metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊2D4, Dic7⋊4SD16, C4.82(D4×D7), D4⋊C4⋊9D7, C7⋊1(C4⋊SD16), C14.D8⋊2C2, Dic7⋊C8⋊10C2, C4⋊C4.131D14, (C2×D4).18D14, C28.2(C4○D4), C4.1(C4○D28), (C2×C8).113D14, C28⋊D4.3C2, C28.101(C2×D4), C2.10(D7×SD16), Dic7⋊3Q8⋊3C2, C2.9(D8⋊D7), C14.21(C2×SD16), C22.164(D4×D7), C14.13(C4⋊D4), C14.26(C8⋊C22), (C2×C56).124C22, (C2×C28).202C23, (C2×Dic7).136D4, (D4×C14).23C22, (C2×D28).45C22, C2.16(D14⋊D4), (C4×Dic7).6C22, (C2×Dic14).51C22, (C2×D4.D7)⋊2C2, (C2×C7⋊C8).8C22, (C7×D4⋊C4)⋊9C2, (C2×C56⋊C2)⋊13C2, (C7×C4⋊C4).7C22, (C2×C14).215(C2×D4), (C2×C4).309(C22×D7), SmallGroup(448,296)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊2D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=dad=a-1, cac-1=a13, bc=cb, dbd=a7b, dcd=c-1 >
Subgroups: 788 in 128 conjugacy classes, 41 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, C2×D4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, D4⋊C4, D4⋊C4, C4⋊C8, C4×Q8, C4⋊1D4, C2×SD16, C7⋊C8, C56, Dic14, Dic14, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C4⋊SD16, C56⋊C2, C2×C7⋊C8, C4×Dic7, C4×Dic7, Dic7⋊C4, D4.D7, C7×C4⋊C4, C2×C56, C2×Dic14, C2×D28, C2×C7⋊D4, D4×C14, C14.D8, Dic7⋊C8, C7×D4⋊C4, Dic7⋊3Q8, C2×C56⋊C2, C2×D4.D7, C28⋊D4, Dic14⋊2D4
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C4⋊D4, C2×SD16, C8⋊C22, C22×D7, C4⋊SD16, C4○D28, D4×D7, D14⋊D4, D8⋊D7, D7×SD16, Dic14⋊2D4
►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)
(1 196 15 182)(2 195 16 181)(3 194 17 180)(4 193 18 179)(5 192 19 178)(6 191 20 177)(7 190 21 176)(8 189 22 175)(9 188 23 174)(10 187 24 173)(11 186 25 172)(12 185 26 171)(13 184 27 170)(14 183 28 169)(29 98 43 112)(30 97 44 111)(31 96 45 110)(32 95 46 109)(33 94 47 108)(34 93 48 107)(35 92 49 106)(36 91 50 105)(37 90 51 104)(38 89 52 103)(39 88 53 102)(40 87 54 101)(41 86 55 100)(42 85 56 99)(57 161 71 147)(58 160 72 146)(59 159 73 145)(60 158 74 144)(61 157 75 143)(62 156 76 142)(63 155 77 141)(64 154 78 168)(65 153 79 167)(66 152 80 166)(67 151 81 165)(68 150 82 164)(69 149 83 163)(70 148 84 162)(113 219 127 205)(114 218 128 204)(115 217 129 203)(116 216 130 202)(117 215 131 201)(118 214 132 200)(119 213 133 199)(120 212 134 198)(121 211 135 197)(122 210 136 224)(123 209 137 223)(124 208 138 222)(125 207 139 221)(126 206 140 220)
(1 206 38 168)(2 219 39 153)(3 204 40 166)(4 217 41 151)(5 202 42 164)(6 215 43 149)(7 200 44 162)(8 213 45 147)(9 198 46 160)(10 211 47 145)(11 224 48 158)(12 209 49 143)(13 222 50 156)(14 207 51 141)(15 220 52 154)(16 205 53 167)(17 218 54 152)(18 203 55 165)(19 216 56 150)(20 201 29 163)(21 214 30 148)(22 199 31 161)(23 212 32 146)(24 197 33 159)(25 210 34 144)(26 223 35 157)(27 208 36 142)(28 221 37 155)(57 189 133 110)(58 174 134 95)(59 187 135 108)(60 172 136 93)(61 185 137 106)(62 170 138 91)(63 183 139 104)(64 196 140 89)(65 181 113 102)(66 194 114 87)(67 179 115 100)(68 192 116 85)(69 177 117 98)(70 190 118 111)(71 175 119 96)(72 188 120 109)(73 173 121 94)(74 186 122 107)(75 171 123 92)(76 184 124 105)(77 169 125 90)(78 182 126 103)(79 195 127 88)(80 180 128 101)(81 193 129 86)(82 178 130 99)(83 191 131 112)(84 176 132 97)
(1 168)(2 167)(3 166)(4 165)(5 164)(6 163)(7 162)(8 161)(9 160)(10 159)(11 158)(12 157)(13 156)(14 155)(15 154)(16 153)(17 152)(18 151)(19 150)(20 149)(21 148)(22 147)(23 146)(24 145)(25 144)(26 143)(27 142)(28 141)(29 215)(30 214)(31 213)(32 212)(33 211)(34 210)(35 209)(36 208)(37 207)(38 206)(39 205)(40 204)(41 203)(42 202)(43 201)(44 200)(45 199)(46 198)(47 197)(48 224)(49 223)(50 222)(51 221)(52 220)(53 219)(54 218)(55 217)(56 216)(57 196)(58 195)(59 194)(60 193)(61 192)(62 191)(63 190)(64 189)(65 188)(66 187)(67 186)(68 185)(69 184)(70 183)(71 182)(72 181)(73 180)(74 179)(75 178)(76 177)(77 176)(78 175)(79 174)(80 173)(81 172)(82 171)(83 170)(84 169)(85 137)(86 136)(87 135)(88 134)(89 133)(90 132)(91 131)(92 130)(93 129)(94 128)(95 127)(96 126)(97 125)(98 124)(99 123)(100 122)(101 121)(102 120)(103 119)(104 118)(105 117)(106 116)(107 115)(108 114)(109 113)(110 140)(111 139)(112 138)
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), (1,196,15,182)(2,195,16,181)(3,194,17,180)(4,193,18,179)(5,192,19,178)(6,191,20,177)(7,190,21,176)(8,189,22,175)(9,188,23,174)(10,187,24,173)(11,186,25,172)(12,185,26,171)(13,184,27,170)(14,183,28,169)(29,98,43,112)(30,97,44,111)(31,96,45,110)(32,95,46,109)(33,94,47,108)(34,93,48,107)(35,92,49,106)(36,91,50,105)(37,90,51,104)(38,89,52,103)(39,88,53,102)(40,87,54,101)(41,86,55,100)(42,85,56,99)(57,161,71,147)(58,160,72,146)(59,159,73,145)(60,158,74,144)(61,157,75,143)(62,156,76,142)(63,155,77,141)(64,154,78,168)(65,153,79,167)(66,152,80,166)(67,151,81,165)(68,150,82,164)(69,149,83,163)(70,148,84,162)(113,219,127,205)(114,218,128,204)(115,217,129,203)(116,216,130,202)(117,215,131,201)(118,214,132,200)(119,213,133,199)(120,212,134,198)(121,211,135,197)(122,210,136,224)(123,209,137,223)(124,208,138,222)(125,207,139,221)(126,206,140,220), (1,206,38,168)(2,219,39,153)(3,204,40,166)(4,217,41,151)(5,202,42,164)(6,215,43,149)(7,200,44,162)(8,213,45,147)(9,198,46,160)(10,211,47,145)(11,224,48,158)(12,209,49,143)(13,222,50,156)(14,207,51,141)(15,220,52,154)(16,205,53,167)(17,218,54,152)(18,203,55,165)(19,216,56,150)(20,201,29,163)(21,214,30,148)(22,199,31,161)(23,212,32,146)(24,197,33,159)(25,210,34,144)(26,223,35,157)(27,208,36,142)(28,221,37,155)(57,189,133,110)(58,174,134,95)(59,187,135,108)(60,172,136,93)(61,185,137,106)(62,170,138,91)(63,183,139,104)(64,196,140,89)(65,181,113,102)(66,194,114,87)(67,179,115,100)(68,192,116,85)(69,177,117,98)(70,190,118,111)(71,175,119,96)(72,188,120,109)(73,173,121,94)(74,186,122,107)(75,171,123,92)(76,184,124,105)(77,169,125,90)(78,182,126,103)(79,195,127,88)(80,180,128,101)(81,193,129,86)(82,178,130,99)(83,191,131,112)(84,176,132,97), (1,168)(2,167)(3,166)(4,165)(5,164)(6,163)(7,162)(8,161)(9,160)(10,159)(11,158)(12,157)(13,156)(14,155)(15,154)(16,153)(17,152)(18,151)(19,150)(20,149)(21,148)(22,147)(23,146)(24,145)(25,144)(26,143)(27,142)(28,141)(29,215)(30,214)(31,213)(32,212)(33,211)(34,210)(35,209)(36,208)(37,207)(38,206)(39,205)(40,204)(41,203)(42,202)(43,201)(44,200)(45,199)(46,198)(47,197)(48,224)(49,223)(50,222)(51,221)(52,220)(53,219)(54,218)(55,217)(56,216)(57,196)(58,195)(59,194)(60,193)(61,192)(62,191)(63,190)(64,189)(65,188)(66,187)(67,186)(68,185)(69,184)(70,183)(71,182)(72,181)(73,180)(74,179)(75,178)(76,177)(77,176)(78,175)(79,174)(80,173)(81,172)(82,171)(83,170)(84,169)(85,137)(86,136)(87,135)(88,134)(89,133)(90,132)(91,131)(92,130)(93,129)(94,128)(95,127)(96,126)(97,125)(98,124)(99,123)(100,122)(101,121)(102,120)(103,119)(104,118)(105,117)(106,116)(107,115)(108,114)(109,113)(110,140)(111,139)(112,138)>;
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), (1,196,15,182)(2,195,16,181)(3,194,17,180)(4,193,18,179)(5,192,19,178)(6,191,20,177)(7,190,21,176)(8,189,22,175)(9,188,23,174)(10,187,24,173)(11,186,25,172)(12,185,26,171)(13,184,27,170)(14,183,28,169)(29,98,43,112)(30,97,44,111)(31,96,45,110)(32,95,46,109)(33,94,47,108)(34,93,48,107)(35,92,49,106)(36,91,50,105)(37,90,51,104)(38,89,52,103)(39,88,53,102)(40,87,54,101)(41,86,55,100)(42,85,56,99)(57,161,71,147)(58,160,72,146)(59,159,73,145)(60,158,74,144)(61,157,75,143)(62,156,76,142)(63,155,77,141)(64,154,78,168)(65,153,79,167)(66,152,80,166)(67,151,81,165)(68,150,82,164)(69,149,83,163)(70,148,84,162)(113,219,127,205)(114,218,128,204)(115,217,129,203)(116,216,130,202)(117,215,131,201)(118,214,132,200)(119,213,133,199)(120,212,134,198)(121,211,135,197)(122,210,136,224)(123,209,137,223)(124,208,138,222)(125,207,139,221)(126,206,140,220), (1,206,38,168)(2,219,39,153)(3,204,40,166)(4,217,41,151)(5,202,42,164)(6,215,43,149)(7,200,44,162)(8,213,45,147)(9,198,46,160)(10,211,47,145)(11,224,48,158)(12,209,49,143)(13,222,50,156)(14,207,51,141)(15,220,52,154)(16,205,53,167)(17,218,54,152)(18,203,55,165)(19,216,56,150)(20,201,29,163)(21,214,30,148)(22,199,31,161)(23,212,32,146)(24,197,33,159)(25,210,34,144)(26,223,35,157)(27,208,36,142)(28,221,37,155)(57,189,133,110)(58,174,134,95)(59,187,135,108)(60,172,136,93)(61,185,137,106)(62,170,138,91)(63,183,139,104)(64,196,140,89)(65,181,113,102)(66,194,114,87)(67,179,115,100)(68,192,116,85)(69,177,117,98)(70,190,118,111)(71,175,119,96)(72,188,120,109)(73,173,121,94)(74,186,122,107)(75,171,123,92)(76,184,124,105)(77,169,125,90)(78,182,126,103)(79,195,127,88)(80,180,128,101)(81,193,129,86)(82,178,130,99)(83,191,131,112)(84,176,132,97), (1,168)(2,167)(3,166)(4,165)(5,164)(6,163)(7,162)(8,161)(9,160)(10,159)(11,158)(12,157)(13,156)(14,155)(15,154)(16,153)(17,152)(18,151)(19,150)(20,149)(21,148)(22,147)(23,146)(24,145)(25,144)(26,143)(27,142)(28,141)(29,215)(30,214)(31,213)(32,212)(33,211)(34,210)(35,209)(36,208)(37,207)(38,206)(39,205)(40,204)(41,203)(42,202)(43,201)(44,200)(45,199)(46,198)(47,197)(48,224)(49,223)(50,222)(51,221)(52,220)(53,219)(54,218)(55,217)(56,216)(57,196)(58,195)(59,194)(60,193)(61,192)(62,191)(63,190)(64,189)(65,188)(66,187)(67,186)(68,185)(69,184)(70,183)(71,182)(72,181)(73,180)(74,179)(75,178)(76,177)(77,176)(78,175)(79,174)(80,173)(81,172)(82,171)(83,170)(84,169)(85,137)(86,136)(87,135)(88,134)(89,133)(90,132)(91,131)(92,130)(93,129)(94,128)(95,127)(96,126)(97,125)(98,124)(99,123)(100,122)(101,121)(102,120)(103,119)(104,118)(105,117)(106,116)(107,115)(108,114)(109,113)(110,140)(111,139)(112,138) );
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)], [(1,196,15,182),(2,195,16,181),(3,194,17,180),(4,193,18,179),(5,192,19,178),(6,191,20,177),(7,190,21,176),(8,189,22,175),(9,188,23,174),(10,187,24,173),(11,186,25,172),(12,185,26,171),(13,184,27,170),(14,183,28,169),(29,98,43,112),(30,97,44,111),(31,96,45,110),(32,95,46,109),(33,94,47,108),(34,93,48,107),(35,92,49,106),(36,91,50,105),(37,90,51,104),(38,89,52,103),(39,88,53,102),(40,87,54,101),(41,86,55,100),(42,85,56,99),(57,161,71,147),(58,160,72,146),(59,159,73,145),(60,158,74,144),(61,157,75,143),(62,156,76,142),(63,155,77,141),(64,154,78,168),(65,153,79,167),(66,152,80,166),(67,151,81,165),(68,150,82,164),(69,149,83,163),(70,148,84,162),(113,219,127,205),(114,218,128,204),(115,217,129,203),(116,216,130,202),(117,215,131,201),(118,214,132,200),(119,213,133,199),(120,212,134,198),(121,211,135,197),(122,210,136,224),(123,209,137,223),(124,208,138,222),(125,207,139,221),(126,206,140,220)], [(1,206,38,168),(2,219,39,153),(3,204,40,166),(4,217,41,151),(5,202,42,164),(6,215,43,149),(7,200,44,162),(8,213,45,147),(9,198,46,160),(10,211,47,145),(11,224,48,158),(12,209,49,143),(13,222,50,156),(14,207,51,141),(15,220,52,154),(16,205,53,167),(17,218,54,152),(18,203,55,165),(19,216,56,150),(20,201,29,163),(21,214,30,148),(22,199,31,161),(23,212,32,146),(24,197,33,159),(25,210,34,144),(26,223,35,157),(27,208,36,142),(28,221,37,155),(57,189,133,110),(58,174,134,95),(59,187,135,108),(60,172,136,93),(61,185,137,106),(62,170,138,91),(63,183,139,104),(64,196,140,89),(65,181,113,102),(66,194,114,87),(67,179,115,100),(68,192,116,85),(69,177,117,98),(70,190,118,111),(71,175,119,96),(72,188,120,109),(73,173,121,94),(74,186,122,107),(75,171,123,92),(76,184,124,105),(77,169,125,90),(78,182,126,103),(79,195,127,88),(80,180,128,101),(81,193,129,86),(82,178,130,99),(83,191,131,112),(84,176,132,97)], [(1,168),(2,167),(3,166),(4,165),(5,164),(6,163),(7,162),(8,161),(9,160),(10,159),(11,158),(12,157),(13,156),(14,155),(15,154),(16,153),(17,152),(18,151),(19,150),(20,149),(21,148),(22,147),(23,146),(24,145),(25,144),(26,143),(27,142),(28,141),(29,215),(30,214),(31,213),(32,212),(33,211),(34,210),(35,209),(36,208),(37,207),(38,206),(39,205),(40,204),(41,203),(42,202),(43,201),(44,200),(45,199),(46,198),(47,197),(48,224),(49,223),(50,222),(51,221),(52,220),(53,219),(54,218),(55,217),(56,216),(57,196),(58,195),(59,194),(60,193),(61,192),(62,191),(63,190),(64,189),(65,188),(66,187),(67,186),(68,185),(69,184),(70,183),(71,182),(72,181),(73,180),(74,179),(75,178),(76,177),(77,176),(78,175),(79,174),(80,173),(81,172),(82,171),(83,170),(84,169),(85,137),(86,136),(87,135),(88,134),(89,133),(90,132),(91,131),(92,130),(93,129),(94,128),(95,127),(96,126),(97,125),(98,124),(99,123),(100,122),(101,121),(102,120),(103,119),(104,118),(105,117),(106,116),(107,115),(108,114),(109,113),(110,140),(111,139),(112,138)]])
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 | 8 | 56 | 2 | 2 | 4 | 4 | 14 | 14 | 28 | 28 | 28 | 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 | D4 | D7 | SD16 | C4○D4 | D14 | D14 | D14 | C4○D28 | C8⋊C22 | D4×D7 | D4×D7 | D8⋊D7 | D7×SD16 |
| kernel | Dic14⋊2D4 | C14.D8 | Dic7⋊C8 | C7×D4⋊C4 | Dic7⋊3Q8 | C2×C56⋊C2 | C2×D4.D7 | C28⋊D4 | Dic14 | C2×Dic7 | D4⋊C4 | Dic7 | C28 | C4⋊C4 | C2×C8 | C2×D4 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 4 | 2 | 3 | 3 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of Dic14⋊2D4 ►in GL4(𝔽113) generated by
| 97 | 0 | 0 | 0 |
| 0 | 7 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 112 | 0 |
| 0 | 15 | 0 | 0 |
| 98 | 0 | 0 | 0 |
| 0 | 0 | 13 | 13 |
| 0 | 0 | 13 | 100 |
| 0 | 1 | 0 | 0 |
| 112 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 1 |
G:=sub<GL(4,GF(113))| [97,0,0,0,0,7,0,0,0,0,0,112,0,0,1,0],[0,98,0,0,15,0,0,0,0,0,13,13,0,0,13,100],[0,112,0,0,1,0,0,0,0,0,112,0,0,0,0,112],[0,1,0,0,1,0,0,0,0,0,112,0,0,0,0,1] >;
Dic14⋊2D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_2D_4 % in TeX
G:=Group("Dic14:2D4"); // GroupNames label
G:=SmallGroup(448,296);
// by ID
G=gap.SmallGroup(448,296);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,253,135,268,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=d*a*d=a^-1,c*a*c^-1=a^13,b*c=c*b,d*b*d=a^7*b,d*c*d=c^-1>;
// generators/relations