metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D4.2Dic14, C4⋊C4.7D14, C56⋊1C4⋊7C2, (C2×C8).7D14, C7⋊2(D4.Q8), (C7×D4).2Q8, C28.4(C2×Q8), Dic7⋊C8⋊5C2, D4⋊C4.3D7, (C2×C56).7C22, C28.3Q8⋊3C2, C4.Dic14⋊3C2, (D4×Dic7).6C2, C4.4(C2×Dic14), (C2×D4).129D14, C14.21(C4○D8), C2.6(D8⋊3D7), C2.9(D56⋊C2), D4⋊Dic7.5C2, C22.168(D4×D7), C28.148(C4○D4), C4.77(D4⋊2D7), C14.54(C8⋊C22), (C2×C28).206C23, (C2×Dic7).138D4, (D4×C14).27C22, C14.10(C22⋊Q8), C4⋊Dic7.65C22, (C4×Dic7).10C22, C2.15(C22⋊Dic14), (C2×C7⋊C8).12C22, (C7×D4⋊C4).3C2, (C2×C14).219(C2×D4), (C7×C4⋊C4).11C22, (C2×C4).313(C22×D7), SmallGroup(448,300)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D4.2Dic14
G = < a,b,c,d | a4=b2=c28=1, d2=a2c14, bab=cac-1=a-1, ad=da, cbc-1=a-1b, bd=db, dcd-1=c-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, C4.Dic14, Dic7⋊C8, C56⋊1C4, D4⋊Dic7, C7×D4⋊C4, C28.3Q8, D4×Dic7, D4.2Dic14
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⋊3D7, D56⋊C2, D4.2Dic14
►On 224 points
Generators in S224
(1 77 95 161)(2 162 96 78)(3 79 97 163)(4 164 98 80)(5 81 99 165)(6 166 100 82)(7 83 101 167)(8 168 102 84)(9 57 103 141)(10 142 104 58)(11 59 105 143)(12 144 106 60)(13 61 107 145)(14 146 108 62)(15 63 109 147)(16 148 110 64)(17 65 111 149)(18 150 112 66)(19 67 85 151)(20 152 86 68)(21 69 87 153)(22 154 88 70)(23 71 89 155)(24 156 90 72)(25 73 91 157)(26 158 92 74)(27 75 93 159)(28 160 94 76)(29 126 195 212)(30 213 196 127)(31 128 169 214)(32 215 170 129)(33 130 171 216)(34 217 172 131)(35 132 173 218)(36 219 174 133)(37 134 175 220)(38 221 176 135)(39 136 177 222)(40 223 178 137)(41 138 179 224)(42 197 180 139)(43 140 181 198)(44 199 182 113)(45 114 183 200)(46 201 184 115)(47 116 185 202)(48 203 186 117)(49 118 187 204)(50 205 188 119)(51 120 189 206)(52 207 190 121)(53 122 191 208)(54 209 192 123)(55 124 193 210)(56 211 194 125)
(1 63)(2 110)(3 65)(4 112)(5 67)(6 86)(7 69)(8 88)(9 71)(10 90)(11 73)(12 92)(13 75)(14 94)(15 77)(16 96)(17 79)(18 98)(19 81)(20 100)(21 83)(22 102)(23 57)(24 104)(25 59)(26 106)(27 61)(28 108)(29 181)(30 199)(31 183)(32 201)(33 185)(34 203)(35 187)(36 205)(37 189)(38 207)(39 191)(40 209)(41 193)(42 211)(43 195)(44 213)(45 169)(46 215)(47 171)(48 217)(49 173)(50 219)(51 175)(52 221)(53 177)(54 223)(55 179)(56 197)(58 72)(60 74)(62 76)(64 78)(66 80)(68 82)(70 84)(85 165)(87 167)(89 141)(91 143)(93 145)(95 147)(97 149)(99 151)(101 153)(103 155)(105 157)(107 159)(109 161)(111 163)(113 196)(114 128)(115 170)(116 130)(117 172)(118 132)(119 174)(120 134)(121 176)(122 136)(123 178)(124 138)(125 180)(126 140)(127 182)(129 184)(131 186)(133 188)(135 190)(137 192)(139 194)(142 156)(144 158)(146 160)(148 162)(150 164)(152 166)(154 168)(198 212)(200 214)(202 216)(204 218)(206 220)(208 222)(210 224)
(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 50 109 174)(2 49 110 173)(3 48 111 172)(4 47 112 171)(5 46 85 170)(6 45 86 169)(7 44 87 196)(8 43 88 195)(9 42 89 194)(10 41 90 193)(11 40 91 192)(12 39 92 191)(13 38 93 190)(14 37 94 189)(15 36 95 188)(16 35 96 187)(17 34 97 186)(18 33 98 185)(19 32 99 184)(20 31 100 183)(21 30 101 182)(22 29 102 181)(23 56 103 180)(24 55 104 179)(25 54 105 178)(26 53 106 177)(27 52 107 176)(28 51 108 175)(57 197 155 125)(58 224 156 124)(59 223 157 123)(60 222 158 122)(61 221 159 121)(62 220 160 120)(63 219 161 119)(64 218 162 118)(65 217 163 117)(66 216 164 116)(67 215 165 115)(68 214 166 114)(69 213 167 113)(70 212 168 140)(71 211 141 139)(72 210 142 138)(73 209 143 137)(74 208 144 136)(75 207 145 135)(76 206 146 134)(77 205 147 133)(78 204 148 132)(79 203 149 131)(80 202 150 130)(81 201 151 129)(82 200 152 128)(83 199 153 127)(84 198 154 126)
