metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊8SD16, Dic14⋊7D4, (C7×Q8)⋊5D4, C4.63(D4×D7), D14⋊C8⋊33C2, Q8⋊2(C7⋊D4), C7⋊4(Q8⋊D4), C28.48(C2×D4), (C2×SD16)⋊11D7, (C2×D4).72D14, (C2×C8).147D14, C28⋊2D4.7C2, C2.29(D7×SD16), C14.58C22≀C2, (C14×SD16)⋊21C2, Q8⋊Dic7⋊28C2, (C2×Q8).116D14, (C2×Dic7).72D4, C14.46(C2×SD16), (C22×D7).92D4, C22.267(D4×D7), C28.44D4⋊35C2, (C2×C28).447C23, (C2×C56).294C22, (D4×C14).96C22, (Q8×C14).76C22, C2.26(C23⋊D14), C2.29(SD16⋊D7), C14.49(C8.C22), C4⋊Dic7.174C22, (C2×Dic14).127C22, (C2×Q8×D7)⋊2C2, C4.43(C2×C7⋊D4), (C2×D4.D7)⋊20C2, (C2×C4×D7).48C22, (C2×C14).359(C2×D4), (C2×C7⋊C8).157C22, (C2×C4).536(C22×D7), SmallGroup(448,704)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊8SD16
G = < a,b,c,d | a14=b2=c8=d2=1, bab=a-1, ac=ca, ad=da, cbc-1=dbd=a7b, dcd=c3 >
Subgroups: 836 in 158 conjugacy classes, 45 normal (37 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×6], C22, C22 [×7], C7, C8 [×2], C2×C4, C2×C4 [×10], D4 [×4], Q8 [×2], Q8 [×8], C23 [×2], D7 [×2], C14 [×3], C14, C22⋊C4, C4⋊C4, C2×C8, C2×C8, SD16 [×4], C22×C4 [×2], C2×D4, C2×D4, C2×Q8, C2×Q8 [×6], Dic7 [×4], C28 [×2], C28 [×2], D14 [×2], D14 [×2], C2×C14, C2×C14 [×3], C22⋊C8, Q8⋊C4 [×2], C4⋊D4, C2×SD16, C2×SD16, C22×Q8, C7⋊C8, C56, Dic14 [×2], Dic14 [×5], C4×D7 [×6], C2×Dic7, C2×Dic7 [×2], C7⋊D4 [×2], C2×C28, C2×C28, C7×D4 [×2], C7×Q8 [×2], C7×Q8, C22×D7, C22×C14, Q8⋊D4, C2×C7⋊C8, C4⋊Dic7, D4.D7 [×2], C23.D7, C2×C56, C7×SD16 [×2], C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, Q8×D7 [×4], C2×C7⋊D4, D4×C14, Q8×C14, C28.44D4, D14⋊C8, Q8⋊Dic7, C2×D4.D7, C28⋊2D4, C14×SD16, C2×Q8×D7, D14⋊8SD16
Quotients: C1, C2 [×7], C22 [×7], D4 [×6], C23, D7, SD16 [×2], C2×D4 [×3], D14 [×3], C22≀C2, C2×SD16, C8.C22, C7⋊D4 [×2], C22×D7, Q8⋊D4, D4×D7 [×2], C2×C7⋊D4, D7×SD16, SD16⋊D7, C23⋊D14, D14⋊8SD16
►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 22)(16 21)(17 20)(18 19)(23 28)(24 27)(25 26)(29 31)(32 42)(33 41)(34 40)(35 39)(36 38)(43 51)(44 50)(45 49)(46 48)(52 56)(53 55)(57 61)(58 60)(62 70)(63 69)(64 68)(65 67)(71 80)(72 79)(73 78)(74 77)(75 76)(81 84)(82 83)(85 92)(86 91)(87 90)(88 89)(93 98)(94 97)(95 96)(99 112)(100 111)(101 110)(102 109)(103 108)(104 107)(105 106)(113 119)(114 118)(115 117)(120 126)(121 125)(122 124)(127 133)(128 132)(129 131)(134 140)(135 139)(136 138)(141 147)(142 146)(143 145)(148 154)(149 153)(150 152)(156 168)(157 167)(158 166)(159 165)(160 164)(161 163)(169 182)(170 181)(171 180)(172 179)(173 178)(174 177)(175 176)(183 196)(184 195)(185 194)(186 193)(187 192)(188 191)(189 190)(197 202)(198 201)(199 200)(203 210)(204 209)(205 208)(206 207)(211 215)(212 214)(216 224)(217 223)(218 222)(219 221)
(1 63 106 113 89 34 83 148)(2 64 107 114 90 35 84 149)(3 65 108 115 91 36 71 150)(4 66 109 116 92 37 72 151)(5 67 110 117 93 38 73 152)(6 68 111 118 94 39 74 153)(7 69 112 119 95 40 75 154)(8 70 99 120 96 41 76 141)(9 57 100 121 97 42 77 142)(10 58 101 122 98 29 78 143)(11 59 102 123 85 30 79 144)(12 60 103 124 86 31 80 145)(13 61 104 125 87 32 81 146)(14 62 105 126 88 33 82 147)(15 155 210 47 193 213 179 137)(16 156 197 48 194 214 180 138)(17 157 198 49 195 215 181 139)(18 158 199 50 196 216 182 140)(19 159 200 51 183 217 169 127)(20 160 201 52 184 218 170 128)(21 161 202 53 185 219 171 129)(22 162 203 54 186 220 172 130)(23 163 204 55 187 221 173 131)(24 164 205 56 188 222 174 132)(25 165 206 43 189 223 175 133)(26 166 207 44 190 224 176 134)(27 167 208 45 191 211 177 135)(28 168 209 46 192 212 178 136)
(1 224)(2 211)(3 212)(4 213)(5 214)(6 215)(7 216)(8 217)(9 218)(10 219)(11 220)(12 221)(13 222)(14 223)(15 66)(16 67)(17 68)(18 69)(19 70)(20 57)(21 58)(22 59)(23 60)(24 61)(25 62)(26 63)(27 64)(28 65)(29 185)(30 186)(31 187)(32 188)(33 189)(34 190)(35 191)(36 192)(37 193)(38 194)(39 195)(40 196)(41 183)(42 184)(43 105)(44 106)(45 107)(46 108)(47 109)(48 110)(49 111)(50 112)(51 99)(52 100)(53 101)(54 102)(55 103)(56 104)(71 136)(72 137)(73 138)(74 139)(75 140)(76 127)(77 128)(78 129)(79 130)(80 131)(81 132)(82 133)(83 134)(84 135)(85 162)(86 163)(87 164)(88 165)(89 166)(90 167)(91 168)(92 155)(93 156)(94 157)(95 158)(96 159)(97 160)(98 161)(113 176)(114 177)(115 178)(116 179)(117 180)(118 181)(119 182)(120 169)(121 170)(122 171)(123 172)(124 173)(125 174)(126 175)(141 200)(142 201)(143 202)(144 203)(145 204)(146 205)(147 206)(148 207)(149 208)(150 209)(151 210)(152 197)(153 198)(154 199)
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)(15,22)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(29,31)(32,42)(33,41)(34,40)(35,39)(36,38)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,61)(58,60)(62,70)(63,69)(64,68)(65,67)(71,80)(72,79)(73,78)(74,77)(75,76)(81,84)(82,83)(85,92)(86,91)(87,90)(88,89)(93,98)(94,97)(95,96)(99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(113,119)(114,118)(115,117)(120,126)(121,125)(122,124)(127,133)(128,132)(129,131)(134,140)(135,139)(136,138)(141,147)(142,146)(143,145)(148,154)(149,153)(150,152)(156,168)(157,167)(158,166)(159,165)(160,164)(161,163)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)(175,176)(183,196)(184,195)(185,194)(186,193)(187,192)(188,191)(189,190)(197,202)(198,201)(199,200)(203,210)(204,209)(205,208)(206,207)(211,215)(212,214)(216,224)(217,223)(218,222)(219,221), (1,63,106,113,89,34,83,148)(2,64,107,114,90,35,84,149)(3,65,108,115,91,36,71,150)(4,66,109,116,92,37,72,151)(5,67,110,117,93,38,73,152)(6,68,111,118,94,39,74,153)(7,69,112,119,95,40,75,154)(8,70,99,120,96,41,76,141)(9,57,100,121,97,42,77,142)(10,58,101,122,98,29,78,143)(11,59,102,123,85,30,79,144)(12,60,103,124,86,31,80,145)(13,61,104,125,87,32,81,146)(14,62,105,126,88,33,82,147)(15,155,210,47,193,213,179,137)(16,156,197,48,194,214,180,138)(17,157,198,49,195,215,181,139)(18,158,199,50,196,216,182,140)(19,159,200,51,183,217,169,127)(20,160,201,52,184,218,170,128)(21,161,202,53,185,219,171,129)(22,162,203,54,186,220,172,130)(23,163,204,55,187,221,173,131)(24,164,205,56,188,222,174,132)(25,165,206,43,189,223,175,133)(26,166,207,44,190,224,176,134)(27,167,208,45,191,211,177,135)(28,168,209,46,192,212,178,136), (1,224)(2,211)(3,212)(4,213)(5,214)(6,215)(7,216)(8,217)(9,218)(10,219)(11,220)(12,221)(13,222)(14,223)(15,66)(16,67)(17,68)(18,69)(19,70)(20,57)(21,58)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,185)(30,186)(31,187)(32,188)(33,189)(34,190)(35,191)(36,192)(37,193)(38,194)(39,195)(40,196)(41,183)(42,184)(43,105)(44,106)(45,107)(46,108)(47,109)(48,110)(49,111)(50,112)(51,99)(52,100)(53,101)(54,102)(55,103)(56,104)(71,136)(72,137)(73,138)(74,139)(75,140)(76,127)(77,128)(78,129)(79,130)(80,131)(81,132)(82,133)(83,134)(84,135)(85,162)(86,163)(87,164)(88,165)(89,166)(90,167)(91,168)(92,155)(93,156)(94,157)(95,158)(96,159)(97,160)(98,161)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(141,200)(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)(151,210)(152,197)(153,198)(154,199)>;
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)(15,22)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(29,31)(32,42)(33,41)(34,40)(35,39)(36,38)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,61)(58,60)(62,70)(63,69)(64,68)(65,67)(71,80)(72,79)(73,78)(74,77)(75,76)(81,84)(82,83)(85,92)(86,91)(87,90)(88,89)(93,98)(94,97)(95,96)(99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(113,119)(114,118)(115,117)(120,126)(121,125)(122,124)(127,133)(128,132)(129,131)(134,140)(135,139)(136,138)(141,147)(142,146)(143,145)(148,154)(149,153)(150,152)(156,168)(157,167)(158,166)(159,165)(160,164)(161,163)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)(175,176)(183,196)(184,195)(185,194)(186,193)(187,192)(188,191)(189,190)(197,202)(198,201)(199,200)(203,210)(204,209)(205,208)(206,207)(211,215)(212,214)(216,224)(217,223)(218,222)(219,221), (1,63,106,113,89,34,83,148)(2,64,107,114,90,35,84,149)(3,65,108,115,91,36,71,150)(4,66,109,116,92,37,72,151)(5,67,110,117,93,38,73,152)(6,68,111,118,94,39,74,153)(7,69,112,119,95,40,75,154)(8,70,99,120,96,41,76,141)(9,57,100,121,97,42,77,142)(10,58,101,122,98,29,78,143)(11,59,102,123,85,30,79,144)(12,60,103,124,86,31,80,145)(13,61,104,125,87,32,81,146)(14,62,105,126,88,33,82,147)(15,155,210,47,193,213,179,137)(16,156,197,48,194,214,180,138)(17,157,198,49,195,215,181,139)(18,158,199,50,196,216,182,140)(19,159,200,51,183,217,169,127)(20,160,201,52,184,218,170,128)(21,161,202,53,185,219,171,129)(22,162,203,54,186,220,172,130)(23,163,204,55,187,221,173,131)(24,164,205,56,188,222,174,132)(25,165,206,43,189,223,175,133)(26,166,207,44,190,224,176,134)(27,167,208,45,191,211,177,135)(28,168,209,46,192,212,178,136), (1,224)(2,211)(3,212)(4,213)(5,214)(6,215)(7,216)(8,217)(9,218)(10,219)(11,220)(12,221)(13,222)(14,223)(15,66)(16,67)(17,68)(18,69)(19,70)(20,57)(21,58)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,185)(30,186)(31,187)(32,188)(33,189)(34,190)(35,191)(36,192)(37,193)(38,194)(39,195)(40,196)(41,183)(42,184)(43,105)(44,106)(45,107)(46,108)(47,109)(48,110)(49,111)(50,112)(51,99)(52,100)(53,101)(54,102)(55,103)(56,104)(71,136)(72,137)(73,138)(74,139)(75,140)(76,127)(77,128)(78,129)(79,130)(80,131)(81,132)(82,133)(83,134)(84,135)(85,162)(86,163)(87,164)(88,165)(89,166)(90,167)(91,168)(92,155)(93,156)(94,157)(95,158)(96,159)(97,160)(98,161)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(141,200)(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)(151,210)(152,197)(153,198)(154,199) );
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),(15,22),(16,21),(17,20),(18,19),(23,28),(24,27),(25,26),(29,31),(32,42),(33,41),(34,40),(35,39),(36,38),(43,51),(44,50),(45,49),(46,48),(52,56),(53,55),(57,61),(58,60),(62,70),(63,69),(64,68),(65,67),(71,80),(72,79),(73,78),(74,77),(75,76),(81,84),(82,83),(85,92),(86,91),(87,90),(88,89),(93,98),(94,97),(95,96),(99,112),(100,111),(101,110),(102,109),(103,108),(104,107),(105,106),(113,119),(114,118),(115,117),(120,126),(121,125),(122,124),(127,133),(128,132),(129,131),(134,140),(135,139),(136,138),(141,147),(142,146),(143,145),(148,154),(149,153),(150,152),(156,168),(157,167),(158,166),(159,165),(160,164),(161,163),(169,182),(170,181),(171,180),(172,179),(173,178),(174,177),(175,176),(183,196),(184,195),(185,194),(186,193),(187,192),(188,191),(189,190),(197,202),(198,201),(199,200),(203,210),(204,209),(205,208),(206,207),(211,215),(212,214),(216,224),(217,223),(218,222),(219,221)], [(1,63,106,113,89,34,83,148),(2,64,107,114,90,35,84,149),(3,65,108,115,91,36,71,150),(4,66,109,116,92,37,72,151),(5,67,110,117,93,38,73,152),(6,68,111,118,94,39,74,153),(7,69,112,119,95,40,75,154),(8,70,99,120,96,41,76,141),(9,57,100,121,97,42,77,142),(10,58,101,122,98,29,78,143),(11,59,102,123,85,30,79,144),(12,60,103,124,86,31,80,145),(13,61,104,125,87,32,81,146),(14,62,105,126,88,33,82,147),(15,155,210,47,193,213,179,137),(16,156,197,48,194,214,180,138),(17,157,198,49,195,215,181,139),(18,158,199,50,196,216,182,140),(19,159,200,51,183,217,169,127),(20,160,201,52,184,218,170,128),(21,161,202,53,185,219,171,129),(22,162,203,54,186,220,172,130),(23,163,204,55,187,221,173,131),(24,164,205,56,188,222,174,132),(25,165,206,43,189,223,175,133),(26,166,207,44,190,224,176,134),(27,167,208,45,191,211,177,135),(28,168,209,46,192,212,178,136)], [(1,224),(2,211),(3,212),(4,213),(5,214),(6,215),(7,216),(8,217),(9,218),(10,219),(11,220),(12,221),(13,222),(14,223),(15,66),(16,67),(17,68),(18,69),(19,70),(20,57),(21,58),(22,59),(23,60),(24,61),(25,62),(26,63),(27,64),(28,65),(29,185),(30,186),(31,187),(32,188),(33,189),(34,190),(35,191),(36,192),(37,193),(38,194),(39,195),(40,196),(41,183),(42,184),(43,105),(44,106),(45,107),(46,108),(47,109),(48,110),(49,111),(50,112),(51,99),(52,100),(53,101),(54,102),(55,103),(56,104),(71,136),(72,137),(73,138),(74,139),(75,140),(76,127),(77,128),(78,129),(79,130),(80,131),(81,132),(82,133),(83,134),(84,135),(85,162),(86,163),(87,164),(88,165),(89,166),(90,167),(91,168),(92,155),(93,156),(94,157),(95,158),(96,159),(97,160),(98,161),(113,176),(114,177),(115,178),(116,179),(117,180),(118,181),(119,182),(120,169),(121,170),(122,171),(123,172),(124,173),(125,174),(126,175),(141,200),(142,201),(143,202),(144,203),(145,204),(146,205),(147,206),(148,207),(149,208),(150,209),(151,210),(152,197),(153,198),(154,199)])
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 | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| 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 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 14 | 14 | 2 | 2 | 4 | 4 | 28 | 28 | 28 | 56 | 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 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | SD16 | D14 | D14 | D14 | C7⋊D4 | C8.C22 | D4×D7 | D4×D7 | D7×SD16 | SD16⋊D7 |
| kernel | D14⋊8SD16 | C28.44D4 | D14⋊C8 | Q8⋊Dic7 | C2×D4.D7 | C28⋊2D4 | C14×SD16 | C2×Q8×D7 | Dic14 | C2×Dic7 | C7×Q8 | C22×D7 | C2×SD16 | D14 | C2×C8 | C2×D4 | C2×Q8 | Q8 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 | 4 | 3 | 3 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D14⋊8SD16 ►in GL6(𝔽113)
| 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 | 90 | 103 |
| 0 | 0 | 0 | 0 | 20 | 102 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 112 |
| 0 | 0 | 0 | 0 | 99 | 103 |
| 100 | 13 | 0 | 0 | 0 | 0 |
| 100 | 100 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 109 | 18 | 0 | 0 | 0 | 0 |
| 18 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,90,20,0,0,0,0,103,102],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,10,99,0,0,0,0,112,103],[100,100,0,0,0,0,13,100,0,0,0,0,0,0,0,112,0,0,0,0,1,0,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[109,18,0,0,0,0,18,4,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
D14⋊8SD16 in GAP, Magma, Sage, TeX
D_{14}\rtimes_8{\rm SD}_{16} % in TeX
G:=Group("D14:8SD16"); // GroupNames label
G:=SmallGroup(448,704);
// by ID
G=gap.SmallGroup(448,704);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,254,219,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=a^7*b,d*c*d=c^3>;
// generators/relations