metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D4.1Dic14, C4⋊C4.4D14, C7⋊1(D4.Q8), (C7×D4).1Q8, C28.3(C2×Q8), C8⋊Dic7⋊11C2, Dic7⋊C8⋊11C2, D4⋊C4.6D7, (C2×C8).114D14, C28.Q8⋊4C2, C28.3Q8⋊1C2, (D4×Dic7).5C2, C4.3(C2×Dic14), (C2×D4).128D14, C14.37(C4○D8), D4⋊Dic7.3C2, C22.165(D4×D7), C14.9(C22⋊Q8), C28.147(C4○D4), C4.76(D4⋊2D7), C2.10(D8⋊D7), C14.27(C8⋊C22), (C2×C28).203C23, (C2×C56).125C22, (C2×Dic7).137D4, (D4×C14).24C22, C4⋊Dic7.62C22, (C4×Dic7).7C22, C2.8(SD16⋊3D7), C2.14(C22⋊Dic14), (C2×C7⋊C8).9C22, (C7×C4⋊C4).8C22, (C7×D4⋊C4).6C2, (C2×C14).216(C2×D4), (C2×C4).310(C22×D7), SmallGroup(448,297)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D4.Dic14
G = < a,b,c,d | a4=b2=c28=1, d2=c14, bab=cac-1=a-1, ad=da, cbc-1=a-1b, bd=db, dcd-1=a2c-1 >
Subgroups: 468 in 102 conjugacy classes, 41 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, D4, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×D4, Dic7, C28, C28, C2×C14, C2×C14, D4⋊C4, D4⋊C4, C4⋊C8, C4.Q8, C2.D8, C4×D4, C42.C2, C7⋊C8, C56, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×D4, C22×C14, D4.Q8, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C7×C4⋊C4, C2×C56, C22×Dic7, D4×C14, C28.Q8, Dic7⋊C8, C8⋊Dic7, D4⋊Dic7, C7×D4⋊C4, C28.3Q8, D4×Dic7, D4.Dic14
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C4○D8, C8⋊C22, Dic14, C22×D7, D4.Q8, C2×Dic14, D4×D7, D4⋊2D7, C22⋊Dic14, D8⋊D7, SD16⋊3D7, D4.Dic14
►On 224 points
Generators in S224
(1 126 155 90)(2 91 156 127)(3 128 157 92)(4 93 158 129)(5 130 159 94)(6 95 160 131)(7 132 161 96)(8 97 162 133)(9 134 163 98)(10 99 164 135)(11 136 165 100)(12 101 166 137)(13 138 167 102)(14 103 168 139)(15 140 141 104)(16 105 142 113)(17 114 143 106)(18 107 144 115)(19 116 145 108)(20 109 146 117)(21 118 147 110)(22 111 148 119)(23 120 149 112)(24 85 150 121)(25 122 151 86)(26 87 152 123)(27 124 153 88)(28 89 154 125)(29 224 64 180)(30 181 65 197)(31 198 66 182)(32 183 67 199)(33 200 68 184)(34 185 69 201)(35 202 70 186)(36 187 71 203)(37 204 72 188)(38 189 73 205)(39 206 74 190)(40 191 75 207)(41 208 76 192)(42 193 77 209)(43 210 78 194)(44 195 79 211)(45 212 80 196)(46 169 81 213)(47 214 82 170)(48 171 83 215)(49 216 84 172)(50 173 57 217)(51 218 58 174)(52 175 59 219)(53 220 60 176)(54 177 61 221)(55 222 62 178)(56 179 63 223)
(1 104)(2 16)(3 106)(4 18)(5 108)(6 20)(7 110)(8 22)(9 112)(10 24)(11 86)(12 26)(13 88)(14 28)(15 90)(17 92)(19 94)(21 96)(23 98)(25 100)(27 102)(29 210)(30 79)(31 212)(32 81)(33 214)(34 83)(35 216)(36 57)(37 218)(38 59)(39 220)(40 61)(41 222)(42 63)(43 224)(44 65)(45 198)(46 67)(47 200)(48 69)(49 202)(50 71)(51 204)(52 73)(53 206)(54 75)(55 208)(56 77)(58 188)(60 190)(62 192)(64 194)(66 196)(68 170)(70 172)(72 174)(74 176)(76 178)(78 180)(80 182)(82 