metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊11D4, C42.167D14, C14.782+ 1+4, C4⋊1D4⋊7D7, C4.72(D4×D7), (C4×D28)⋊50C2, C28⋊5(C4○D4), C7⋊4(Q8⋊6D4), C28.67(C2×D4), C4⋊1(D4⋊2D7), C28⋊2D4⋊37C2, C28⋊D4⋊27C2, (D4×Dic7)⋊35C2, (C4×Dic14)⋊51C2, (C2×D4).115D14, Dic7.29(C2×D4), C14.96(C22×D4), Dic7⋊D4⋊37C2, (C2×C28).636C23, (C2×C14).262C24, (C4×C28).204C22, C2.82(D4⋊6D14), C23.68(C22×D7), D14⋊C4.149C22, (C2×D28).270C22, (D4×C14).214C22, C4⋊Dic7.381C22, (C22×C14).76C23, C22.283(C23×D7), C23.D7.73C22, Dic7⋊C4.164C22, (C2×Dic7).269C23, (C4×Dic7).155C22, (C22×D7).116C23, (C2×Dic14).301C22, (C22×Dic7).158C22, C2.69(C2×D4×D7), (C7×C4⋊1D4)⋊9C2, C14.97(C2×C4○D4), (C2×D4⋊2D7)⋊22C2, C2.61(C2×D4⋊2D7), (C2×C4×D7).139C22, (C2×C4).598(C22×D7), (C2×C7⋊D4).78C22, SmallGroup(448,1171)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊11D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, dad=a15, bc=cb, dbd=a14b, dcd=c-1 >
Subgroups: 1484 in 312 conjugacy classes, 107 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C4⋊1D4, C4⋊1D4, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C7×D4, C22×D7, C22×C14, Q8⋊6D4, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C2×Dic14, C2×C4×D7, C2×D28, D4⋊2D7, C22×Dic7, C2×C7⋊D4, D4×C14, C4×Dic14, C4×D28, D4×Dic7, C28⋊2D4, Dic7⋊D4, C28⋊D4, C7×C4⋊1D4, C2×D4⋊2D7, Dic14⋊11D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2+ 1+4, C22×D7, Q8⋊6D4, D4×D7, D4⋊2D7, C23×D7, C2×D4×D7, C2×D4⋊2D7, D4⋊6D14, Dic14⋊11D4
►On 224 points
Generators in S224
(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)
(1 137 15 123)(2 136 16 122)(3 135 17 121)(4 134 18 120)(5 133 19 119)(6 132 20 118)(7 131 21 117)(8 130 22 116)(9 129 23 115)(10 128 24 114)(11 127 25 113)(12 126 26 140)(13 125 27 139)(14 124 28 138)(29 198 43 212)(30 197 44 211)(31 224 45 210)(32 223 46 209)(33 222 47 208)(34 221 48 207)(35 220 49 206)(36 219 50 205)(37 218 51 204)(38 217 52 203)(39 216 53 202)(40 215 54 201)(41 214 55 200)(42 213 56 199)(57 186 71 172)(58 185 72 171)(59 184 73 170)(60 183 74 169)(61 182 75 196)(62 181 76 195)(63 180 77 194)(64 179 78 193)(65 178 79 192)(66 177 80 191)(67 176 81 190)(68 175 82 189)(69 174 83 188)(70 173 84 187)(85 154 99 168)(86 153 100 167)(87 152 101 166)(88 151 102 165)(89 150 103 164)(90 149 104 163)(91 148 105 162)(92 147 106 161)(93 146 107 160)(94 145 108 159)(95 144 109 158)(96 143 110 157)(97 142 111 156)(98 141 112 155)
