metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊5Q16, Dic14.17D4, (C2×Q16)⋊3D7, C4.67(D4×D7), (C7×Q8).9D4, C28.52(C2×D4), (C2×C8).38D14, C2.18(D7×Q16), D14⋊C8.12C2, (C14×Q16)⋊13C2, (C2×Q8).62D14, C14.29(C2×Q16), Q8.8(C7⋊D4), C7⋊4(C22⋊Q16), C14.61C22≀C2, Q8⋊Dic7⋊33C2, D14⋊3Q8.7C2, (C2×Dic7).76D4, (C22×D7).93D4, C22.277(D4×D7), C28.44D4⋊30C2, (C2×C56).252C22, (C2×C28).460C23, (Q8×C14).89C22, C2.29(C23⋊D14), C2.28(Q16⋊D7), C14.78(C8.C22), C4⋊Dic7.183C22, (C2×Dic14).132C22, (C2×Q8×D7).5C2, C4.48(C2×C7⋊D4), (C2×C7⋊Q16)⋊20C2, (C2×C4×D7).52C22, (C2×C14).371(C2×D4), (C2×C7⋊C8).165C22, (C2×C4).548(C22×D7), SmallGroup(448,720)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊5Q16
G = < a,b,c,d | a14=b2=c8=1, d2=c4, bab=a-1, ac=ca, ad=da, cbc-1=dbd-1=a7b, dcd-1=c-1 >
Subgroups: 740 in 148 conjugacy classes, 45 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C2×C8, C2×C8, Q16, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C22⋊C8, Q8⋊C4, C22⋊Q8, C2×Q16, C2×Q16, C22×Q8, C7⋊C8, C56, Dic14, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×D7, C22⋊Q16, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7⋊Q16, C2×C56, C7×Q16, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, Q8×D7, Q8×C14, C28.44D4, D14⋊C8, Q8⋊Dic7, C2×C7⋊Q16, D14⋊3Q8, C14×Q16, C2×Q8×D7, D14⋊5Q16
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, D14, C22≀C2, C2×Q16, C8.C22, C7⋊D4, C22×D7, C22⋊Q16, D4×D7, C2×C7⋊D4, D7×Q16, Q16⋊D7, C23⋊D14, D14⋊5Q16
►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 14)(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 20)(16 19)(17 18)(21 28)(22 27)(23 26)(24 25)(29 34)(30 33)(31 32)(35 42)(36 41)(37 40)(38 39)(43 52)(44 51)(45 50)(46 49)(47 48)(53 56)(54 55)(57 61)(58 60)(62 70)(63 69)(64 68)(65 67)(71 79)(72 78)(73 77)(74 76)(80 84)(81 83)(85 93)(86 92)(87 91)(88 90)(94 98)(95 97)(99 105)(100 104)(101 103)(106 112)(107 111)(108 110)(113 126)(114 125)(115 124)(116 123)(117 122)(118 121)(119 120)(127 132)(128 131)(129 130)(133 140)(134 139)(135 138)(136 137)(141 154)(142 153)(143 152)(144 151)(145 150)(146 149)(147 148)(155 167)(156 166)(157 165)(158 164)(159 163)(160 162)(169 173)(170 172)(174 182)(175 181)(176 180)(177 179)(183 185)(186 196)(187 195)(188 194)(189 193)(190 192)(197 201)(198 200)(202 210)(203 209)(204 208)(205 207)(211 224)(212 223)(213 222)(214 221)(215 220)(216 219)(217 218)
(1 63 120 165 25 86 148 203)(2 64 121 166 26 87 149 204)(3 65 122 167 27 88 150 205)(4 66 123 168 28 89 151 206)(5 67 124 155 15 90 152 207)(6 68 125 156 16 91 153 208)(7 69 126 157 17 92 154 209)(8 70 113 158 18 93 141 210)(9 57 114 159 19 94 142 197)(10 58 115 160 20 95 143 198)(11 59 116 161 21 96 144 199)(12 60 117 162 22 97 145 200)(13 61 118 163 23 98 146 201)(14 62 119 164 24 85 147 202)(29 110 52 172 222 83 127 185)(30 111 53 173 223 84 128 186)(31 112 54 174 224 71 129 187)(32 99 55 175 211 72 130 188)(33 100 56 176 212 73 131 189)(34 101 43 177 213 74 132 190)(35 102 44 178 214 75 133 191)(36 103 45 179 215 76 134 192)(37 104 46 180 216 77 135 193)(38 105 47 181 217 78 136 194)(39 106 48 182 218 79 137 195)(40 107 49 169 219 80 138 196)(41 108 50 170 220 81 139 183)(42 109 51 171 221 82 140 184)