184)(84 186)(85 135)(87 137)(89 139)(91 113)(93 115)(95 117)(97 119)(99 121)(101 123)(103 125)(105 127)(107 129)(109 131)(111 133)(114 157)(116 159)(118 161)(120 163)(122 165)(124 167)(126 141)(128 143)(130 145)(132 147)(134 149)(136 151)(138 153)(140 155)(142 156)(144 158)(146 160)(148 162)(150 164)(152 166)(154 168)(169 183)(171 185)(173 187)(175 189)(177 191)(179 193)(181 195)(197 211)(199 213)(201 215)(203 217)(205 219)(207 221)(209 223)
(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)
(1 178 15 192)(2 221 16 207)(3 176 17 190)(4 219 18 205)(5 174 19 188)(6 217 20 203)(7 172 21 186)(8 215 22 201)(9 170 23 184)(10 213 24 199)(11 196 25 182)(12 211 26 197)(13 194 27 180)(14 209 28 223)(29 138 43 124)(30 101 44 87)(31 136 45 122)(32 99 46 85)(33 134 47 120)(34 97 48 111)(35 132 49 118)(36 95 50 109)(37 130 51 116)(38 93 52 107)(39 128 53 114)(40 91 54 105)(41 126 55 140)(42 89 56 103)(57 117 71 131)(58 108 72 94)(59 115 73 129)(60 106 74 92)(61 113 75 127)(62 104 76 90)(63 139 77 125)(64 102 78 88)(65 137 79 123)(66 100 80 86)(67 135 81 121)(68 98 82 112)(69 133 83 119)(70 96 84 110)(141 208 155 222)(142 191 156 177)(143 206 157 220)(144 189 158 175)(145 204 159 218)(146 187 160 173)(147 202 161 216)(148 185 162 171)(149 200 163 214)(150 183 164 169)(151 198 165 212)(152 181 166 195)(153 224 167 210)(154 179 168 193)
G:=sub<Sym(224)| (1,126,155,90)(2,91,156,127)(3,128,157,92)(4,93,158,129)(5,130,159,94)(6,95,160,131)(7,132,161,96)(8,97,162,133)(9,134,163,98)(10,99,164,135)(11,136,165,100)(12,101,166,137)(13,138,167,102)(14,103,168,139)(15,140,141,104)(16,105,142,113)(17,114,143,106)(18,107,144,115)(19,116,145,108)(20,109,146,117)(21,118,147,110)(22,111,148,119)(23,120,149,112)(24,85,150,121)(25,122,151,86)(26,87,152,123)(27,124,153,88)(28,89,154,125)(29,224,64,180)(30,181,65,197)(31,198,66,182)(32,183,67,199)(33,200,68,184)(34,185,69,201)(35,202,70,186)(36,187,71,203)(37,204,72,188)(38,189,73,205)(39,206,74,190)(40,191,75,207)(41,208,76,192)(42,193,77,209)(43,210,78,194)(44,195,79,211)(45,212,80,196)(46,169,81,213)(47,214,82,170)(48,171,83,215)(49,216,84,172)(50,173,57,217)(51,218,58,174)(52,175,59,219)(53,220,60,176)(54,177,61,221)(55,222,62,178)(56,179,63,223), (1,104)(2,16)(3,106)(4,18)(5,108)(6,20)(7,110)(8,22)(9,112)(10,24)(11,86)(12,26)(13,88)(14,28)(15,90)(17,92)(19,94)(21,96)(23,98)(25,100)(27,102)(29,210)(30,79)(31,212)(32,81)(33,214)(34,83)(35,216)(36,57)(37,218)(38,59)(39,220)(40,61)(41,222)(42,63)(43,224)(44,65)(45,198)(46,67)(47,200)(48,69)(49,202)(50,71)(51,204)(52,73)(53,206)(54,75)(55,208)(56,77)(58,188)(60,190)(62,192)(64,194)(66,196)(68,170)(70,172)(72,174)(74,176)(76,178)(78,180)(80,182)(82,184)(84,186)(85,135)(87,137)(89,139)(91,113)(93,115)(95,117)(97,119)(99,121