metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14.37D4, (C2×C14)⋊2Q16, C4⋊C4.69D14, (C2×C28).79D4, C4.103(D4×D7), C22⋊Q8.5D7, C28.156(C2×D4), (C2×Q8).31D14, C14.38(C2×Q16), C7⋊3(C22⋊Q16), C14.49C22≀C2, C14.Q16⋊38C2, (C22×C14).96D4, C22⋊2(C7⋊Q16), (C2×C28).369C23, C28.55D4.9C2, (C22×C4).130D14, C23.63(C7⋊D4), (Q8×C14).49C22, C2.17(C23⋊D14), C2.15(D4.9D14), C14.117(C8.C22), (C22×C28).173C22, (C22×Dic14).13C2, (C2×Dic14).271C22, (C2×C7⋊Q16)⋊9C2, C2.9(C2×C7⋊Q16), (C7×C22⋊Q8).4C2, (C2×C14).500(C2×D4), (C2×C4).57(C7⋊D4), (C2×C7⋊C8).117C22, (C7×C4⋊C4).116C22, (C2×C4).469(C22×D7), C22.175(C2×C7⋊D4), SmallGroup(448,584)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14.37D4
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=a14c-1 >
Subgroups: 668 in 148 conjugacy classes, 47 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, Q16, C22×C4, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C22⋊C8, Q8⋊C4, C22⋊Q8, C2×Q16, C22×Q8, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×C14, C22⋊Q16, C2×C7⋊C8, C7⋊Q16, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, Q8×C14, C14.Q16, C28.55D4, C2×C7⋊Q16, C7×C22⋊Q8, C22×Dic14, Dic14.37D4
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, D14, C22≀C2, C2×Q16, C8.C22, C7⋊D4, C22×D7, C22⋊Q16, C7⋊Q16, D4×D7, C2×C7⋊D4, C23⋊D14, C2×C7⋊Q16, D4.9D14, Dic14.37D4
►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 73 15 59)(2 72 16 58)(3 71 17 57)(4 70 18 84)(5 69 19 83)(6 68 20 82)(7 67 21 81)(8 66 22 80)(9 65 23 79)(10 64 24 78)(11 63 25 77)(12 62 26 76)(13 61 27 75)(14 60 28 74)(29 197 43 211)(30 224 44 210)(31 223 45 209)(32 222 46 208)(33 221 47 207)(34 220 48 206)(35 219 49 205)(36 218 50 204)(37 217 51 203)(38 216 52 202)(39 215 53 201)(40 214 54 200)(41 213 55 199)(42 212 56 198)(85 164 99 150)(86 163 100 149)(87 162 101 148)(88 161 102 147)(89 160 103 146)(90 159 104 145)(91 158 105 144)(92 157 106 143)(93 156 107 142)(94 155 108 141)(95 154 109 168)(96 153 110 167)(97 152 111 166)(98 151 112 165)(113 174 127 188)(114 173 128 187)(115 172 129 186)(116 171 130 185)(117 170 131 184)(118 169 132 183)(119 196 133 182)(120 195 134 181)(121 194 135 180)(122 193 136 179)(123 192 137 178)(124 191 138 177)(125 190 139 176)(126 189 140 175)
(1 118 38 92)(2 133 39 107)(3 120 40 94)(4 135 41 109)(5 122 42 96)(6 137 43 111)(7 124 44 98)(8 139 45 85)(9 126 46 100)(10 113 47 87)(11 128 48 102)(12 115 49 89)(13 130 50 104)(14 117 51 91)(15 132 52 106)(16 119 53 93)(17 134 54 108)(18 121 55 95)(19 136 56 110)(20 123 29 97)(21 138 30 112)(22 125 31 99)(23 140 32 86)(24 127 33 101)(25 114 34 88)(26 129 35 103)(27 116 36 90)(28 131 37 105)(57 188 200 148)(58 175 201 163)(59 190 202 150)(60 177 203 165)(61 192 204 152)(62 179 205 167)(63 194 206 154)(64 181 207 141)(65 196 208 156)(66 183 209 143)(67 170 210 158)(68 185 211 145)(69 172 212 160)(70 187 213 147)(71 174 214 162)(72 189 215 149)(73 176 216 164)(74 191 217 151)(75 178 218 166)(76 193 219 153)(77 180 220 168)(78 195 221 155)(79 182 222 142)(80 169 223 157)(81 184 224 144)(82 171 197 159)(83 186 198 146)(84 173 199 161)
