)(108 217)(109 216)(110 215)(111 214)(112 213)
G:=sub<Sym(224)| (1,96)(2,97)(3,98)(4,99)(5,100)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,85)(19,86)(20,87)(21,88)(22,89)(23,90)(24,91)(25,92)(26,93)(27,94)(28,95)(29,192)(30,193)(31,194)(32,195)(33,196)(34,169)(35,170)(36,171)(37,172)(38,173)(39,174)(40,175)(41,176)(42,177)(43,178)(44,179)(45,180)(46,181)(47,182)(48,183)(49,184)(50,185)(51,186)(52,187)(53,188)(54,189)(55,190)(56,191)(57,153)(58,154)(59,155)(60,156)(61,157)(62,158)(63,159)(64,160)(65,161)(66,162)(67,163)(68,164)(69,165)(70,166)(71,167)(72,168)(73,141)(74,142)(75,143)(76,144)(77,145)(78,146)(79,147)(80,148)(81,149)(82,150)(83,151)(84,152)(113,199)(114,200)(115,201)(116,202)(117,203)(118,204)(119,205)(120,206)(121,207)(122,208)(123,209)(124,210)(125,211)(126,212)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,222)(137,223)(138,224)(139,197)(140,198), (1,66,223,193)(2,67,224,194)(3,68,197,195)(4,69,198,196)(5,70,199,169)(6,71,200,170)(7,72,201,171)(8,73,202,172)(9,74,203,173)(10,75,204,174)(11,76,205,175)(12,77,206,176)(13,78,207,177)(14,79,208,178)(15,80,209,179)(16,81,210,180)(17,82,211,181)(18,83,212,182)(19,84,213,183)(20,57,214,184)(21,58,215,185)(22,59,216,186)(23,60,217,187)(24,61,218,188)(25,62,219,189)(26,63,220,190)(27,64,221,191)(28,65,222,192)(29,95,161,136)(30,96,162,137)(31,97,163,138)(32,98,164,139)(33,99,165,140)(34,100,166,113)(35,101,167,114)(36,102,168,115)(37,103,141,116)(38,104,142,117)(39,105,143,118)(40,106,144,119)(41,107,145,120)(42,108,146,121)(43,109,147,122)(44,110,148,123)(45,111,149,124)(46,112,150,125)(47,85,151,126)(48,86,152,127)(49,87,153,128)(50,88,154,129)(51,89,155,130)(52,90,156,131)(53,91,157,132)(54,92,158,133)(55,93,159,134)(56,94,160,135), (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), (1,115)(2,114)(3,113)(4,140)(5,139)(6,138)(7,137)(8,136)(9,135)(10,134)(11,133)(12,132)(13,131)(14,130)(15,129)(16,128)(17,127)(18,126)(19,125)(20,124)(21,123)(22,122)(23,121)(24,120)(25,119)(26,118)(27,117)(28,116)(29,141)(30,168)(31,167)(32,166)(33,165)(34,164)(35,163)(36,162)(37,161)(38,160)(39,159)(40,158)(41,157)(42,156)(43,155)(44,154)(45,153)(46,152)(47,151)(48,150)(49,149)(50,148)(51,147)(52,146)(53,145)(54,144)(55,143)(56,142)(57,180)(58,179)(59,178)(60,177)(61,176)(62,175)(63,174)(64,173)(65,172)(66,171)(67,170)(68,169)(69,196)(70,195)(71,194)(72,193)(73,192)(74,191)(75,190)(76,189)(77,188)(78,187)(79,186)(80,185)(81,184)(82,183)(83,182)(84,181)(85,212)(86,211)(87,210)(88,209)(89,208)(90,207)(91,206)(92,205)(93,204)(94,203)(95,202)(96,201)(97,200)(98,199)(99,198)(100,197)(101,224)(102,223)(103,222)(104,221)(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)>;
G:=Group( (1,96)(2,97)(3,98)(4,99)(5,100)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,85)(19,86)(20,87)(21,88)(22,89)(23,90)(24,91)(25,92)(26,93)(27,94)(28,95)(29,192)(30,193)(31,194)(32,195)(33,196)(34,169)(35,170)(36,171)(37,172)(38,173)(39,174)(40,175)(41,176)(42,177)(43,178)(44,179)(45,180)(46,181)(47,182)(48,183)(49,184)(50,185)(51,186)(52,187)(53,188)(54,189)(55,190)(56,191)(57,153)(58,154)(59,155)(60,156)(61,157)(62,158)(63,159)(64,160)(65,161)(66,162)(67,163)(68,164)(69,165)(70,166)(71,167)(72,168)(73,141)(74,142)(75,143)(76,144)(77,145)(78,146)(79,147)(80,148)(81,149)(82,150)(83,151)(84,152)(113,199)