)(101,123)(103,125)(105,127)(107,129)(109,131)(111,133)(114,157)(116,159)(118,161)(120,163)(122,165)(124,167)(126,141)(128,143)(130,145)(132,147)(134,149)(136,151)(138,153)(140,155)(142,156)(144,158)(146,160)(148,162)(150,164)(152,166)(154,168)(169,183)(171,185)(173,187)(175,189)(177,191)(179,193)(181,195)(197,211)(199,213)(201,215)(203,217)(205,219)(207,221)(209,223), (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), (1,178,15,192)(2,221,16,207)(3,176,17,190)(4,219,18,205)(5,174,19,188)(6,217,20,203)(7,172,21,186)(8,215,22,201)(9,170,23,184)(10,213,24,199)(11,196,25,182)(12,211,26,197)(13,194,27,180)(14,209,28,223)(29,138,43,124)(30,101,44,87)(31,136,45,122)(32,99,46,85)(33,134,47,120)(34,97,48,111)(35,132,49,118)(36,95,50,109)(37,130,51,116)(38,93,52,107)(39,128,53,114)(40,91,54,105)(41,126,55,140)(42,89,56,103)(57,117,71,131)(58,108,72,94)(59,115,73,129)(60,106,74,92)(61,113,75,127)(62,104,76,90)(63,139,77,125)(64,102,78,88)(65,137,79,123)(66,100,80,86)(67,135,81,121)(68,98,82,112)(69,133,83,119)(70,96,84,110)(141,208,155,222)(142,191,156,177)(143,206,157,220)(144,189,158,175)(145,204,159,218)(146,187,160,173)(147,202,161,216)(148,185,162,171)(149,200,163,214)(150,183,164,169)(151,198,165,212)(152,181,166,195)(153,224,167,210)(154,179,168,193)>;
G:=Group( (1,126,155,90)(2,91,156,127)(3,128,157,92)(4,93,158,129)(5,130,159,94)(6,95,160,131)(7,132,161,96)(8,97,162,133)(9,134,163,98)(10,99,164,135)(11,136,165,100)(12,101,166,137)(13,138,167,102)(14,103,168,139)(15,140,141,104)(16,105,142,113)(17,114,143,106)(18,107,144,115)(19,116,145,108)(20,109,146,117)(21,118,147,110)(22,111,148,119)(23,120,149,112)(24,85,150,121)(25,122,151,86)(26,87,152,123)(27,124,153,88)(28,89,154,125)(29,224,64,180)(30,181,65,197)(31,198,66,182)(32,183,67,199)(33,200,68,184)(34,185,69,201)(35,202,70,186)(36,187,71,203)(37,204,72,188)(38,189,73,205)(39,206,74,190)(40,191,75,207)(41,208,76,192)(42,193,77,209)(43,210,78,194)(44,195,79,211)(45,212,80,196)(46,169,81,213)(47,214,82,170)(48,171,83,215)(49,216,84,172)(50,173,57,217)(51,218,58,174)(52,175,59,219)(53,220,60,176)(54,177,61,221)(55,222,62,178)(56,179,63,223), (1,104)(2,16)(3,106)(4,18)(5,108)(6,20)(7,110)(8,22)(9,112)(10,24)(11,86)(12,26)(13,88)(14,28)(15,90)(17,92)(19,94)(21,96)(23,98)(25,100)(27,102)(29,210)(30,79)(31,212)(32,81)(33,214)(34,83)(35,216)(36,57)(37,218)(38,59)(39,220)(40,61)(41,222)(42,63)(43,224)(44,65)(45,198)(46,67)(47,200)(48,69)(49,202)(50,71)(51,204)(52,73)(53,206)(54,75)(55,208)(56,77)(58,188)(60,190)(62,192)(64,194)(66,196)(68,170)(70,172)(72,174)(74,176)(76,178)(78,180)(80,182)(82,184)(84,186)(85,135)(87,137)(89,139)(91,113)(93,115)(95,117)(97,119)(99,121)(101,123)(103,125)(105,127)(107,129)(109,131)(111,133)(114,157)(116,159)(