G:=sub<Sym(224)| (1,77,95,161)(2,162,96,78)(3,79,97,163)(4,164,98,80)(5,81,99,165)(6,166,100,82)(7,83,101,167)(8,168,102,84)(9,57,103,141)(10,142,104,58)(11,59,105,143)(12,144,106,60)(13,61,107,145)(14,146,108,62)(15,63,109,147)(16,148,110,64)(17,65,111,149)(18,150,112,66)(19,67,85,151)(20,152,86,68)(21,69,87,153)(22,154,88,70)(23,71,89,155)(24,156,90,72)(25,73,91,157)(26,158,92,74)(27,75,93,159)(28,160,94,76)(29,126,195,212)(30,213,196,127)(31,128,169,214)(32,215,170,129)(33,130,171,216)(34,217,172,131)(35,132,173,218)(36,219,174,133)(37,134,175,220)(38,221,176,135)(39,136,177,222)(40,223,178,137)(41,138,179,224)(42,197,180,139)(43,140,181,198)(44,199,182,113)(45,114,183,200)(46,201,184,115)(47,116,185,202)(48,203,186,117)(49,118,187,204)(50,205,188,119)(51,120,189,206)(52,207,190,121)(53,122,191,208)(54,209,192,123)(55,124,193,210)(56,211,194,125), (1,63)(2,110)(3,65)(4,112)(5,67)(6,86)(7,69)(8,88)(9,71)(10,90)(11,73)(12,92)(13,75)(14,94)(15,77)(16,96)(17,79)(18,98)(19,81)(20,100)(21,83)(22,102)(23,57)(24,104)(25,59)(26,106)(27,61)(28,108)(29,181)(30,199)(31,183)(32,201)(33,185)(34,203)(35,187)(36,205)(37,189)(38,207)(39,191)(40,209)(41,193)(42,211)(43,195)(44,213)(45,169)(46,215)(47,171)(48,217)(49,173)(50,219)(51,175)(52,221)(53,177)(54,223)(55,179)(56,197)(58,72)(60,74)(62,76)(64,78)(66,80)(68,82)(70,84)(85,165)(87,167)(89,141)(91,143)(93,145)(95,147)(97,149)(99,151)(101,153)(103,155)(105,157)(107,159)(109,161)(111,163)(113,196)(114,128)(115,170)(116,130)(117,172)(118,132)(119,174)(120,134)(121,176)(122,136)(123,178)(124,138)(125,180)(126,140)(127,182)(129,184)(131,186)(133,188)(135,190)(137,192)(139,194)(142,156)(144,158)(146,160)(148,162)(150,164)(152,166)(154,168)(198,212)(200,214)(202,216)(204,218)(206,220)(208,222)(210,224), (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), (1,50,109,174)(2,49,110,173)(3,48,111,172)(4,47,112,171)(5,46,85,170)(6,45,86,169)(7,44,87,196)(8,43,88,195)(9,42,89,194)(10,41,90,193)(11,40,91,192)(12,39,92,191)(13,38,93,190)(14,37,94,189)(15,36,95,188)(16,35,96,187)(17,34,97,186)(18,33,98,185)(19,32,99,184)(20,31,100,183)(21,30,101,182)(22,29,102,181)(23,56,103,180)(24,55,104,179)(25,54,105,178)(26,53,106,177)(27,52,107,176)(28,51,108,175)(57,197,155,125)(58,224,156,124)(59,223,157,123)(60,222,158,122)(61,221,159,121)(62,220,160,120)(63,219,161,119)(64,218,162,118)(65,217,163,117)(66,216,164,116)(67,215,165,115)(68,214,166,114)(69,213,167,113)(70,212,168,140)(71,211,141,139)(72,210,142,138)(73,209,143,137)(74,208,144,136)(75,207,145,135)(76,206,146,134)(77,205,147,133)(78,204,148,132)(79,203,149,131)(80,202,150,130)(81,201,151,129)(82,200,152,128)(83,199,153,127)(84,198,154,126)>;
G:=Group( (1,77,95,161)(2,162,96,78)(3,79,97,163)(4,164,98,80)(5,81,99,165)(6,166,100,82)(7,83,101,167)(8,168,102,84)(9,57,103,141)(10,142,104,58)(11,59,105,143)(12,144,106,60)(13,61,107,145)(14,146,108,62)(15,63,109,147)(16,148,110,64)(17,65,111,149)(18,150,112,66)(19,67,85,151)(20,152,86,68)(21,69,87,153)(22,154,88,70)(23,71,89,155)(24,156,90,72)(25,73,91,157)(26,158,92,74)(27,75,93,159)(28,160,94,76)(29,126,195,212)(30,213,196,127)(31,128,169,214)(32,215,170,129)(33,130,171,216)(34,217,172,131)(35,132,173,218)(36,219,174,133)(37,134,175,220)(38,221,176,135)(39,136,177,222)(40,223,178,137)(41,138,179,224)(42,197,180,139)(43,140,181,198)(44,199,182,113)(45,114,183,200)(46,201,184,115)(47,116,185,202)(48,203,186,117)(49,118,187,204)(50,205,188,119)(51,120,189,206)(52,207,190,121)(53,122,191,208)(54,209,192,123)(55,124,193,210)(56,211,194,125), (1,63)(2,110)(3,65)(4,112)(5,67)(6,86)(7,69)(8,88)(9,71)(10,90)(11,73)(12,92)(13,75)(14,94)(15,77)(16,96)(17,79)(18,98)(19,81)(20,100)(21,83)(22,102)(23,57)(24,104)(25,59)(26,106)(27,61)(28,108)(29,181)(30,199)(31,183)(32,201)(33,185)(34,203)(35,187)(36,205)(37,189)(38,207)(39,191)(40,209)(41,193)(42,211)(43,195)(44,213)(45,169)(46,215)(47,171)(48,217)(49,173)(50,219)(51,175)(52,221)(53,177)(54,223)(55,179)(56,197)(58,72)(60,74)(62,76)(64,78)(66,80)(68,82)(70,84)(85,165)(87,167)(89,141)(91,143)(93,145)(95,147)(97,149)(99,151)(101,153)(103,155)(105,157)(107,159)(109,161)(111,163)(113,196)(114,128)(115,170)(116,130)(117,172)(118,132)(119,174)(120,134)(121,176)(122,136)(123,178)(124,138)(125,180)(126,140)(127,182)(129,184)(131,186)(133,188)(135,190)(137,192)(139,194)(142,156)(144,158)(146,160)(148,162)(150,164)(152,166)(154,168)(198,212)(200,214)(202,216)(204,218)(206,220)(208,222)(210,224), (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), (1,50,109,174)(2,49,110,173)(3,48,111,172)(4,47,112,171)(5,46,85,170)(6,45,86,169)(7,44,87,196)(8,43,88,195)(9,42,89,194)(10,41,90,193)(11,40,91,192)(12,39,92,191)(13,38,93,190)(14,37,94,189)(15,36,95,188)(16,35,96,187)(17,34,97,186)(18,33,98,185)(19,32,99,184)(20,31,100,183)(21,30,101,182)(22,29,102,181)(23,56,103,180)(24,55,104,179)(25,54,105,178)(26,53,106,177)(27,52,107,176)(28,51,108,175)(57,197,155,125)(58,224,156,124)(59,223,157,123)(60,222,158,122)(61,221,159,121)(62,220,160,120)(63,219,161,119)(64,218,162,118)(65,217,163,117)(66,216,164,116)(67,215,165,115)(68,214,166,114)(69,213,167,113)(70,212,168,140)(71,211,141,139)(72,210,142,138)(73,209,143,137)(74,208,144,136)(75,207,145,135)(76,206,146,134)(77,205,147,133)(78,204,148,132)(79,203,149,131)(80,202,150,130)(81,201,151,129)(82,200,152,128)(83,199,153,127)(84,198,154,126) );
G=PermutationGroup([[(1,77,95,161),(2,162,96,78),(3,79,97,163),(4,164,98,80),(5,81,99,165),(6,166,100,82),(7,83,101,167),(8,168,102,84),(9,57,103,141),(10,142,104,58),(11,59,105,143),(12,144,106,60),(13,61,107,145),(14,146,108,62),(15,63,109,147),(16,148,110,64),(17,65,111,149),(18,150,112,66),(19,67,85,151),(20,152,86,68),(21,69,87,153),(22,154,88,70),(23,71,89,155),(24,156,90,72),(25,73,91,157),(26,158,92,74),(27,75,93,159),(28,160,94,76),(29,126,195,212),(30,213,196,127),(31,128,169,214),(32,215,170,129),(33,130,171,216),(34,217,172,131),(35,132,173,218),(36,219,174,133),(37,134,175,220),(38,221,176,135),(39,136,177,222),(40,223,178,137),(41,138,179,224),(42,197,180,139),(43,140,181,198),(44,199,182,113