(114,200)(115,201)(116,202)(117,203)(118,204)(119,205)(120,206)(121,207)(122,208)(123,209)(124,210)(125,211)(126,212)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,222)(137,223)(138,224)(139,197)(140,198), (1,66,223,193)(2,67,224,194)(3,68,197,195)(4,69,198,196)(5,70,199,169)(6,71,200,170)(7,72,201,171)(8,73,202,172)(9,74,203,173)(10,75,204,174)(11,76,205,175)(12,77,206,176)(13,78,207,177)(14,79,208,178)(15,80,209,179)(16,81,210,180)(17,82,211,181)(18,83,212,182)(19,84,213,183)(20,57,214,184)(21,58,215,185)(22,59,216,186)(23,60,217,187)(24,61,218,188)(25,62,219,189)(26,63,220,190)(27,64,221,191)(28,65,222,192)(29,95,161,136)(30,96,162,137)(31,97,163,138)(32,98,164,139)(33,99,165,140)(34,100,166,113)(35,101,167,114)(36,102,168,115)(37,103,141,116)(38,104,142,117)(39,105,143,118)(40,106,144,119)(41,107,145,120)(42,108,146,121)(43,109,147,122)(44,110,148,123)(45,111,149,124)(46,112,150,125)(47,85,151,126)(48,86,152,127)(49,87,153,128)(50,88,154,129)(51,89,155,130)(52,90,156,131)(53,91,157,132)(54,92,158,133)(55,93,159,134)(56,94,160,135), (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), (1,115)(2,114)(3,113)(4,140)(5,139)(6,138)(7,137)(8,136)(9,135)(10,134)(11,133)(12,132)(13,131)(14,130)(15,129)(16,128)(17,127)(18,126)(19,125)(20,124)(21,123)(22,122)(23,121)(24,120)(25,119)(26,118)(27,117)(28,116)(29,141)(30,168)(31,167)(32,166)(33,165)(34,164)(35,163)(36,162)(37,161)(38,160)(39,159)(40,158)(41,157)(42,156)(43,155)(44,154)(45,153)(46,152)(47,151)(48,150)(49,149)(50,148)(51,147)(52,146)(53,145)(54,144)(55,143)(56,142)(57,180)(58,179)(59,178)(60,177)(61,176)(62,175)(63,174)(64,173)(65,172)(66,171)(67,170)(68,169)(69,196)(70,195)(71,194)(72,193)(73,192)(74,191)(75,190)(76,189)(77,188)(78,187)(79,186)(80,185)(81,184)(82,183)(83,182)(84,181)(85,212)(86,211)(87,210)(88,209)(89,208)(90,207)(91,206)(92,205)(93,204)(94,203)(95,202)(96,201)(97,200)(98,199)(99,198)(100,197)(101,224)(102,223)(103,222)(104,221)(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213) );
G=PermutationGroup([[(1,96),(2,97),(3,98),(4,99),(5,100),(6,101),(7,102),(8,103),(9,104),(10,105),(11,106),(12,107),(13,108),(14,109),(15,110),(16,111),(17,112),(18,85),(19,86),(20,87),(21,88),(22,89),(23,90),(24,91),(25,92),(26,93),(27,94),(28,95),(29,192),(30,193),(31,194),(32,195),(33,196),(34,169),(35,170),(36,171),(37,172),(38,173),(39,174),(40,175),(41,176),(42,177),(43,178),(44,179),(45,180),(46,181),(47,182),(48,183),(49,184),(50,185),(51,186),(52,187),(53,188),(54,189),(55,190),(56,191),(57,153),(58,154),(59,155),(60,156),(61,157),(62,158),(63,159),(64,160),(65,161),(66,162),(67,163),(68,164),(69,165),(70,166),(71,167),(72,168),(73,141),(74,142),(75,143),(76,144),(77,145),(78,146),(79,147),(80,148),(81,149),(82,150),(83,151),(84,152),(113,199),(114,200),(115,201),(116,202),(117,203),(118,204),(119,205),(120,206),(121,207),(122,208),(123,209),(124,210),(125,211),(126,212),(127,213),(128,214),(129,215),(130,216),(131,217),(132,218),(133,219),(134,220),(135,221),(136,222),(137,223),(138,224),(139,197),(140,198)], [(1,66,223,193),(2,67,224,194),(3,68,197,195),(4,69,198,196),(5,70,199,169),(6,71,200,170),(7,72,201,171),(8,73,202,172),(9,74,203,173),(10,75,204,174),(11,76,205,175),(12,77,206,176),(13,78,207,177),(14,79,208,178),(15,80,209,179),(16,81,210,180),(17,82,211,181),