118,161)(120,163)(122,165)(124,167)(126,141)(128,143)(130,145)(132,147)(134,149)(136,151)(138,153)(140,155)(142,156)(144,158)(146,160)(148,162)(150,164)(152,166)(154,168)(169,183)(171,185)(173,187)(175,189)(177,191)(179,193)(181,195)(197,211)(199,213)(201,215)(203,217)(205,219)(207,221)(209,223), (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), (1,178,15,192)(2,221,16,207)(3,176,17,190)(4,219,18,205)(5,174,19,188)(6,217,20,203)(7,172,21,186)(8,215,22,201)(9,170,23,184)(10,213,24,199)(11,196,25,182)(12,211,26,197)(13,194,27,180)(14,209,28,223)(29,138,43,124)(30,101,44,87)(31,136,45,122)(32,99,46,85)(33,134,47,120)(34,97,48,111)(35,132,49,118)(36,95,50,109)(37,130,51,116)(38,93,52,107)(39,128,53,114)(40,91,54,105)(41,126,55,140)(42,89,56,103)(57,117,71,131)(58,108,72,94)(59,115,73,129)(60,106,74,92)(61,113,75,127)(62,104,76,90)(63,139,77,125)(64,102,78,88)(65,137,79,123)(66,100,80,86)(67,135,81,121)(68,98,82,112)(69,133,83,119)(70,96,84,110)(141,208,155,222)(142,191,156,177)(143,206,157,220)(144,189,158,175)(145,204,159,218)(146,187,160,173)(147,202,161,216)(148,185,162,171)(149,200,163,214)(150,183,164,169)(151,198,165,212)(152,181,166,195)(153,224,167,210)(154,179,168,193) );
G=PermutationGroup([[(1,126,155,90),(2,91,156,127),(3,128,157,92),(4,93,158,129),(5,130,159,94),(6,95,160,131),(7,132,161,96),(8,97,162,133),(9,134,163,98),(10,99,164,135),(11,136,165,100),(12,101,166,137),(13,138,167,102),(14,103,168,139),(15,140,141,104),(16,105,142,113),(17,114,143,106),(18,107,144,115),(19,116,145,108),(20,109,146,117),(21,118,147,110),(22,111,148,119),(23,120,149,112),(24,85,150,121),(25,122,151,86),(26,87,152,123),(27,124,153,88),(28,89,154,125),(29,224,64,180),(30,181,65,197),(31,198,66,182),(32,183,67,199),(33,200,68,184),(34,185,69,201),(35,202,70,186),(36,187,71,203),(37,204,72,188),(38,189,73,205),(39,206,74,190),(40,191,75,207),(41,208,76,192),(42,193,77,209),(43,210,78,194),(44,195,79,211),(45,212,80,196),(46,169,81,213),(47,214,82,170),(48,171,83,215),(49,216,84,172),(50,173,57,217),(51,218,58,174),(52,175,59,219),(53,220,60,176),(54,177,61,221),(55,222,62,178),(56,179,63,223)], [(1,104),(2,16),(3,106),(4,18),(5,108),(6,20),(7,110),(8,22),(9,112),(10,24),(11,86),(12,26),(13,88),(14,28),(15,90),(17,92),(19,94),(21,96),(23,98),(25,100),(27,102),(29,210),(30,79),(31,212),(32,81),(33,214),(34,83),(35,216),(36,57),(37,218),(38,59),(39,220),(40,61),(41,222),(42,63),(43,224),(44,65),(45,198),(46,67),(47,200),(48,69),(49,202),(50,71),(51,204),(52,73),(53,206),(54,75),(55,208),(56,77),(58,188),(60,190),(62,192),(64,194),(66,196),(68,170),(70,172),(72,174),(74,176),(76,178),(78,180),(80,182),(82,184),(84,186),(85,135),(87,137),(89,139),(91,113),(93,115),(95,117),(97,119),(99,121),(101,123),