),(45,114,183,200),(46,201,184,115),(47,116,185,202),(48,203,186,117),(49,118,187,204),(50,205,188,119),(51,120,189,206),(52,207,190,121),(53,122,191,208),(54,209,192,123),(55,124,193,210),(56,211,194,125)], [(1,63),(2,110),(3,65),(4,112),(5,67),(6,86),(7,69),(8,88),(9,71),(10,90),(11,73),(12,92),(13,75),(14,94),(15,77),(16,96),(17,79),(18,98),(19,81),(20,100),(21,83),(22,102),(23,57),(24,104),(25,59),(26,106),(27,61),(28,108),(29,181),(30,199),(31,183),(32,201),(33,185),(34,203),(35,187),(36,205),(37,189),(38,207),(39,191),(40,209),(41,193),(42,211),(43,195),(44,213),(45,169),(46,215),(47,171),(48,217),(49,173),(50,219),(51,175),(52,221),(53,177),(54,223),(55,179),(56,197),(58,72),(60,74),(62,76),(64,78),(66,80),(68,82),(70,84),(85,165),(87,167),(89,141),(91,143),(93,145),(95,147),(97,149),(99,151),(101,153),(103,155),(105,157),(107,159),(109,161),(111,163),(113,196),(114,128),(115,170),(116,130),(117,172),(118,132),(119,174),(120,134),(121,176),(122,136),(123,178),(124,138),(125,180),(126,140),(127,182),(129,184),(131,186),(133,188),(135,190),(137,192),(139,194),(142,156),(144,158),(146,160),(148,162),(150,164),(152,166),(154,168),(198,212),(200,214),(202,216),(204,218),(206,220),(208,222),(210,224)], [(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)], [(1,50,109,174),(2,49,110,173),(3,48,111,172),(4,47,112,171),(5,46,85,170),(6,45,86,169),(7,44,87,196),(8,43,88,195),(9,42,89,194),(10,41,90,193),(11,40,91,192),(12,39,92,191),(13,38,93,190),(14,37,94,189),(15,36,95,188),(16,35,96,187),(17,34,97,186),(18,33,98,185),(19,32,99,184),(20,31,100,183),(21,30,101,182),(22,29,102,181),(23,56,103,180),(24,55,104,179),(25,54,105,178),(26,53,106,177),(27,52,107,176),(28,51,108,175),(57,197,155,125),(58,224,156,124),(59,223,157,123),(60,222,158,122),(61,221,159,121),(62,220,160,120),(63,219,161,119),(64,218,162,118),(65,217,163,117),(66,216,164,116),(67,215,165,115),(68,214,166,114),(69,213,167,113),(70,212,168,140),(71,211,141,139),(72,210,142,138),(73,209,143,137),(74,208,144,136),(75,207,145,135),(76,206,146,134),(77,205,147,133),(78,204,148,132),(79,203,149,131),(80,202,150,130),(81,201,151,129),(82,200,152,128),(83,199,153,127),(84,198,154,126)]])
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⋊3D7 | D56⋊C2 |
| kernel | D4.2Dic14 | C4.Dic14 | Dic7⋊C8 | C56⋊1C4 | 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 D4.2Dic14 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 19 | 7 |
| 0 | 0 | 29 | 94 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 94 | 106 |
| 0 | 0 | 3 | 19 |
| 14 | 104 | 0 | 0 |
| 18 | 45 | 0 | 0 |
| 0 | 0 | 58 | 9 |
| 0 | 0 | 3 | 55 |
| 75 | 82 | 0 | 0 |
| 94 | 38 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,19,29,0,0,7,94],[112,0,0,0,0,112,0,0,0,0,94,3,0,0,106,19],[14,18,0,0,104,45,0,0,0,0,58,3,0,0,9,55],[75,94,0,0,82,38,0,0,0,0,15,0,0,0,0,15] >;
D4.2Dic14 in GAP, Magma, Sage, TeX
D_4._2{\rm Dic}_{14} % in TeX
G:=Group("D4.2Dic14"); // GroupNames label
G:=SmallGroup(448,300);
// by ID
G=gap.SmallGroup(448,300);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,926,219,226,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^2=c^28=1,d^2=a^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=c^-1>;
// generators/relations