(1 223 101 190)(2 224 102 191)(3 197 103 192)(4 198 104 193)(5 199 105 194)(6 200 106 195)(7 201 107 196)(8 202 108 169)(9 203 109 170)(10 204 110 171)(11 205 111 172)(12 206 112 173)(13 207 85 174)(14 208 86 175)(15 209 87 176)(16 210 88 177)(17 211 89 178)(18 212 90 179)(19 213 91 180)(20 214 92 181)(21 215 93 182)(22 216 94 183)(23 217 95 184)(24 218 96 185)(25 219 97 186)(26 220 98 187)(27 221 99 188)(28 222 100 189)(29 149 78 120)(30 150 79 121)(31 151 80 122)(32 152 81 123)(33 153 82 124)(34 154 83 125)(35 155 84 126)(36 156 57 127)(37 157 58 128)(38 158 59 129)(39 159 60 130)(40 160 61 131)(41 161 62 132)(42 162 63 133)(43 163 64 134)(44 164 65 135)(45 165 66 136)(46 166 67 137)(47 167 68 138)(48 168 69 139)(49 141 70 140)(50 142 71 113)(51 143 72 114)(52 144 73 115)(53 145 74 116)(54 146 75 117)(55 147 76 118)(56 148 77 119)
(1 166)(2 153)(3 168)(4 155)(5 142)(6 157)(7 144)(8 159)(9 146)(10 161)(11 148)(12 163)(13 150)(14 165)(15 152)(16 167)(17 154)(18 141)(19 156)(20 143)(21 158)(22 145)(23 160)(24 147)(25 162)(26 149)(27 164)(28 151)(29 220)(30 207)(31 222)(32 209)(33 224)(34 211)(35 198)(36 213)(37 200)(38 215)(39 202)(40 217)(41 204)(42 219)(43 206)(44 221)(45 208)(46 223)(47 210)(48 197)(49 212)(50 199)(51 214)(52 201)(53 216)(54 203)(55 218)(56 205)(57 180)(58 195)(59 182)(60 169)(61 184)(62 171)(63 186)(64 173)(65 188)(66 175)(67 190)(68 177)(69 192)(70 179)(71 194)(72 181)(73 196)(74 183)(75 170)(76 185)(77 172)(78 187)(79 174)(80 189)(81 176)(82 191)(83 178)(84 193)(85 121)(86 136)(87 123)(88 138)(89 125)(90 140)(91 127)(92 114)(93 129)(94 116)(95 131)(96 118)(97 133)(98 120)(99 135)(100 122)(101 137)(102 124)(103 139)(104 126)(105 113)(106 128)(107 115)(108 130)(109 117)(110 132)(111 119)(112 134)
G:=sub<Sym(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), (1,137,15,123)(2,136,16,122)(3,135,17,121)(4,134,18,120)(5,133,19,119)(6,132,20,118)(7,131,21,117)(8,130,22,116)(9,129,23,115)(10,128,24,114)(11,127,25,113)(12,126,26,140)(13,125,27,139)(14,124,28,138)(29,198,43,212)(30,197,44,211)(31,224,45,210)(32,223,46,209)(33,222,47,208)(34,221,48,207)(35,220,49,206)(36,219,50,205)(37,218,51,204)(38,217,52,203)(39,216,53,202)(40,215,54,201)(41,214,55,200)(42,213,56,199)(57,186,71,172)(58,185,72,171)(59,184,73,170)(60,183,74,169)(61,182,75,196)(62,181,76,195)(63,180,77,194)(64,179,78,193)(65,178,79,192)(66,177,80,191)(67,176,81,190)(68,175,82,189)(69,174,83,188)(70,173,84,187)(85,154,99,168)(86,153,100,167)(87,152,101,166)(88,151,102,165)(89,150,103,164)(90,149,104,163)(91,148,105,162)(92,147,106,161)(93,146,107,160)(94,145,108,159)(95,144,109,158)(96,143,110,157)(97,142,111,156)(98,141,112,155), (1,223,101,190)(2,224,102,191)(3,197,103,192)(4,198,104,193)(5,199,105,194)(6,200,106,195)(7,201,107,196)(8,202,108,169)(9,203,109,170)(10,204,110,171)(11,205,111,172)(12,206,112,173)(13,207,85,174)(14,208,86,175)(15,209,87,176)(16,210,88,177)(17,211,89,178)(18,212,90,179)(19,213,91,180)(20,214,92,181)(21,215,93,182)(22,216,94,183)(23,217,95,184)(24,218,96,185)(25,219,97