(1 79 25 106)(2 80 26 107)(3 81 27 108)(4 82 28 109)(5 83 15 110)(6 84 16 111)(7 71 17 112)(8 72 18 99)(9 73 19 100)(10 74 20 101)(11 75 21 102)(12 76 22 103)(13 77 23 104)(14 78 24 105)(29 67 222 90)(30 68 223 91)(31 69 224 92)(32 70 211 93)(33 57 212 94)(34 58 213 95)(35 59 214 96)(36 60 215 97)(37 61 216 98)(38 62 217 85)(39 63 218 86)(40 64 219 87)(41 65 220 88)(42 66 221 89)(43 198 132 160)(44 199 133 161)(45 200 134 162)(46 201 135 163)(47 202 136 164)(48 203 137 165)(49 204 138 166)(50 205 139 167)(51 206 140 168)(52 207 127 155)(53 208 128 156)(54 209 129 157)(55 210 130 158)(56 197 131 159)(113 175 141 188)(114 176 142 189)(115 177 143 190)(116 178 144 191)(117 179 145 192)(118 180 146 193)(119 181 147 194)(120 182 148 195)(121 169 149 196)(122 170 150 183)(123 171 151 184)(124 172 152 185)(125 173 153 186)(126 174 154 187)
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,20)(16,19)(17,18)(21,28)(22,27)(23,26)(24,25)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,52)(44,51)(45,50)(46,49)(47,48)(53,56)(54,55)(57,61)(58,60)(62,70)(63,69)(64,68)(65,67)(71,79)(72,78)(73,77)(74,76)(80,84)(81,83)(85,93)(86,92)(87,91)(88,90)(94,98)(95,97)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,132)(128,131)(129,130)(133,140)(134,139)(135,138)(136,137)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,173)(170,172)(174,182)(175,181)(176,180)(177,179)(183,185)(186,196)(187,195)(188,194)(189,193)(190,192)(197,201)(198,200)(202,210)(203,209)(204,208)(205,207)(211,224)(212,223)(213,222)(214,221)(215,220)(216,219)(217,218), (1,63,120,165,25,86,148,203)(2,64,121,166,26,87,149,204)(3,65,122,167,27,88,150,205)(4,66,123,168,28,89,151,206)(5,67,124,155,15,90,152,207)(6,68,125,156,16,91,153,208)(7,69,126,157,17,92,154,209)(8,70,113,158,18,93,141,210)(9,57,114,159,19,94,142,197)(10,58,115,160,20,95,143,198)(11,59,116,161,21,96,144,199)(12,60,117,162,22,97,145,200)(13,61,118,163,23,98,146,201)(14,62,119,164,24,85,147,202)(29,110,52,172,222,83,127,185)(30,111,53,173,223,84,128,186)(31,112,54,174,224,71,129,187)(32,99,55,175,211,72,130,188)(33,100,56,176,212,73,131,189)(34,101,43,177,213,74,132,190)(35,102,44,178,214,75,133,191)(36,103,45,179,215,76,134,192)(37,104,46,180,216,77,135,193)(38,105,47,181,217,78,136,194)(39,106,48,182,218,79,137,195)(40,107,49,169,219,80,138,196)(41,108,50,170,220,81,139,183)(42,109,51,171,221,82,140,184), (1,79,25,106)(2,80,26,107)(3,81,27,108)(4,82,28,109)(5,83,15,110)(6,84,16,111)(7,71,17,112)(8,72,18,99)(9,73,19,100)(10,74,20,101)(11,75,21,102)(12,76,22,103)(13,77,23,104)(14,78,24,105)(29,67,222,90)(30,68,223,91)(31,69,224,92)(32,70,211,93)(33,57,212,94)(34,58,213,95)(35,59,214,96)(36,60,215,97)(37,61,216,98)(38,62,217,85)(39,63,218,86)(40,64,219,87)(41,65,220,88)(42,66,221,89)(43,198,132,160)(44,199,133,161)(45,200,134,162)(46,201,135,163)(47,202,136,164)(48,203,137,165)(49,204,138,166)(50,205,139,167)(51,206,140,168)(52,207,127,155)(53,208,128,156)(54,209,129,157)(55,210,130,158)(56,197,131,159)(113,175,141,188)(114,176,142,189)(115,177,143,190)(116,178,144,191)(117,179,145,192)(118,180,146,193)(119,181,147,194)(120,182,148,195)(121,169,149,196)(122,170,150,183)(123,171,151,184)(124,172,152,185)(125,173,153,186)(126,174,154,187)>;