(103,125),(105,127),(107,129),(109,131),(111,133),(114,157),(116,159),(118,161),(120,163),(122,165),(124,167),(126,141),(128,143),(130,145),(132,147),(134,149),(136,151),(138,153),(140,155),(142,156),(144,158),(146,160),(148,162),(150,164),(152,166),(154,168),(169,183),(171,185),(173,187),(175,189),(177,191),(179,193),(181,195),(197,211),(199,213),(201,215),(203,217),(205,219),(207,221),(209,223)], [(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)], [(1,178,15,192),(2,221,16,207),(3,176,17,190),(4,219,18,205),(5,174,19,188),(6,217,20,203),(7,172,21,186),(8,215,22,201),(9,170,23,184),(10,213,24,199),(11,196,25,182),(12,211,26,197),(13,194,27,180),(14,209,28,223),(29,138,43,124),(30,101,44,87),(31,136,45,122),(32,99,46,85),(33,134,47,120),(34,97,48,111),(35,132,49,118),(36,95,50,109),(37,130,51,116),(38,93,52,107),(39,128,53,114),(40,91,54,105),(41,126,55,140),(42,89,56,103),(57,117,71,131),(58,108,72,94),(59,115,73,129),(60,106,74,92),(61,113,75,127),(62,104,76,90),(63,139,77,125),(64,102,78,88),(65,137,79,123),(66,100,80,86),(67,135,81,121),(68,98,82,112),(69,133,83,119),(70,96,84,110),(141,208,155,222),(142,191,156,177),(143,206,157,220),(144,189,158,175),(145,204,159,218),(146,187,160,173),(147,202,161,216),(148,185,162,171),(149,200,163,214),(150,183,164,169),(151,198,165,212),(152,181,166,195),(153,224,167,210),(154,179,168,193)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 8 | 14 | 14 | 28 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | Q8 | D7 | C4○D4 | D14 | D14 | D14 | C4○D8 | Dic14 | C8⋊C22 | D4⋊2D7 | D4×D7 | D8⋊D7 | SD16⋊3D7 |
| kernel | D4.Dic14 | C28.Q8 | Dic7⋊C8 | C8⋊Dic7 | D4⋊Dic7 | C7×D4⋊C4 | C28.3Q8 | D4×Dic7 | C2×Dic7 | C7×D4 | D4⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×D4 | C14 | D4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 3 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D4.Dic14 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 111 |
| 0 | 0 | 1 | 1 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 1 | 1 |
| 38 | 55 | 0 | 0 |
| 58 | 81 | 0 | 0 |
| 0 | 0 | 26 | 26 |
| 0 | 0 | 100 | 87 |
| 4 | 86 | 0 | 0 |
| 9 | 109 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,112,1,0,0,111,1],[112,0,0,0,0,112,0,0,0,0,112,1,0,0,0,1],[38,58,0,0,55,81,0,0,0,0,26,100,0,0,26,87],[4,9,0,0,86,109,0,0,0,0,15,0,0,0,0,15] >;
D4.Dic14 in GAP, Magma, Sage, TeX
D_4.{\rm Dic}_{14} % in TeX
G:=Group("D4.Dic14"); // GroupNames label
G:=SmallGroup(448,297);
// by ID
G=gap.SmallGroup(448,297);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,926,219,58,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^2=c^28=1,d^2=c^14,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^-1*b,b*d=d*b,d*c*d^-1=a^2*c^-1>;
// generators/relations