(18,83,212,182),(19,84,213,183),(20,57,214,184),(21,58,215,185),(22,59,216,186),(23,60,217,187),(24,61,218,188),(25,62,219,189),(26,63,220,190),(27,64,221,191),(28,65,222,192),(29,95,161,136),(30,96,162,137),(31,97,163,138),(32,98,164,139),(33,99,165,140),(34,100,166,113),(35,101,167,114),(36,102,168,115),(37,103,141,116),(38,104,142,117),(39,105,143,118),(40,106,144,119),(41,107,145,120),(42,108,146,121),(43,109,147,122),(44,110,148,123),(45,111,149,124),(46,112,150,125),(47,85,151,126),(48,86,152,127),(49,87,153,128),(50,88,154,129),(51,89,155,130),(52,90,156,131),(53,91,157,132),(54,92,158,133),(55,93,159,134),(56,94,160,135)], [(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)], [(1,115),(2,114),(3,113),(4,140),(5,139),(6,138),(7,137),(8,136),(9,135),(10,134),(11,133),(12,132),(13,131),(14,130),(15,129),(16,128),(17,127),(18,126),(19,125),(20,124),(21,123),(22,122),(23,121),(24,120),(25,119),(26,118),(27,117),(28,116),(29,141),(30,168),(31,167),(32,166),(33,165),(34,164),(35,163),(36,162),(37,161),(38,160),(39,159),(40,158),(41,157),(42,156),(43,155),(44,154),(45,153),(46,152),(47,151),(48,150),(49,149),(50,148),(51,147),(52,146),(53,145),(54,144),(55,143),(56,142),(57,180),(58,179),(59,178),(60,177),(61,176),(62,175),(63,174),(64,173),(65,172),(66,171),(67,170),(68,169),(69,196),(70,195),(71,194),(72,193),(73,192),(74,191),(75,190),(76,189),(77,188),(78,187),(79,186),(80,185),(81,184),(82,183),(83,182),(84,181),(85,212),(86,211),(87,210),(88,209),(89,208),(90,207),(91,206),(92,205),(93,204),(94,203),(95,202),(96,201),(97,200),(98,199),(99,198),(100,197),(101,224),(102,223),(103,222),(104,221),(105,220),(106,219),(107,218),(108,217),(109,216),(110,215),(111,214),(112,213)]])
124 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | C4×D7 | D28 | C7⋊D4 | C4○D28 |
| kernel | (C2×C4)⋊6D28 | C2×C4⋊Dic7 | C2×D14⋊C4 | C2×C4×C28 | C22×D28 | C2×D28 | C2×C28 | C2×C42 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 |
| # reps | 1 | 1 | 4 | 1 | 1 | 8 | 8 | 3 | 4 | 9 | 12 | 36 | 12 | 24 |
Matrix representation of (C2×C4)⋊6D28 ►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 |
| 3 | 27 | 0 | 0 | 0 | 0 |
| 4 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 15 | 18 | 0 | 0 | 0 | 0 |
| 22 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 7 | 0 | 0 |
| 0 | 0 | 15 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 4 |
| 0 | 0 | 0 | 0 | 25 | 8 |
| 17 | 25 | 0 | 0 | 0 | 0 |
| 14 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 10 | 0 | 0 |
| 0 | 0 | 11 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 7 |
| 0 | 0 | 0 | 0 | 19 | 19 |
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],[3,4,0,0,0,0,27,26,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[15,22,0,0,0,0,18,11,0,0,0,0,0,0,18,15,0,0,0,0,7,22,0,0,0,0,0,0,9,25,0,0,0,0,4,8],[17,14,0,0,0,0,25,12,0,0,0,0,0,0,6,11,0,0,0,0,10,23,0,0,0,0,0,0,10,19,0,0,0,0,7,19] >;
(C2×C4)⋊6D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)\rtimes_6D_{28} % in TeX
G:=Group("(C2xC4):6D28"); // GroupNames label
G:=SmallGroup(448,473);
// by ID
G=gap.SmallGroup(448,473);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,758,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=d^2=1,d*b*d=a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*c*d=c^-1>;
// generators/relations