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,20)(16,19)(17,18)(21,28)(22,27)(23,26)(24,25)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,52)(44,51)(45,50)(46,49)(47,48)(53,56)(54,55)(57,61)(58,60)(62,70)(63,69)(64,68)(65,67)(71,79)(72,78)(73,77)(74,76)(80,84)(81,83)(85,93)(86,92)(87,91)(88,90)(94,98)(95,97)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,132)(128,131)(129,130)(133,140)(134,139)(135,138)(136,137)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,173)(170,172)(174,182)(175,181)(176,180)(177,179)(183,185)(186,196)(187,195)(188,194)(189,193)(190,192)(197,201)(198,200)(202,210)(203,209)(204,208)(205,207)(211,224)(212,223)(213,222)(214,221)(215,220)(216,219)(217,218), (1,63,120,165,25,86,148,203)(2,64,121,166,26,87,149,204)(3,65,122,167,27,88,150,205)(4,66,123,168,28,89,151,206)(5,67,124,155,15,90,152,207)(6,68,125,156,16,91,153,208)(7,69,126,157,17,92,154,209)(8,70,113,158,18,93,141,210)(9,57,114,159,19,94,142,197)(10,58,115,160,20,95,143,198)(11,59,116,161,21,96,144,199)(12,60,117,162,22,97,145,200)(13,61,118,163,23,98,146,201)(14,62,119,164,24,85,147,202)(29,110,52,172,222,83,127,185)(30,111,53,173,223,84,128,186)(31,112,54,174,224,71,129,187)(32,99,55,175,211,72,130,188)(33,100,56,176,212,73,131,189)(34,101,43,177,213,74,132,190)(35,102,44,178,214,75,133,191)(36,103,45,179,215,76,134,192)(37,104,46,180,216,77,135,193)(38,105,47,181,217,78,136,194)(39,106,48,182,218,79,137,195)(40,107,49,169,219,80,138,196)(41,108,50,170,220,81,139,183)(42,109,51,171,221,82,140,184), (1,79,25,106)(2,80,26,107)(3,81,27,108)(4,82,28,109)(5,83,15,110)(6,84,16,111)(7,71,17,112)(8,72,18,99)(9,73,19,100)(10,74,20,101)(11,75,21,102)(12,76,22,103)(13,77,23,104)(14,78,24,105)(29,67,222,90)(30,68,223,91)(31,69,224,92)(32,70,211,93)(33,57,212,94)(34,58,213,95)(35,59,214,96)(36,60,215,97)(37,61,216,98)(38,62,217,85)(39,63,218,86)(40,64,219,87)(41,65,220,88)(42,66,221,89)(43,198,132,160)(44,199,133,161)(45,200,134,162)(46,201,135,163)(47,202,136,164)(48,203,137,165)(49,204,138,166)(50,205,139,167)(51,206,140,168)(52,207,127,155)(53,208,128,156)(54,209,129,157)(55,210,130,158)(56,197,131,159)(113,175,141,188)(114,176,142,189)(115,177,143,190)(116,178,144,191)(117,179,145,192)(118,180,146,193)(119,181,147,194)(120,182,148,195)(121,169,149,196)(122,170,150,183)(123,171,151,184)(124,172,152,185)(125,173,153,186)(126,174,154,187) );
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)], [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,20),(16,19),(17,18),(21,28),(22,27),(23,26),(24,25),(29,34),(30,33),(31,32),(35,42),(36,41),(37,40),(38,39),(43,52),(44,51),(45,50),(46,49),(47,48),(53,56),(54,55),(57,61),(58,60),(62,70),(63,69),(64,68),(65,67),(71,79),(72,78),(73,77),(74,76),(80,84),(81,83),(85,93),(86,92),(87,91),(88,90),(94,98),(95,97),(99,105),(100,104),(101,103),(106,112),(107,111),(108,110),(113,126),(114,125),(115,124),(116,123),(117,122),(118,121),(119,120),(127,132),(128,131),(129,130),(133,140),(134,139),(135,138),(136,137),(141,154),(142,153),(143,152),(144,151),(145,150),(146,149),(147,148),(155,167),(156,166),(157,165),(158,164),(159,163),(160,162),(169,173),(170,172),(174,182),(175,181),(176,180),(177,179),(183,185),(186,196),(187,195),(188,194),(189,193),(190,192),(197,201),(198,200),(202,210),(203,209),(204,208),(205,207),(211,224),(212,223),(213,222),(214,221),(215,220),(216,219),(217,218)], [(1,63,120,165,25,86,148,203),(2,64,121,166,26,87,149,204),(3,65,122,167,27,88,150,205),(4,66,123,168,28,89,151,206),(5,67,124,155,15,90,152,207),(6,68,125,156,16,91,153,208),(7,69,126,157,17,92,154,209),(8,70,113,158,18,93,141,210),(9,57,114,159,19,94,142,197),(10,58,115,160,20,95,143,198),(11,59,116,161,21,96,144,199),(12,60,117,162,22,97,145,200),(13,61,118,163,23,98,146,201),(14,62,119,164,24,85,147,202),(29,110,52,172,222,83,127,185),(30,111,53,173,223,84,128,186),(31,112,54,174,224,71,129,187),(32,99,55,175,211,72,130,188),(33,100,56,176,212,73,131,189),(34,101,43,177,213,74,132,190),(35,102,44,178,214,75,133,191),(36,103,45,179,215,76,134,192),(37,104,46,180,216,77,135,193),(38,105,47,181,217,78,136,194),(39,106,48,182,218,79,137,195),(40,107,49,169,219,80,138,196),(41,108,50,170,220,81,139,183),(42,109,51,171,221,82,140,184)], [(1,79,25,106),(2,80,26,107),(3,81,27,108),(4,82,28,109),(5,83,15,110),(6,84,16,111),(7,71,17,112),(8,72,18,99),(9,73,19,100),(10,74,20,101),(11,75,21,102),(12,76,22,103),(13,77,23,104),(14,78,24,105),(29,67,222,90),(30,68,223,91),(31,69,224,92),(32,70,211,93),(33,57,212,94),(34,58,213,95),(35,59,214,96),(36,60,215,97),(37,61,216,98),(38,62,217,85),(39,63,218,86),(40,64,219,87),(41,65,220,88),(42,66,221,89),(43,198,132,160),(44,199,133,161),(45,200,134,162),(46,201,135,163),(47,202,136,164),(48,203,137,165),(49,204,138,166),(50,205,139,167),(51,206,140,168),(52,207,127,155),(53,208,128,156),(54,209,129,157),(55,210,130,158),(56,197,131,159),(113,175,141,188),(114,176,142,189),(115,177,143,190),(116,178,144,191),(117,179,145,192),(118,180,146,193),(119,181,147,194),(120,182,148,195),(121,169,149,196),(122,170,150,183),(123,171,151,184),(124,172,152,185),(125,173,153,186),(126,174,154,187)]])
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 | 28A | ··· | 28F | 28G | ··· | 28R | 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 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | 2 | 4 | 4 | 8 | 28 | 28 | 28 | 56 | 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 | D4 | D4 | D7 | Q16 | D14 | D14 | C7⋊D4 | C8.C22 | D4×D7 | D4×D7 | D7×Q16 | Q16⋊D7 |
| kernel | D14⋊5Q16 | C28.44D4 | D14⋊C8 | Q8⋊Dic7 | C2×C7⋊Q16 | D14⋊3Q8 | C14×Q16 | C2×Q8×D7 | Dic14 | C2×Dic7 | C7×Q8 | C22×D7 | C2×Q16 | D14 | C2×C8 | C2×Q8 | Q8 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 | 4 | 3 | 6 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D14⋊5Q16 ►in GL4(𝔽113) generated by
| 104 | 25 | 0 | 0 |
| 9 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 112 | 0 | 0 | 0 |
| 81 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 34 | 12 | 0 | 0 |
| 45 | 79 | 0 | 0 |
| 0 | 0 | 0 | 99 |
| 0 | 0 | 105 | 51 |
| 79 | 101 | 0 | 0 |
| 68 | 34 | 0 | 0 |
| 0 | 0 | 20 | 91 |
| 0 | 0 | 85 | 93 |
G:=sub<GL(4,GF(113))| [104,9,0,0,25,0,0,0,0,0,1,0,0,0,0,1],[112,81,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[34,45,0,0,12,79,0,0,0,0,0,105,0,0,99,51],[79,68,0,0,101,34,0,0,0,0,20,85,0,0,91,93] >;
D14⋊5Q16 in GAP, Magma, Sage, TeX
D_{14}\rtimes_5Q_{16} % in TeX
G:=Group("D14:5Q16"); // GroupNames label
G:=SmallGroup(448,720);
// by ID
G=gap.SmallGroup(448,720);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,254,219,184,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=c^4,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=a^7*b,d*c*d^-1=c^-1>;
// generators/relations