(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 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(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)(85 139)(86 140)(87 113)(88 114)(89 115)(90 116)(91 117)(92 118)(93 119)(94 120)(95 121)(96 122)(97 123)(98 124)(99 125)(100 126)(101 127)(102 128)(103 129)(104 130)(105 131)(106 132)(107 133)(108 134)(109 135)(110 136)(111 137)(112 138)(141 181)(142 182)(143 183)(144 184)(145 185)(146 186)(147 187)(148 188)(149 189)(150 190)(151 191)(152 192)(153 193)(154 194)(155 195)(156 196)(157 169)(158 170)(159 171)(160 172)(161 173)(162 174)(163 175)(164 176)(165 177)(166 178)(167 179)(168 180)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)
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), (1,73,15,59)(2,72,16,58)(3,71,17,57)(4,70,18,84)(5,69,19,83)(6,68,20,82)(7,67,21,81)(8,66,22,80)(9,65,23,79)(10,64,24,78)(11,63,25,77)(12,62,26,76)(13,61,27,75)(14,60,28,74)(29,197,43,211)(30,224,44,210)(31,223,45,209)(32,222,46,208)(33,221,47,207)(34,220,48,206)(35,219,49,205)(36,218,50,204)(37,217,51,203)(38,216,52,202)(39,215,53,201)(40,214,54,200)(41,213,55,199)(42,212,56,198)(85,164,99,150)(86,163,100,149)(87,162,101,148)(88,161,102,147)(89,160,103,146)(90,159,104,145)(91,158,105,144)(92,157,106,143)(93,156,107,142)(94,155,108,141)(95,154,109,168)(96,153,110,167)(97,152,111,166)(98,151,112,165)(113,174,127,188)(114,173,128,187)(115,172,129,186)(116,171,130,185)(117,170,131,184)(118,169,132,183)(119,196,133,182)(120,195,134,181)(121,194,135,180)(122,193,136,179)(123,192,137,178)(124,191,138,177)(125,190,139,176)(126,189,140,175), (1,118,38,92)(2,133,39,107)(3,120,40,94)(4,135,41,109)(5,122,42,96)(6,137,43,111)(7,124,44,98)(8,139,45,85)(9,126,46,100)(10,113,47,87)(11,128,48,102)(12,115,49,89)(13,130,50,104)(14,117,51,91)(15,132,52,106)(16,119,53,93)(17,134,54,108)(18,121,55,95)(19,136,56,110)(20,123,29,97)(21,138,30,112)(22,125,31,99)(23,140,32,86)(24,127,33,101)(25,114,34,88)(26,129,35,103)(27,116,36,90)(28,131,37,105)(57,188,200,148)(58,175,201,163)(59,190,202,150)(60,177,203,165)(61,192,204,152)(62,179,205,167)(63,194,206,154)(64,181,207,141)(65,196,208,156)(66,183,209,143)(67,170,210,158)(68,185,211,145)(69,172,212,160)(70,187,213,147)(71,174,214,162)(72,189,215,149)(73,176,216,164)(74,191,217,151)(75,178,218,166)(76,193,219,153)(77,180,220,168)(78,195,221,155)(79,182,222,142)(80,169,223,157)(81,184,224,144)(82,171,197,159)(83,186,198,146)(84,173,199,161), (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)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(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)(85,139)(86,140)(87,113)(88,114)(89,115)(90,116)(91,117)(92,118)(93,119)(94,120)(95,121)(96,122)(97,123)(98,124)(99,125)(100,126)(101,127)(102,128)(103,129)(104,130)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(141,181)(142,182)(143,183)(144,184)(145,185)(146,186)(147,187)(148,188)(149,189)(150,190)(151,191)(152,192)(153,193)(154,194)(155,195)(156,196)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)>;
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), (1,73,15,59)(2,72,16,58)(3,71,17,57)(4,70,18,84)(5,69,19,83)(6,68,20,82)(7,67,21,81)(8,66,22,80)(9,65,23,79)(10,64,24,78)(11,63,25,77)(12,62,26,76)(13,61,27,75)(14,60,28,74)(29,197,43,211)(30,224,44,210)(31,223,45,209)(32,222,46,208)(33,221,47,207)(34,220,48,206)(35,219,49,205)(36,218,50,204)(37,217,51,203)(38,216,52,202)(39,215,53,201)(40,214,54,200)(41,213,55,199)(42,212,56,198)(85,164,99,150)(86,163,100,149)(87,162,101,148)(88,161,102,147)(89,160,103,146)(90,159,104,145)(91,158,105,144)(92,157,106,143)(93,156,107,142)(94,155,108,141)(95,154,109,168)(96,153,110,167)(97,152,111,166)(98,151,112,165)(113,174,127,188)(114,173,128,187)(115,172,129,186)(116,171,130,185)(117,170,131,184)(118,169,132,183)(119,196,133,182)(120,195,134,181)(121,194,135,180)(122,193,136,179)(123,192,137,178)(124,191,138,177)(125,190,139,176)(126,189,140,175), (1,118,38,92)(2,133,39,107)(3,120,40,94)(4,135,41,109)(5,122,42,96)(6,137,43,111)(7,124,44,98)(8,139,45,85)(9,126,46,100)(10,113,47,87)(11,128,48,102)(12,115,49,89)(13,130,50,104)(14,117,51,91)(15,132,52,106)(16,119,53,93)(17,134,54,108)(18,121,55,95)(19,136,56,110)(20,123,29,97)(21,138,30,112)(22,125,31,99)(23,140,32,86)(24,127,33,101)(25,114,34,88)(26,129,35,103)(27,116,36,90)(28,131,37,105)(57,188,200,148)(58,175,201,163)(59,190,202,150)(60,177,203,165)(61,192,204,152)(62,179,205,167)(63,194,206,154)(64,181,207,141)(65,196,208,156)(66,183,209,143)(67,170,210,158)(68,185,211,145)(69,172,212,160)(70,187,213,147)(71,174,214,162)(72,189,215,149)(73,176,216,164)(74,191,217,151)(75,178,218,166)(76,193,219,153)(77,180,220,168)(78,195,221,155)(79,182,222,142)(80,169,223,157)(81,184,224,144)(82,171,197,159)(83,186,198,146)(84,173,199,161), (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)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(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)(85,139)(86,140)(87,113)(88,114)(89,115)(90,116)(91,117)(92,118)(93,119)(94,120)(95,121)(96,122)(97,123)(98,124)(99,125)(100,126)(101,127)(102,128)(103,129)(104,130)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(141,181)(142,182)(143,183)(144,184)(145,185)(146,186)(147,187)(148,188)(149,189)(150,190)(151,191)(152,192)(153,193)(154,194)(155,195)(156,196)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224) );
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)], [(1,73,15,59),(2,72,16,58),(3,71,17,57),(4,70,18,84),(5,69,19,83),(6,68,20,82),(7,67,21,81),(8,66,22,80),(9,65,23,79),(10,64,24,78),(11,63,25,77),(12,62,26,76),(13,61,27,75),(14,60,28,74),(29,197,43,211),(30,224,44,210),(31,223,45,209),(32,222,46,208),(33,221,47,207),(34,220,48,206),(35,219,49,205),(36,218,50,204),(37,217,51,203),(38,216,52,202),(39,215,53,201),(40,214,54,200),(41,213,55,199),(42,212,56,198),(85,164,99,150),(86,163,100,149),(87,162,101,148),(88,161,102,147),(89,160,103,146),(90,159,104,145),(91,158,105,144),(92,157,106,143),(93,156,107,142),(94,155,108,141),(95,154,109,168),(96,153,110,167),(97,152,111,166),(98,151,112,165),(113,174,127,188),(114,173,128,187),(115,172,129,186),(116,171,130,185),(117,170,131,184),(118,169,132,183),(119,196,133,182),(120,195,134,181),(121,194,135,180),(122,193,136,179),(123,192,137,178),(124,191,138,177),(125,190,139,176),(126,189,140,175)], [(1,118,38,92),(2,133,39,107),(3,120,40,94),(4,135,41,109),(5,122,42,96),(6,137,43,111),(7,124,44,98),(8,139,45,85),(9,126,46,100),(10,113,47,87),(11,128,48,102),(12,115,49,89),(13,130,50,104),(14,117,51,91),(15,132,52,106),(16,119,53,93),(17,134,54,108),(18,121,55,95),(19,136,56,110),(20,123,29,97),(21,138,30,112),(22,125,31,99),(23,140,32,86),(24,127,33,101),(25,114,34,88),(26,129,35,103),(27,116,36,90),(28,131,37,105),(57,188,200,148),(58,175,201,163),(59,190,202,150),(60,177,203,165),(61,192,204,152),(62,179,205,167),(63,194,206,154),(64,181,207,141),(65,196,208,156),(66,183,209,143),(67,170,210,158),(68,185,211,145),(69,172,212,160),(70,187,213,147),(71,174,214,162),(72,189,215,149),(73,176,216,164),(74,191,217,151),(75,178,218,166),(76,193,219,153),(77,180,220,168),(78,195,221,155),(79,182,222,142),(80,169,223,157),(81,184,224,144),(82,171,197,159),(83,186,198,146),(84,173,199,161)], [(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),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(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),(85,139),(86,140),(87,113),(88,114),(89,115),(90,116),(91,117),(92,118),(93,119),(94,120),(95,121),(96,122),(97,123),(98,124),(99,125),(100,126),(101,127),(102,128),(103,129),(104,130),(105,131),(106,132),(107,133),(108,134),(109,135),(110,136),(111,137),(112,138),(141,181),(142,182),(143,183),(144,184),(145,185),(146,186),(147,187),(148,188),(149,189),(150,190),(151,191),(152,192),(153,193),(154,194),(155,195),(156,196),(157,169),(158,170),(159,171),(160,172),(161,173),(162,174),(163,175),(164,176),(165,177),(166,178),(167,179),(168,180),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224)]])
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 | ··· | 28L | 28M | ··· | 28X |
| 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 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 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 | Q16 | D14 | D14 | D14 | C7⋊D4 | C7⋊D4 | C8.C22 | D4×D7 | C7⋊Q16 | D4.9D14 |
| kernel | Dic14.37D4 | C14.Q16 | C28.55D4 | C2×C7⋊Q16 | C7×C22⋊Q8 | C22×Dic14 | Dic14 | C2×C28 | C22×C14 | C22⋊Q8 | C2×C14 | C4⋊C4 | C22×C4 | C2×Q8 | 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 Dic14.37D4 ►in GL6(𝔽113)
| 0 | 112 | 0 | 0 | 0 | 0 |
| 1 | 89 | 0 | 0 | 0 | 0 |
| 0 | 0 | 83 | 112 | 0 | 0 |
| 0 | 0 | 110 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 103 | 103 | 0 | 0 | 0 | 0 |
| 89 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 0 | 0 | 0 |
| 0 | 0 | 4 | 98 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 91 | 1 |
| 84 | 106 | 0 | 0 | 0 | 0 |
| 7 | 29 | 0 | 0 | 0 | 0 |
| 0 | 0 | 38 | 13 | 0 | 0 |
| 0 | 0 | 54 | 75 | 0 | 0 |
| 0 | 0 | 0 | 0 | 53 | 26 |
| 0 | 0 | 0 | 0 | 31 | 60 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 22 | 112 |
G:=sub<GL(6,GF(113))| [0,1,0,0,0,0,112,89,0,0,0,0,0,0,83,110,0,0,0,0,112,30,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[103,89,0,0,0,0,103,10,0,0,0,0,0,0,15,4,0,0,0,0,0,98,0,0,0,0,0,0,112,91,0,0,0,0,0,1],[84,7,0,0,0,0,106,29,0,0,0,0,0,0,38,54,0,0,0,0,13,75,0,0,0,0,0,0,53,31,0,0,0,0,26,60],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,22,0,0,0,0,0,112] >;
Dic14.37D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}._{37}D_4 % in TeX
G:=Group("Dic14.37D4"); // GroupNames label
G:=SmallGroup(448,584);
// by ID
G=gap.SmallGroup(448,584);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,254,219,184,1123,297,136,18822]);
// 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=a^14*c^-1>;
// generators/relations