metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊17D4, C4⋊C4.60D14, C7⋊3(Q8⋊D4), (C2×C14)⋊3SD16, C4⋊D4.5D7, C4.100(D4×D7), (C2×C28).73D4, (C2×D4).40D14, C28.149(C2×D4), C14.46C22≀C2, C14.Q16⋊34C2, C22⋊2(D4.D7), C14.55(C2×SD16), (C22×C14).86D4, C28.55D4⋊12C2, (C2×C28).359C23, (D4×C14).56C22, (C22×C4).122D14, C23.59(C7⋊D4), C2.14(C23⋊D14), (C22×Dic14)⋊13C2, C2.12(D4.9D14), C14.114(C8.C22), (C22×C28).163C22, (C2×Dic14).269C22, (C2×D4.D7)⋊9C2, C2.9(C2×D4.D7), (C7×C4⋊D4).4C2, (C2×C14).490(C2×D4), (C2×C4).51(C7⋊D4), (C2×C7⋊C8).110C22, (C7×C4⋊C4).107C22, (C2×C4).459(C22×D7), C22.165(C2×C7⋊D4), SmallGroup(448,574)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊17D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, cac-1=a15, ad=da, cbc-1=a21b, bd=db, dcd=c-1 >
Subgroups: 716 in 158 conjugacy classes, 47 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C23, C14, C14, C22⋊C4, C4⋊C4, C2×C8, SD16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C22⋊C8, Q8⋊C4, C4⋊D4, C2×SD16, C22×Q8, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, Q8⋊D4, C2×C7⋊C8, D4.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, D4×C14, D4×C14, C14.Q16, C28.55D4, C2×D4.D7, C7×C4⋊D4, C22×Dic14, Dic14⋊17D4
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, D14, C22≀C2, C2×SD16, C8.C22, C7⋊D4, C22×D7, Q8⋊D4, D4.D7, D4×D7, C2×C7⋊D4, C2×D4.D7, C23⋊D14, D4.9D14, Dic14⋊17D4
►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)
(1 169 15 183)(2 196 16 182)(3 195 17 181)(4 194 18 180)(5 193 19 179)(6 192 20 178)(7 191 21 177)(8 190 22 176)(9 189 23 175)(10 188 24 174)(11 187 25 173)(12 186 26 172)(13 185 27 171)(14 184 28 170)(29 162 43 148)(30 161 44 147)(31 160 45 146)(32 159 46 145)(33 158 47 144)(34 157 48 143)(35 156 49 142)(36 155 50 141)(37 154 51 168)(38 153 52 167)(39 152 53 166)(40 151 54 165)(41 150 55 164)(42 149 56 163)(57 91 71 105)(58 90 72 104)(59 89 73 103)(60 88 74 102)(61 87 75 101)(62 86 76 100)(63 85 77 99)(64 112 78 98)(65 111 79 97)(66 110 80 96)(67 109 81 95)(68 108 82 94)(69 107 83 93)(70 106 84 92)(113 216 127 202)(114 215 128 201)(115 214 129 200)(116 213 130 199)(117 212 131 198)(118 211 132 197)(119 210 133 224)(120 209 134 223)(121 208 135 222)(122 207 136 221)(123 206 137 220)(124 205 138 219)(125 204 139 218)(126 203 140 217)
(1 212 73 38)(2 199 74 53)(3 214 75 40)(4 201 76 55)(5 216 77 42)(6 203 78 29)(7 218 79 44)(8 205 80 31)(9 220 81 46)(10 207 82 33)(11 222 83 48)(12 209 84 35)(13 224 57 50)(14 211 58 37)(15 198 59 52)(16 213 60 39)(17 200 61 54)(18 215 62 41)(19 202 63 56)(20 217 64 43)(21 204 65 30)(22 219 66 45)(23 206 67 32)(24 221 68 47)(25 208 69 34)(26 223 70 49)(27 210 71 36)(28 197 72 51)(85 142 179 120)(86 157 180 135)(87 144 181 122)(88 159 182 137)(89 146 183 124)(90 161 184 139)(91 148 185 126)(92 163 186 113)(93 150 187 128)(94 165 188 115)(95 152 189 130)(96 167 190 117)(97 154 191 132)(98 141 192 119)(99 156 193 134)(100 143 194 121)(101 158 195 136)(102 145 196 123)(103 160 169 138)(104 147 170 125)(105 162 171 140)(106 149 172 127)(107 164 173 114)(108 151 174 129)(109 166 175 116)(110 153 176 131)(111 168 177 118)(112 155 178 133)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 217)(30 218)(31 219)(32 220)(33 221)(34 222)(35 223)(36 224)(37 197)(38 198)(39 199)(40 200)(41 201)(42 202)(43 203)(44 204)(45 205)(46 206)(47 207)(48 208)(49 209)(50 210)(51 211)(52 212)(53 213)(54 214)(55 215)(56 216)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(113 149)(114 150)(115 151)(116 152)(117 153)(118 154)(119 155)(120 156)(121 157)(122 158)(123 159)(124 160)(125 161)(126 162)(127 163)(128 164)(129 165)(130 166)(131 167)(132 168)(133 141)(134 142)(135 143)(136 144)(137 145)(138 146)(139 147)(140 148)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)(175 189)(176 190)(177 191)(178 192)(179 193)(180 194)(181 195)(182 196)
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), (1,169,15,183)(2,196,16,182)(3,195,17,181)(4,194,18,180)(5,193,19,179)(6,192,20,178)(7,191,21,177)(8,190,22,176)(9,189,23,175)(10,188,24,174)(11,187,25,173)(12,186,26,172)(13,185,27,171)(14,184,28,170)(29,162,43,148)(30,161,44,147)(31,160,45,146)(32,159,46,145)(33,158,47,144)(34,157,48,143)(35,156,49,142)(36,155,50,141)(37,154,51,168)(38,153,52,167)(39,152,53,166)(40,151,54,165)(41,150,55,164)(42,149,56,163)(57,91,71,105)(58,90,72,104)(59,89,73,103)(60,88,74,102)(61,87,75,101)(62,86,76,100)(63,85,77,99)(64,112,78,98)(65,111,79,97)(66,110,80,96)(67,109,81,95)(68,108,82,94)(69,107,83,93)(70,106,84,92)(113,216,127,202)(114,215,128,201)(115,214,129,200)(116,213,130,199)(117,212,131,198)(118,211,132,197)(119,210,133,224)(120,209,134,223)(121,208,135,222)(122,207,136,221)(123,206,137,220)(124,205,138,219)(125,204,139,218)(126,203,140,217), (1,212,73,38)(2,199,74,53)(3,214,75,40)(4,201,76,55)(5,216,77,42)(6,203,78,29)(7,218,79,44)(8,205,80,31)(9,220,81,46)(10,207,82,33)(11,222,83,48)(12,209,84,35)(13,224,57,50)(14,211,58,37)(15,198,59,52)(16,213,60,39)(17,200,61,54)(18,215,62,41)(19,202,63,56)(20,217,64,43)(21,204,65,30)(22,219,66,45)(23,206,67,32)(24,221,68,47)(25,208,69,34)(26,223,70,49)(27,210,71,36)(28,197,72,51)(85,142,179,120)(86,157,180,135)(87,144,181,122)(88,159,182,137)(89,146,183,124)(90,161,184,139)(91,148,185,126)(92,163,186,113)(93,150,187,128)(94,165,188,115)(95,152,189,130)(96,167,190,117)(97,154,191,132)(98,141,192,119)(99,156,193,134)(100,143,194,121)(101,158,195,136)(102,145,196,123)(103,160,169,138)(104,147,170,125)(105,162,171,140)(106,149,172,127)(107,164,173,114)(108,151,174,129)(109,166,175,116)(110,153,176,131)(111,168,177,118)(112,155,178,133), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,217)(30,218)(31,219)(32,220)(33,221)(34,222)(35,223)(36,224)(37,197)(38,198)(39,199)(40,200)(41,201)(42,202)(43,203)(44,204)(45,205)(46,206)(47,207)(48,208)(49,209)(50,210)(51,211)(52,212)(53,213)(54,214)(55,215)(56,216)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,149)(114,150)(115,151)(116,152)(117,153)(118,154)(119,155)(120,156)(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,163)(128,164)(129,165)(130,166)(131,167)(132,168)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)(139,147)(140,148)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)>;
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), (1,169,15,183)(2,196,16,182)(3,195,17,181)(4,194,18,180)(5,193,19,179)(6,192,20,178)(7,191,21,177)(8,190,22,176)(9,189,23,175)(10,188,24,174)(11,187,25,173)(12,186,26,172)(13,185,27,171)(14,184,28,170)(29,162,43,148)(30,161,44,147)(31,160,45,146)(32,159,46,145)(33,158,47,144)(34,157,48,143)(35,156,49,142)(36,155,50,141)(37,154,51,168)(38,153,52,167)(39,152,53,166)(40,151,54,165)(41,150,55,164)(42,149,56,163)(57,91,71,105)(58,90,72,104)(59,89,73,103)(60,88,74,102)(61,87,75,101)(62,86,76,100)(63,85,77,99)(64,112,78,98)(65,111,79,97)(66,110,80,96)(67,109,81,95)(68,108,82,94)(69,107,83,93)(70,106,84,92)(113,216,127,202)(114,215,128,201)(115,214,129,200)(116,213,130,199)(117,212,131,198)(118,211,132,197)(119,210,133,224)(120,209,134,223)(121,208,135,222)(122,207,136,221)(123,206,137,220)(124,205,138,219)(125,204,139,218)(126,203,140,217), (1,212,73,38)(2,199,74,53)(3,214,75,40)(4,201,76,55)(5,216,77,42)(6,203,78,29)(7,218,79,44)(8,205,80,31)(9,220,81,46)(10,207,82,33)(11,222,83,48)(12,209,84,35)(13,224,57,50)(14,211,58,37)(15,198,59,52)(16,213,60,39)(17,200,61,54)(18,215,62,41)(19,202,63,56)(20,217,64,43)(21,204,65,30)(22,219,66,45)(23,206,67,32)(24,221,68,47)(25,208,69,34)(26,223,70,49)(27,210,71,36)(28,197,72,51)(85,142,179,120)(86,157,180,135)(87,144,181,122)(88,159,182,137)(89,146,183,124)(90,161,184,139)(91,148,185,126)(92,163,186,113)(93,150,187,128)(94,165,188,115)(95,152,189,130)(96,167,190,117)(97,154,191,132)(98,141,192,119)(99,156,193,134)(100,143,194,121)(101,158,195,136)(102,145,196,123)(103,160,169,138)(104,147,170,125)(105,162,171,140)(106,149,172,127)(107,164,173,114)(108,151,174,129)(109,166,175,116)(110,153,176,131)(111,168,177,118)(112,155,178,133), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,217)(30,218)(31,219)(32,220)(33,221)(34,222)(35,223)(36,224)(37,197)(38,198)(39,199)(40,200)(41,201)(42,202)(43,203)(44,204)(45,205)(46,206)(47,207)(48,208)(49,209)(50,210)(51,211)(52,212)(53,213)(54,214)(55,215)(56,216)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,149)(114,150)(115,151)(116,152)(117,153)(118,154)(119,155)(120,156)(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,163)(128,164)(129,165)(130,166)(131,167)(132,168)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)(139,147)(140,148)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196) );
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)], [(1,169,15,183),(2,196,16,182),(3,195,17,181),(4,194,18,180),(5,193,19,179),(6,192,20,178),(7,191,21,177),(8,190,22,176),(9,189,23,175),(10,188,24,174),(11,187,25,173),(12,186,26,172),(13,185,27,171),(14,184,28,170),(29,162,43,148),(30,161,44,147),(31,160,45,146),(32,159,46,145),(33,158,47,144),(34,157,48,143),(35,156,49,142),(36,155,50,141),(37,154,51,168),(38,153,52,167),(39,152,53,166),(40,151,54,165),(41,150,55,164),(42,149,56,163),(57,91,71,105),(58,90,72,104),(59,89,73,103),(60,88,74,102),(61,87,75,101),(62,86,76,100),(63,85,77,99),(64,112,78,98),(65,111,79,97),(66,110,80,96),(67,109,81,95),(68,108,82,94),(69,107,83,93),(70,106,84,92),(113,216,127,202),(114,215,128,201),(115,214,129,200),(116,213,130,199),(117,212,131,198),(118,211,132,197),(119,210,133,224),(120,209,134,223),(121,208,135,222),(122,207,136,221),(123,206,137,220),(124,205,138,219),(125,204,139,218),(126,203,140,217)], [(1,212,73,38),(2,199,74,53),(3,214,75,40),(4,201,76,55),(5,216,77,42),(6,203,78,29),(7,218,79,44),(8,205,80,31),(9,220,81,46),(10,207,82,33),(11,222,83,48),(12,209,84,35),(13,224,57,50),(14,211,58,37),(15,198,59,52),(16,213,60,39),(17,200,61,54),(18,215,62,41),(19,202,63,56),(20,217,64,43),(21,204,65,30),(22,219,66,45),(23,206,67,32),(24,221,68,47),(25,208,69,34),(26,223,70,49),(27,210,71,36),(28,197,72,51),(85,142,179,120),(86,157,180,135),(87,144,181,122),(88,159,182,137),(89,146,183,124),(90,161,184,139),(91,148,185,126),(92,163,186,113),(93,150,187,128),(94,165,188,115),(95,152,189,130),(96,167,190,117),(97,154,191,132),(98,141,192,119),(99,156,193,134),(100,143,194,121),(101,158,195,136),(102,145,196,123),(103,160,169,138),(104,147,170,125),(105,162,171,140),(106,149,172,127),(107,164,173,114),(108,151,174,129),(109,166,175,116),(110,153,176,131),(111,168,177,118),(112,155,178,133)], [(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,217),(30,218),(31,219),(32,220),(33,221),(34,222),(35,223),(36,224),(37,197),(38,198),(39,199),(40,200),(41,201),(42,202),(43,203),(44,204),(45,205),(46,206),(47,207),(48,208),(49,209),(50,210),(51,211),(52,212),(53,213),(54,214),(55,215),(56,216),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(113,149),(114,150),(115,151),(116,152),(117,153),(118,154),(119,155),(120,156),(121,157),(122,158),(123,159),(124,160),(125,161),(126,162),(127,163),(128,164),(129,165),(130,166),(131,167),(132,168),(133,141),(134,142),(135,143),(136,144),(137,145),(138,146),(139,147),(140,148),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188),(175,189),(176,190),(177,191),(178,192),(179,193),(180,194),(181,195),(182,196)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 2 | 2 | 4 | 8 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | SD16 | D14 | D14 | D14 | C7⋊D4 | C7⋊D4 | C8.C22 | D4×D7 | D4.D7 | D4.9D14 |
| kernel | Dic14⋊17D4 | C14.Q16 | C28.55D4 | C2×D4.D7 | C7×C4⋊D4 | C22×Dic14 | Dic14 | C2×C28 | C22×C14 | C4⋊D4 | C2×C14 | C4⋊C4 | C22×C4 | C2×D4 | C2×C4 | C23 | C14 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 4 | 1 | 1 | 3 | 4 | 3 | 3 | 3 | 6 | 6 | 1 | 6 | 6 | 6 |
Matrix representation of Dic14⋊17D4 ►in GL6(𝔽113)
| 16 | 67 | 0 | 0 | 0 | 0 |
| 67 | 97 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 1 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 99 | 106 | 0 | 0 | 0 | 0 |
| 12 | 14 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 80 | 0 | 0 |
| 0 | 0 | 112 | 104 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 75 | 19 | 0 | 0 | 0 | 0 |
| 43 | 38 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 111 |
| 0 | 0 | 0 | 0 | 39 | 90 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 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 | 23 | 112 |
G:=sub<GL(6,GF(113))| [16,67,0,0,0,0,67,97,0,0,0,0,0,0,9,112,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[99,12,0,0,0,0,106,14,0,0,0,0,0,0,9,112,0,0,0,0,80,104,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[75,43,0,0,0,0,19,38,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,23,39,0,0,0,0,111,90],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,23,0,0,0,0,0,112] >;
Dic14⋊17D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_{17}D_4 % in TeX
G:=Group("Dic14:17D4"); // GroupNames label
G:=SmallGroup(448,574);
// by ID
G=gap.SmallGroup(448,574);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,254,219,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,c*a*c^-1=a^15,a*d=d*a,c*b*c^-1=a^21*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations