metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14.11D4, C4.91(D4×D7), Q8⋊C4⋊9D7, Dic7⋊C8⋊13C2, C4⋊C4.146D14, C4.6(C4○D28), C28.115(C2×D4), (C2×C8).120D14, (C2×Q8).13D14, C7⋊2(Q8.D4), Dic7⋊3Q8⋊5C2, C14.D8.2C2, C28.17(C4○D4), C14.45(C4○D8), (C2×Dic7).28D4, C22.192(D4×D7), C14.22(C4⋊D4), (C2×C28).238C23, (C2×C56).131C22, C28.23D4.3C2, (C2×D28).58C22, (Q8×C14).21C22, C2.25(D14⋊D4), C2.11(Q16⋊D7), C14.56(C8.C22), (C4×Dic7).22C22, C2.14(SD16⋊3D7), (C2×Dic14).67C22, (C2×C7⋊Q16)⋊2C2, (C7×Q8⋊C4)⋊9C2, (C2×C56⋊C2).3C2, (C2×C7⋊C8).33C22, (C2×C14).251(C2×D4), (C7×C4⋊C4).39C22, (C2×C4).345(C22×D7), SmallGroup(448,332)
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=dad=a-1, cac-1=a13, bc=cb, dbd=a7b, dcd=a14c-1 >
Subgroups: 628 in 112 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, Q16, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, D4⋊C4, Q8⋊C4, C4⋊C8, C4×Q8, C4.4D4, C2×SD16, C2×Q16, C7⋊C8, C56, Dic14, Dic14, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, Q8.D4, C56⋊C2, C2×C7⋊C8, C4×Dic7, C4×Dic7, Dic7⋊C4, D14⋊C4, C7⋊Q16, C7×C4⋊C4, C2×C56, C2×Dic14, C2×D28, Q8×C14, C14.D8, Dic7⋊C8, C7×Q8⋊C4, Dic7⋊3Q8, C2×C56⋊C2, C2×C7⋊Q16, C28.23D4, Dic14.11D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C4○D8, C8.C22, C22×D7, Q8.D4, C4○D28, D4×D7, D14⋊D4, SD16⋊3D7, Q16⋊D7, 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 99 15 85)(2 98 16 112)(3 97 17 111)(4 96 18 110)(5 95 19 109)(6 94 20 108)(7 93 21 107)(8 92 22 106)(9 91 23 105)(10 90 24 104)(11 89 25 103)(12 88 26 102)(13 87 27 101)(14 86 28 100)(29 139 43 125)(30 138 44 124)(31 137 45 123)(32 136 46 122)(33 135 47 121)(34 134 48 120)(35 133 49 119)(36 132 50 118)(37 131 51 117)(38 130 52 116)(39 129 53 115)(40 128 54 114)(41 127 55 113)(42 126 56 140)(57 162 71 148)(58 161 72 147)(59 160 73 146)(60 159 74 145)(61 158 75 144)(62 157 76 143)(63 156 77 142)(64 155 78 141)(65 154 79 168)(66 153 80 167)(67 152 81 166)(68 151 82 165)(69 150 83 164)(70 149 84 163)(169 211 183 197)(170 210 184 224)(171 209 185 223)(172 208 186 222)(173 207 187 221)(174 206 188 220)(175 205 189 219)(176 204 190 218)(177 203 191 217)(178 202 192 216)(179 201 193 215)(180 200 194 214)(181 199 195 213)(182 198 196 212)
(1 115 166 201)(2 128 167 214)(3 113 168 199)(4 126 141 212)(5 139 142 197)(6 124 143 210)(7 137 144 223)(8 122 145 208)(9 135 146 221)(10 120 147 206)(11 133 148 219)(12 118 149 204)(13 131 150 217)(14 116 151 202)(15 129 152 215)(16 114 153 200)(17 127 154 213)(18 140 155 198)(19 125 156 211)(20 138 157 224)(21 123 158 209)(22 136 159 222)(23 121 160 207)(24 134 161 220)(25 119 162 205)(26 132 163 218)(27 117 164 203)(28 130 165 216)(29 77 183 109)(30 62 184 94)(31 75 185 107)(32 60 186 92)(33 73 187 105)(34 58 188 90)(35 71 189 103)(36 84 190 88)(37 69 191 101)(38 82 192 86)(39 67 193 99)(40 80 194 112)(41 65 195 97)(42 78 196 110)(43 63 169 95)(44 76 170 108)(45 61 171 93)(46 74 172 106)(47 59 173 91)(48 72 174 104)(49 57 175 89)(50 70 176 102)(51 83 177 87)(52 68 178 100)(53 81 179 85)(54 66 180 98)(55 79 181 111)(56 64 182 96)
(2 28)(3 27)(4 26)(5 25)(6 24)(7 23)(8 22)(9 21)(10 20)(11 19)(12 18)(13 17)(14 16)(29 182)(30 181)(31 180)(32 179)(33 178)(34 177)(35 176)(36 175)(37 174)(38 173)(39 172)(40 171)(41 170)(42 169)(43 196)(44 195)(45 194)(46 193)(47 192)(48 191)(49 190)(50 189)(51 188)(52 187)(53 186)(54 185)(55 184)(56 183)(57 70)(58 69)(59 68)(60 67)(61 66)(62 65)(63 64)(71 84)(72 83)(73 82)(74 81)(75 80)(76 79)(77 78)(85 106)(86 105)(87 104)(88 103)(89 102)(90 101)(91 100)(92 99)(93 98)(94 97)(95 96)(107 112)(108 111)(109 110)(113 217)(114 216)(115 215)(116 214)(117 213)(118 212)(119 211)(120 210)(121 209)(122 208)(123 207)(124 206)(125 205)(126 204)(127 203)(128 202)(129 201)(130 200)(131 199)(132 198)(133 197)(134 224)(135 223)(136 222)(137 221)(138 220)(139 219)(140 218)(141 163)(142 162)(143 161)(144 160)(145 159)(146 158)(147 157)(148 156)(149 155)(150 154)(151 153)(164 168)(165 167)
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), (1,99,15,85)(2,98,16,112)(3,97,17,111)(4,96,18,110)(5,95,19,109)(6,94,20,108)(7,93,21,107)(8,92,22,106)(9,91,23,105)(10,90,24,104)(11,89,25,103)(12,88,26,102)(13,87,27,101)(14,86,28,100)(29,139,43,125)(30,138,44,124)(31,137,45,123)(32,136,46,122)(33,135,47,121)(34,134,48,120)(35,133,49,119)(36,132,50,118)(37,131,51,117)(38,130,52,116)(39,129,53,115)(40,128,54,114)(41,127,55,113)(42,126,56,140)(57,162,71,148)(58,161,72,147)(59,160,73,146)(60,159,74,145)(61,158,75,144)(62,157,76,143)(63,156,77,142)(64,155,78,141)(65,154,79,168)(66,153,80,167)(67,152,81,166)(68,151,82,165)(69,150,83,164)(70,149,84,163)(169,211,183,197)(170,210,184,224)(171,209,185,223)(172,208,186,222)(173,207,187,221)(174,206,188,220)(175,205,189,219)(176,204,190,218)(177,203,191,217)(178,202,192,216)(179,201,193,215)(180,200,194,214)(181,199,195,213)(182,198,196,212), (1,115,166,201)(2,128,167,214)(3,113,168,199)(4,126,141,212)(5,139,142,197)(6,124,143,210)(7,137,144,223)(8,122,145,208)(9,135,146,221)(10,120,147,206)(11,133,148,219)(12,118,149,204)(13,131,150,217)(14,116,151,202)(15,129,152,215)(16,114,153,200)(17,127,154,213)(18,140,155,198)(19,125,156,211)(20,138,157,224)(21,123,158,209)(22,136,159,222)(23,121,160,207)(24,134,161,220)(25,119,162,205)(26,132,163,218)(27,117,164,203)(28,130,165,216)(29,77,183,109)(30,62,184,94)(31,75,185,107)(32,60,186,92)(33,73,187,105)(34,58,188,90)(35,71,189,103)(36,84,190,88)(37,69,191,101)(38,82,192,86)(39,67,193,99)(40,80,194,112)(41,65,195,97)(42,78,196,110)(43,63,169,95)(44,76,170,108)(45,61,171,93)(46,74,172,106)(47,59,173,91)(48,72,174,104)(49,57,175,89)(50,70,176,102)(51,83,177,87)(52,68,178,100)(53,81,179,85)(54,66,180,98)(55,79,181,111)(56,64,182,96), (2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(29,182)(30,181)(31,180)(32,179)(33,178)(34,177)(35,176)(36,175)(37,174)(38,173)(39,172)(40,171)(41,170)(42,169)(43,196)(44,195)(45,194)(46,193)(47,192)(48,191)(49,190)(50,189)(51,188)(52,187)(53,186)(54,185)(55,184)(56,183)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)(107,112)(108,111)(109,110)(113,217)(114,216)(115,215)(116,214)(117,213)(118,212)(119,211)(120,210)(121,209)(122,208)(123,207)(124,206)(125,205)(126,204)(127,203)(128,202)(129,201)(130,200)(131,199)(132,198)(133,197)(134,224)(135,223)(136,222)(137,221)(138,220)(139,219)(140,218)(141,163)(142,162)(143,161)(144,160)(145,159)(146,158)(147,157)(148,156)(149,155)(150,154)(151,153)(164,168)(165,167)>;
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), (1,99,15,85)(2,98,16,112)(3,97,17,111)(4,96,18,110)(5,95,19,109)(6,94,20,108)(7,93,21,107)(8,92,22,106)(9,91,23,105)(10,90,24,104)(11,89,25,103)(12,88,26,102)(13,87,27,101)(14,86,28,100)(29,139,43,125)(30,138,44,124)(31,137,45,123)(32,136,46,122)(33,135,47,121)(34,134,48,120)(35,133,49,119)(36,132,50,118)(37,131,51,117)(38,130,52,116)(39,129,53,115)(40,128,54,114)(41,127,55,113)(42,126,56,140)(57,162,71,148)(58,161,72,147)(59,160,73,146)(60,159,74,145)(61,158,75,144)(62,157,76,143)(63,156,77,142)(64,155,78,141)(65,154,79,168)(66,153,80,167)(67,152,81,166)(68,151,82,165)(69,150,83,164)(70,149,84,163)(169,211,183,197)(170,210,184,224)(171,209,185,223)(172,208,186,222)(173,207,187,221)(174,206,188,220)(175,205,189,219)(176,204,190,218)(177,203,191,217)(178,202,192,216)(179,201,193,215)(180,200,194,214)(181,199,195,213)(182,198,196,212), (1,115,166,201)(2,128,167,214)(3,113,168,199)(4,126,141,212)(5,139,142,197)(6,124,143,210)(7,137,144,223)(8,122,145,208)(9,135,146,221)(10,120,147,206)(11,133,148,219)(12,118,149,204)(13,131,150,217)(14,116,151,202)(15,129,152,215)(16,114,153,200)(17,127,154,213)(18,140,155,198)(19,125,156,211)(20,138,157,224)(21,123,158,209)(22,136,159,222)(23,121,160,207)(24,134,161,220)(25,119,162,205)(26,132,163,218)(27,117,164,203)(28,130,165,216)(29,77,183,109)(30,62,184,94)(31,75,185,107)(32,60,186,92)(33,73,187,105)(34,58,188,90)(35,71,189,103)(36,84,190,88)(37,69,191,101)(38,82,192,86)(39,67,193,99)(40,80,194,112)(41,65,195,97)(42,78,196,110)(43,63,169,95)(44,76,170,108)(45,61,171,93)(46,74,172,106)(47,59,173,91)(48,72,174,104)(49,57,175,89)(50,70,176,102)(51,83,177,87)(52,68,178,100)(53,81,179,85)(54,66,180,98)(55,79,181,111)(56,64,182,96), (2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(29,182)(30,181)(31,180)(32,179)(33,178)(34,177)(35,176)(36,175)(37,174)(38,173)(39,172)(40,171)(41,170)(42,169)(43,196)(44,195)(45,194)(46,193)(47,192)(48,191)(49,190)(50,189)(51,188)(52,187)(53,186)(54,185)(55,184)(56,183)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)(107,112)(108,111)(109,110)(113,217)(114,216)(115,215)(116,214)(117,213)(118,212)(119,211)(120,210)(121,209)(122,208)(123,207)(124,206)(125,205)(126,204)(127,203)(128,202)(129,201)(130,200)(131,199)(132,198)(133,197)(134,224)(135,223)(136,222)(137,221)(138,220)(139,219)(140,218)(141,163)(142,162)(143,161)(144,160)(145,159)(146,158)(147,157)(148,156)(149,155)(150,154)(151,153)(164,168)(165,167) );
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)], [(1,99,15,85),(2,98,16,112),(3,97,17,111),(4,96,18,110),(5,95,19,109),(6,94,20,108),(7,93,21,107),(8,92,22,106),(9,91,23,105),(10,90,24,104),(11,89,25,103),(12,88,26,102),(13,87,27,101),(14,86,28,100),(29,139,43,125),(30,138,44,124),(31,137,45,123),(32,136,46,122),(33,135,47,121),(34,134,48,120),(35,133,49,119),(36,132,50,118),(37,131,51,117),(38,130,52,116),(39,129,53,115),(40,128,54,114),(41,127,55,113),(42,126,56,140),(57,162,71,148),(58,161,72,147),(59,160,73,146),(60,159,74,145),(61,158,75,144),(62,157,76,143),(63,156,77,142),(64,155,78,141),(65,154,79,168),(66,153,80,167),(67,152,81,166),(68,151,82,165),(69,150,83,164),(70,149,84,163),(169,211,183,197),(170,210,184,224),(171,209,185,223),(172,208,186,222),(173,207,187,221),(174,206,188,220),(175,205,189,219),(176,204,190,218),(177,203,191,217),(178,202,192,216),(179,201,193,215),(180,200,194,214),(181,199,195,213),(182,198,196,212)], [(1,115,166,201),(2,128,167,214),(3,113,168,199),(4,126,141,212),(5,139,142,197),(6,124,143,210),(7,137,144,223),(8,122,145,208),(9,135,146,221),(10,120,147,206),(11,133,148,219),(12,118,149,204),(13,131,150,217),(14,116,151,202),(15,129,152,215),(16,114,153,200),(17,127,154,213),(18,140,155,198),(19,125,156,211),(20,138,157,224),(21,123,158,209),(22,136,159,222),(23,121,160,207),(24,134,161,220),(25,119,162,205),(26,132,163,218),(27,117,164,203),(28,130,165,216),(29,77,183,109),(30,62,184,94),(31,75,185,107),(32,60,186,92),(33,73,187,105),(34,58,188,90),(35,71,189,103),(36,84,190,88),(37,69,191,101),(38,82,192,86),(39,67,193,99),(40,80,194,112),(41,65,195,97),(42,78,196,110),(43,63,169,95),(44,76,170,108),(45,61,171,93),(46,74,172,106),(47,59,173,91),(48,72,174,104),(49,57,175,89),(50,70,176,102),(51,83,177,87),(52,68,178,100),(53,81,179,85),(54,66,180,98),(55,79,181,111),(56,64,182,96)], [(2,28),(3,27),(4,26),(5,25),(6,24),(7,23),(8,22),(9,21),(10,20),(11,19),(12,18),(13,17),(14,16),(29,182),(30,181),(31,180),(32,179),(33,178),(34,177),(35,176),(36,175),(37,174),(38,173),(39,172),(40,171),(41,170),(42,169),(43,196),(44,195),(45,194),(46,193),(47,192),(48,191),(49,190),(50,189),(51,188),(52,187),(53,186),(54,185),(55,184),(56,183),(57,70),(58,69),(59,68),(60,67),(61,66),(62,65),(63,64),(71,84),(72,83),(73,82),(74,81),(75,80),(76,79),(77,78),(85,106),(86,105),(87,104),(88,103),(89,102),(90,101),(91,100),(92,99),(93,98),(94,97),(95,96),(107,112),(108,111),(109,110),(113,217),(114,216),(115,215),(116,214),(117,213),(118,212),(119,211),(120,210),(121,209),(122,208),(123,207),(124,206),(125,205),(126,204),(127,203),(128,202),(129,201),(130,200),(131,199),(132,198),(133,197),(134,224),(135,223),(136,222),(137,221),(138,220),(139,219),(140,218),(141,163),(142,162),(143,161),(144,160),(145,159),(146,158),(147,157),(148,156),(149,155),(150,154),(151,153),(164,168),(165,167)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 56 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 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 | C4○D4 | D14 | D14 | D14 | C4○D8 | C4○D28 | C8.C22 | D4×D7 | D4×D7 | SD16⋊3D7 | Q16⋊D7 |
| kernel | Dic14.11D4 | C14.D8 | Dic7⋊C8 | C7×Q8⋊C4 | Dic7⋊3Q8 | C2×C56⋊C2 | C2×C7⋊Q16 | C28.23D4 | Dic14 | C2×Dic7 | Q8⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×Q8 | C14 | C4 | 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 Dic14.11D4 ►in GL6(𝔽113)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 112 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 112 | 112 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 24 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 87 | 87 |
| 0 | 0 | 0 | 0 | 13 | 26 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 24 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 109 | 77 | 0 | 0 |
| 0 | 0 | 35 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 24 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 50 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 112 | 112 |
G:=sub<GL(6,GF(113))| [0,112,0,0,0,0,1,24,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,112,0,0,0,0,2,112],[1,24,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,87,13,0,0,0,0,87,26],[1,24,0,0,0,0,0,112,0,0,0,0,0,0,109,35,0,0,0,0,77,4,0,0,0,0,0,0,15,0,0,0,0,0,0,15],[1,24,0,0,0,0,0,112,0,0,0,0,0,0,1,50,0,0,0,0,0,112,0,0,0,0,0,0,1,112,0,0,0,0,0,112] >;
Dic14.11D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}._{11}D_4 % in TeX
G:=Group("Dic14.11D4"); // GroupNames label
G:=SmallGroup(448,332);
// by ID
G=gap.SmallGroup(448,332);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,344,1094,135,184,570,297,136,18822]);
// 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=a^14*c^-1>;
// generators/relations