,186)(26,220,98,187)(27,221,99,188)(28,222,100,189)(29,149,78,120)(30,150,79,121)(31,151,80,122)(32,152,81,123)(33,153,82,124)(34,154,83,125)(35,155,84,126)(36,156,57,127)(37,157,58,128)(38,158,59,129)(39,159,60,130)(40,160,61,131)(41,161,62,132)(42,162,63,133)(43,163,64,134)(44,164,65,135)(45,165,66,136)(46,166,67,137)(47,167,68,138)(48,168,69,139)(49,141,70,140)(50,142,71,113)(51,143,72,114)(52,144,73,115)(53,145,74,116)(54,146,75,117)(55,147,76,118)(56,148,77,119), (1,166)(2,153)(3,168)(4,155)(5,142)(6,157)(7,144)(8,159)(9,146)(10,161)(11,148)(12,163)(13,150)(14,165)(15,152)(16,167)(17,154)(18,141)(19,156)(20,143)(21,158)(22,145)(23,160)(24,147)(25,162)(26,149)(27,164)(28,151)(29,220)(30,207)(31,222)(32,209)(33,224)(34,211)(35,198)(36,213)(37,200)(38,215)(39,202)(40,217)(41,204)(42,219)(43,206)(44,221)(45,208)(46,223)(47,210)(48,197)(49,212)(50,199)(51,214)(52,201)(53,216)(54,203)(55,218)(56,205)(57,180)(58,195)(59,182)(60,169)(61,184)(62,171)(63,186)(64,173)(65,188)(66,175)(67,190)(68,177)(69,192)(70,179)(71,194)(72,181)(73,196)(74,183)(75,170)(76,185)(77,172)(78,187)(79,174)(80,189)(81,176)(82,191)(83,178)(84,193)(85,121)(86,136)(87,123)(88,138)(89,125)(90,140)(91,127)(92,114)(93,129)(94,116)(95,131)(96,118)(97,133)(98,120)(99,135)(100,122)(101,137)(102,124)(103,139)(104,126)(105,113)(106,128)(107,115)(108,130)(109,117)(110,132)(111,119)(112,134)>;
G:=Group( (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), (1,137,15,123)(2,136,16,122)(3,135,17,121)(4,134,18,120)(5,133,19,119)(6,132,20,118)(7,131,21,117)(8,130,22,116)(9,129,23,115)(10,128,24,114)(11,127,25,113)(12,126,26,140)(13,125,27,139)(14,124,28,138)(29,198,43,212)(30,197,44,211)(31,224,45,210)(32,223,46,209)(33,222,47,208)(34,221,48,207)(35,220,49,206)(36,219,50,205)(37,218,51,204)(38,217,52,203)(39,216,53,202)(40,215,54,201)(41,214,55,200)(42,213,56,199)(57,186,71,172)(58,185,72,171)(59,184,73,170)(60,183,74,169)(61,182,75,196)(62,181,76,195)(63,180,77,194)(64,179,78,193)(65,178,79,192)(66,177,80,191)(67,176,81,190)(68,175,82,189)(69,174,83,188)(70,173,84,187)(85,154,99,168)(86,153,100,167)(87,152,101,166)(88,151,102,165)(89,150,103,164)(90,149,104,163)(91,148,105,162)(92,147,106,161)(93,146,107,160)(94,145,108,159)(95,144,109,158)(96,143,110,157)(97,142,111,156)(98,141,112,155), (1,223,101,190)(2,224,102,191)(3,197,103,192)(4,198,104,193)(5,199,105,194)(6,200,106,195)(7,201,107,196)(8,202,108,169)(9,203,109,170)(10,204,110,171)(11,205,111,172)(12,206,112,173)(13,207,85,174)(14,208,86,175)(15,209,87,176)(16,210,88,177)(17,211,89,178)(18,212,90,179)(19,213,91,180)(20,214,92,181)(21,215,93,182)(22,216,94,183)(23,217,95,184)(24,218,96,185)(25,219,97,186)(26,220,98,187)(27,221,99,188)(28,222,100,189)(29,149,78,120)(30,150,79,121)(31,151,80,122)(32,152,81,123)(33,153,82,124)(34,154,83,125)(35,155,84,126)(36,156,57,127)(37,157,58,128)(38,158,59,129)(39,159,60,130)(40,160,61,131)(41,161,62,132)(42,162,63,133)(43,163,64,134)(44,164,65,135)(45,165,66,136)(46,166,67,137)(47,167,68,138)(48,168,69,139)(49,141,70,140)(50,142,71,113)(51,143,72,114)(52,144,73,115)(53,145,74,116)(54,146,75,117)(55,147,76,118)(56,148,77,119), (1,166)(2,153)(3,168)(4,155)(5,142)(6,157)(7,144)(8,159)(9,146)(10,161)(11,148)(12,163)(13,150)(14,165)(15,152)(16,167)(17,154)(18,141)(19,156)(20,143)(21,158)(22,145)(23,160)(24,147)(25,162)(26,149)(27,164)(28,151)(29,220)(30,207)(31,222)(32,209)(33,224)(34,211)(35,198)(36,213)(37,200)(38,215)(39,202)(40,217)(41,204)(42,219)(43,206)(44,221)(45,208)(46,223)(47,210)(48,197)(49,212)(50,199)(51,214)(52,201)(53,216)(54,203)(55,218)(56,205)(57,180)(58,195)(59,182)(60,169)(61,184)(62,171)(63,186)(64,173)(65,188)(66,175)(67,190)(68,177)(69,192)(70,179)(71,194)(72,181)(73,196)(74,183)(75,170)(76,185)(77,172)(78,187)(79,174)(80,189)(81,176)(82,191)(83,178)(84,193)(85,121)(86,136)(87,123)(88,138)(89,125)(90,140)(91,127)(92,114)(93,129)(94,116)(95,131)(96,118)(97,133)(98,120)(99,135)(100,122)(101,137)(102,124)(103,139)(104,126)(105,113)(106,128)(107,115)(108,130)(109,117)(110,132)(111,119)(112,134) );
G=PermutationGroup([[(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)], [(1,137,15,123),(2,136,16,122),(3,135,17,121),(4,134,18,120),(5,133,19,119),(6,132,20,118),(7,131,21,117),(8,130,22,116),(9,129,23,115),(10,128,24,114),(11,127,25,113),(12,126,26,140),(13,125,27,139),(14,124,28,138),(29,198,43,212),(30,197,44,211),(31,224,45,210),(32,223,46,209),(33,222,47,208),(34,221,48,207),(35,220,49,206),(36,219,50,205),(37,218,51,204),(38,217,52,203),(39,216,53,202),(40,215,54,201),(41,214,55,200),(42,213,56,199),(57,186,71,172),(58,185,72,171),(59,184,73,170),(60,183,74,169),(61,182,75,196),(62,181,76,195),(63,180,77,194),(64,179,78,193),(65,178,79,192),(66,177,80,191),(67,176,81,190),(68,175,82,189),(69,174,83,188),(70,173,84,187),(85,154,99,168),(86,153,100,167),(87,152,101,166),(88,151,102,165),(89,150,103,164),(90,149,104,163),(91,148,105,162),(92,147,106,161),(93,146,107,160),(94,145,108,159),(95,144,109,158),(96,143,110,157),(97,142,111,156),(98,141,112,155)], [(1,223,101,190),(2,224,102,191),(3,197,103,192),(4,198,104,193),(5,199,105,194),(6,200,106,195),(7,201,107,196),(8,202,108,169),(9,203,109,170),(10,204,110,171),(11,205,111,172),(12,206,112,173),(13,207,85,174),(14,208,86,175),(15,209,87,176),(16,210,88,177),(17,211,89,178),(18,212,90,179),(19,213,91,180),(20,214,92,181),(21,215,93,182),(22,216,94,183),(23,217,95,184),(24,218,96,185),(25,219,97,186),(26,220,98,187),(27,221,99,188),(28,222,100,189),(29,149,78,120),(30,150,79,121),(31,151,80,122),(32,152,81,123),(33,153,82,124),(34,154,83,125),(35,155,84,126),(36,156,57,127),(37,157,58,128),(38,158,59,129),(39,159,60,130),(40,160,61,131),(41,161,62,132),(42,162,63,133),(43,163,64,134),(44,164,65,135),(45,165,66,136),(46,166,67,137),(47,167,68,138),(48,168,69,139),(49,141,70,140),(50,142,71,113),(51,143,72,114),(52,144,73,115),(53,145,74,116),(54,146,75,117),(55,147,76,118),(56,148,77,119)], [(1,166),(2,153),(3,168),(4,155),(5,142),(6,157),(7,144),(8,159),(9,146),(10,161),(11,148),(12,163),(13,150),(14,165),(15,152),(16,167),(17,154),(18,141),(19,156),(20,143),(21,158),(22,145),(23,160),(24,147),(25,162),(26,149),(27,164),(28,151),(29,220),(30,207),(31,222),(32,209),(33,224),(34,211),(35,198),(36,213),(37,200),(38,215),(39,202),(40,217),(41,204),(42,219),(43,206),(44,221),(45,208),(46,223),(47,210),(48,197),(49,212),(50,199),(51,214),(52,201),(53,216),(54,203),(55,218),(56,205),(57,180),(58,195),(59,182),(60,169),(61,184),(62,171),(63,186),(64,173),(65,188),(66,175),(67,190),(68,177),(69,192),(70,179),(71,194),(72,181),(73,196),(74,183),(75,170),(76,185),(77,172),(78,187),(79,174),(80,189),(81,176),(82,191),(83,178),(84,193),(85,121),(86,136),(87,123),(88,138),(89,125),(90,140),(91,127),(92,114),(93,129),(94,116),(95,131),(96,118),(97,133),(98,120),(99,135),(100,122),(101,137),(102,124),(103,139),(104,126),(105,113),(106,128),(107,115),(108,130),(109,117),(110,132),(111,119),(112,134)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | 2+ 1+4 | D4×D7 | D4⋊2D7 | D4⋊6D14 |
| kernel | Dic14⋊11D4 | C4×Dic14 | C4×D28 | D4×Dic7 | C28⋊2D4 | Dic7⋊D4 | C28⋊D4 | C7×C4⋊1D4 | C2×D4⋊2D7 | Dic14 | C4⋊1D4 | C28 | C42 | C2×D4 | C14 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 4 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 18 | 1 | 6 | 6 | 6 |
Matrix representation of Dic14⋊11D4 ►in GL6(𝔽29)
| 0 | 28 | 0 | 0 | 0 | 0 |
| 1 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 11 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 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 | 0 | 28 |
| 0 | 0 | 0 | 0 | 28 | 0 |
G:=sub<GL(6,GF(29))| [0,1,0,0,0,0,28,11,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,12],[28,11,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,28,0] >;
Dic14⋊11D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_{11}D_4 % in TeX
G:=Group("Dic14:11D4"); // GroupNames label
G:=SmallGroup(448,1171);
// by ID
G=gap.SmallGroup(448,1171);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,675,570,185,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,a*c=c*a,d*a*d=a^15,b*c=c*b,d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations