direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C14.D8, C4⋊C4⋊35D14, (C2×D28)⋊9C4, D28⋊19(C2×C4), (C2×C14).39D8, C4.59(C2×D28), C14.48(C2×D8), C4.7(D14⋊C4), (C2×C4).139D28, (C2×C28).133D4, C28.139(C2×D4), C14⋊1(D4⋊C4), C28.59(C22×C4), (C2×C14).40SD16, C14.66(C2×SD16), C28.19(C22⋊C4), (C2×C28).318C23, C22.20(D4⋊D7), (C22×D28).10C2, (C22×C14).183D4, (C22×C4).329D14, C23.97(C7⋊D4), C22.11(Q8⋊D7), C22.45(D14⋊C4), (C2×D28).232C22, (C22×C28).133C22, (C2×C4⋊C4)⋊1D7, (C14×C4⋊C4)⋊1C2, C4.48(C2×C4×D7), C7⋊2(C2×D4⋊C4), (C22×C7⋊C8)⋊1C2, C2.2(C2×D4⋊D7), C2.2(C2×Q8⋊D7), (C2×C7⋊C8)⋊31C22, (C2×C4).75(C4×D7), (C7×C4⋊C4)⋊40C22, (C2×C28).77(C2×C4), C2.11(C2×D14⋊C4), (C2×C14).438(C2×D4), C14.38(C2×C22⋊C4), C22.57(C2×C7⋊D4), (C2×C4).124(C7⋊D4), (C2×C4).418(C22×D7), (C2×C14).57(C22⋊C4), SmallGroup(448,499)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C14.D8
G = < a,b,c,d | a2=b14=c8=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=b7c-1 >
Subgroups: 1284 in 202 conjugacy classes, 79 normal (27 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×D4, C24, C28, C28, C28, D14, C2×C14, C2×C14, D4⋊C4, C2×C4⋊C4, C22×C8, C22×D4, C7⋊C8, D28, D28, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C2×D4⋊C4, C2×C7⋊C8, C2×C7⋊C8, C7×C4⋊C4, C7×C4⋊C4, C2×D28, C2×D28, C22×C28, C22×C28, C23×D7, C14.D8, C22×C7⋊C8, C14×C4⋊C4, C22×D28, C2×C14.D8
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, D8, SD16, C22×C4, C2×D4, D14, D4⋊C4, C2×C22⋊C4, C2×D8, C2×SD16, C4×D7, D28, C7⋊D4, C22×D7, C2×D4⋊C4, D14⋊C4, D4⋊D7, Q8⋊D7, C2×C4×D7, C2×D28, C2×C7⋊D4, C14.D8, C2×D14⋊C4, C2×D4⋊D7, C2×Q8⋊D7, C2×C14.D8
►On 224 points
Generators in S224
(1 37)(2 38)(3 39)(4 40)(5 41)(6 42)(7 29)(8 30)(9 31)(10 32)(11 33)(12 34)(13 35)(14 36)(15 61)(16 62)(17 63)(18 64)(19 65)(20 66)(21 67)(22 68)(23 69)(24 70)(25 57)(26 58)(27 59)(28 60)(43 85)(44 86)(45 87)(46 88)(47 89)(48 90)(49 91)(50 92)(51 93)(52 94)(53 95)(54 96)(55 97)(56 98)(71 132)(72 133)(73 134)(74 135)(75 136)(76 137)(77 138)(78 139)(79 140)(80 127)(81 128)(82 129)(83 130)(84 131)(99 215)(100 216)(101 217)(102 218)(103 219)(104 220)(105 221)(106 222)(107 223)(108 224)(109 211)(110 212)(111 213)(112 214)(113 204)(114 205)(115 206)(116 207)(117 208)(118 209)(119 210)(120 197)(121 198)(122 199)(123 200)(124 201)(125 202)(126 203)(141 160)(142 161)(143 162)(144 163)(145 164)(146 165)(147 166)(148 167)(149 168)(150 155)(151 156)(152 157)(153 158)(154 159)(169 194)(170 195)(171 196)(172 183)(173 184)(174 185)(175 186)(176 187)(177 188)(178 189)(179 190)(180 191)(181 192)(182 193)
(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)
(1 106 116 55 129 179 149 26)(2 105 117 54 130 178 150 25)(3 104 118 53 131 177 151 24)(4 103 119 52 132 176 152 23)(5 102 120 51 133 175 153 22)(6 101 121 50 134 174 154 21)(7 100 122 49 135 173 141 20)(8 99 123 48 136 172 142 19)(9 112 124 47 137 171 143 18)(10 111 125 46 138 170 144 17)(11 110 126 45 139 169 145 16)(12 109 113 44 140 182 146 15)(13 108 114 43 127 181 147 28)(14 107 115 56 128 180 148 27)(29 216 199 91 74 184 160 66)(30 215 200 90 75 183 161 65)(31 214 201 89 76 196 162 64)(32 213 202 88 77 195 163 63)(33 212 203 87 78 194 164 62)(34 211 204 86 79 193 165 61)(35 224 205 85 80 192 166 60)(36 223 206 98 81 191 167 59)(37 222 207 97 82 190 168 58)(38 221 208 96 83 189 155 57)(39 220 209 95 84 188 156 70)(40 219 210 94 71 187 157 69)(41 218 197 93 72 186 158 68)(42 217 198 92 73 185 159 67)
(1 75)(2 74)(3 73)(4 72)(5 71)(6 84)(7 83)(8 82)(9 81)(10 80)(11 79)(12 78)(13 77)(14 76)(15 187)(16 186)(17 185)(18 184)(19 183)(20 196)(21 195)(22 194)(23 193)(24 192)(25 191)(26 190)(27 189)(28 188)(29 130)(30 129)(31 128)(32 127)(33 140)(34 139)(35 138)(36 137)(37 136)(38 135)(39 134)(40 133)(41 132)(42 131)(43 220)(44 219)(45 218)(46 217)(47 216)(48 215)(49 214)(50 213)(51 212)(52 211)(53 224)(54 223)(55 222)(56 221)(57 180)(58 179)(59 178)(60 177)(61 176)(62 175)(63 174)(64 173)(65 172)(66 171)(67 170)(68 169)(69 182)(70 181)(85 104)(86 103)(87 102)(88 101)(89 100)(90 99)(91 112)(92 111)(93 110)(94 109)(95 108)(96 107)(97 106)(98 105)(113 203)(114 202)(115 201)(116 200)(117 199)(118 198)(119 197)(120 210)(121 209)(122 208)(123 207)(124 206)(125 205)(126 204)(141 155)(142 168)(143 167)(144 166)(145 165)(146 164)(147 163)(148 162)(149 161)(150 160)(151 159)(152 158)(153 157)(154 156)
G:=sub<Sym(224)| (1,37)(2,38)(3,39)(4,40)(5,41)(6,42)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,61)(16,62)(17,63)(18,64)(19,65)(20,66)(21,67)(22,68)(23,69)(24,70)(25,57)(26,58)(27,59)(28,60)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,97)(56,98)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,127)(81,128)(82,129)(83,130)(84,131)(99,215)(100,216)(101,217)(102,218)(103,219)(104,220)(105,221)(106,222)(107,223)(108,224)(109,211)(110,212)(111,213)(112,214)(113,204)(114,205)(115,206)(116,207)(117,208)(118,209)(119,210)(120,197)(121,198)(122,199)(123,200)(124,201)(125,202)(126,203)(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,155)(151,156)(152,157)(153,158)(154,159)(169,194)(170,195)(171,196)(172,183)(173,184)(174,185)(175,186)(176,187)(177,188)(178,189)(179,190)(180,191)(181,192)(182,193), (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), (1,106,116,55,129,179,149,26)(2,105,117,54,130,178,150,25)(3,104,118,53,131,177,151,24)(4,103,119,52,132,176,152,23)(5,102,120,51,133,175,153,22)(6,101,121,50,134,174,154,21)(7,100,122,49,135,173,141,20)(8,99,123,48,136,172,142,19)(9,112,124,47,137,171,143,18)(10,111,125,46,138,170,144,17)(11,110,126,45,139,169,145,16)(12,109,113,44,140,182,146,15)(13,108,114,43,127,181,147,28)(14,107,115,56,128,180,148,27)(29,216,199,91,74,184,160,66)(30,215,200,90,75,183,161,65)(31,214,201,89,76,196,162,64)(32,213,202,88,77,195,163,63)(33,212,203,87,78,194,164,62)(34,211,204,86,79,193,165,61)(35,224,205,85,80,192,166,60)(36,223,206,98,81,191,167,59)(37,222,207,97,82,190,168,58)(38,221,208,96,83,189,155,57)(39,220,209,95,84,188,156,70)(40,219,210,94,71,187,157,69)(41,218,197,93,72,186,158,68)(42,217,198,92,73,185,159,67), (1,75)(2,74)(3,73)(4,72)(5,71)(6,84)(7,83)(8,82)(9,81)(10,80)(11,79)(12,78)(13,77)(14,76)(15,187)(16,186)(17,185)(18,184)(19,183)(20,196)(21,195)(22,194)(23,193)(24,192)(25,191)(26,190)(27,189)(28,188)(29,130)(30,129)(31,128)(32,127)(33,140)(34,139)(35,138)(36,137)(37,136)(38,135)(39,134)(40,133)(41,132)(42,131)(43,220)(44,219)(45,218)(46,217)(47,216)(48,215)(49,214)(50,213)(51,212)(52,211)(53,224)(54,223)(55,222)(56,221)(57,180)(58,179)(59,178)(60,177)(61,176)(62,175)(63,174)(64,173)(65,172)(66,171)(67,170)(68,169)(69,182)(70,181)(85,104)(86,103)(87,102)(88,101)(89,100)(90,99)(91,112)(92,111)(93,110)(94,109)(95,108)(96,107)(97,106)(98,105)(113,203)(114,202)(115,201)(116,200)(117,199)(118,198)(119,197)(120,210)(121,209)(122,208)(123,207)(124,206)(125,205)(126,204)(141,155)(142,168)(143,167)(144,166)(145,165)(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)>;
G:=Group( (1,37)(2,38)(3,39)(4,40)(5,41)(6,42)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,61)(16,62)(17,63)(18,64)(19,65)(20,66)(21,67)(22,68)(23,69)(24,70)(25,57)(26,58)(27,59)(28,60)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92)(51,93)(52,94)(53,95)(54,96)(55,97)(56,98)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,127)(81,128)(82,129)(83,130)(84,131)(99,215)(100,216)(101,217)(102,218)(103,219)(104,220)(105,221)(106,222)(107,223)(108,224)(109,211)(110,212)(111,213)(112,214)(113,204)(114,205)(115,206)(116,207)(117,208)(118,209)(119,210)(120,197)(121,198)(122,199)(123,200)(124,201)(125,202)(126,203)(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,155)(151,156)(152,157)(153,158)(154,159)(169,194)(170,195)(171,196)(172,183)(173,184)(174,185)(175,186)(176,187)(177,188)(178,189)(179,190)(180,191)(181,192)(182,193), (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), (1,106,116,55,129,179,149,26)(2,105,117,54,130,178,150,25)(3,104,118,53,131,177,151,24)(4,103,119,52,132,176,152,23)(5,102,120,51,133,175,153,22)(6,101,121,50,134,174,154,21)(7,100,122,49,135,173,141,20)(8,99,123,48,136,172,142,19)(9,112,124,47,137,171,143,18)(10,111,125,46,138,170,144,17)(11,110,126,45,139,169,145,16)(12,109,113,44,140,182,146,15)(13,108,114,43,127,181,147,28)(14,107,115,56,128,180,148,27)(29,216,199,91,74,184,160,66)(30,215,200,90,75,183,161,65)(31,214,201,89,76,196,162,64)(32,213,202,88,77,195,163,63)(33,212,203,87,78,194,164,62)(34,211,204,86,79,193,165,61)(35,224,205,85,80,192,166,60)(36,223,206,98,81,191,167,59)(37,222,207,97,82,190,168,58)(38,221,208,96,83,189,155,57)(39,220,209,95,84,188,156,70)(40,219,210,94,71,187,157,69)(41,218,197,93,72,186,158,68)(42,217,198,92,73,185,159,67), (1,75)(2,74)(3,73)(4,72)(5,71)(6,84)(7,83)(8,82)(9,81)(10,80)(11,79)(12,78)(13,77)(14,76)(15,187)(16,186)(17,185)(18,184)(19,183)(20,196)(21,195)(22,194)(23,193)(24,192)(25,191)(26,190)(27,189)(28,188)(29,130)(30,129)(31,128)(32,127)(33,140)(34,139)(35,138)(36,137)(37,136)(38,135)(39,134)(40,133)(41,132)(42,131)(43,220)(44,219)(45,218)(46,217)(47,216)(48,215)(49,214)(50,213)(51,212)(52,211)(53,224)(54,223)(55,222)(56,221)(57,180)(58,179)(59,178)(60,177)(61,176)(62,175)(63,174)(64,173)(65,172)(66,171)(67,170)(68,169)(69,182)(70,181)(85,104)(86,103)(87,102)(88,101)(89,100)(90,99)(91,112)(92,111)(93,110)(94,109)(95,108)(96,107)(97,106)(98,105)(113,203)(114,202)(115,201)(116,200)(117,199)(118,198)(119,197)(120,210)(121,209)(122,208)(123,207)(124,206)(125,205)(126,204)(141,155)(142,168)(143,167)(144,166)(145,165)(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156) );
G=PermutationGroup([[(1,37),(2,38),(3,39),(4,40),(5,41),(6,42),(7,29),(8,30),(9,31),(10,32),(11,33),(12,34),(13,35),(14,36),(15,61),(16,62),(17,63),(18,64),(19,65),(20,66),(21,67),(22,68),(23,69),(24,70),(25,57),(26,58),(27,59),(28,60),(43,85),(44,86),(45,87),(46,88),(47,89),(48,90),(49,91),(50,92),(51,93),(52,94),(53,95),(54,96),(55,97),(56,98),(71,132),(72,133),(73,134),(74,135),(75,136),(76,137),(77,138),(78,139),(79,140),(80,127),(81,128),(82,129),(83,130),(84,131),(99,215),(100,216),(101,217),(102,218),(103,219),(104,220),(105,221),(106,222),(107,223),(108,224),(109,211),(110,212),(111,213),(112,214),(113,204),(114,205),(115,206),(116,207),(117,208),(118,209),(119,210),(120,197),(121,198),(122,199),(123,200),(124,201),(125,202),(126,203),(141,160),(142,161),(143,162),(144,163),(145,164),(146,165),(147,166),(148,167),(149,168),(150,155),(151,156),(152,157),(153,158),(154,159),(169,194),(170,195),(171,196),(172,183),(173,184),(174,185),(175,186),(176,187),(177,188),(178,189),(179,190),(180,191),(181,192),(182,193)], [(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)], [(1,106,116,55,129,179,149,26),(2,105,117,54,130,178,150,25),(3,104,118,53,131,177,151,24),(4,103,119,52,132,176,152,23),(5,102,120,51,133,175,153,22),(6,101,121,50,134,174,154,21),(7,100,122,49,135,173,141,20),(8,99,123,48,136,172,142,19),(9,112,124,47,137,171,143,18),(10,111,125,46,138,170,144,17),(11,110,126,45,139,169,145,16),(12,109,113,44,140,182,146,15),(13,108,114,43,127,181,147,28),(14,107,115,56,128,180,148,27),(29,216,199,91,74,184,160,66),(30,215,200,90,75,183,161,65),(31,214,201,89,76,196,162,64),(32,213,202,88,77,195,163,63),(33,212,203,87,78,194,164,62),(34,211,204,86,79,193,165,61),(35,224,205,85,80,192,166,60),(36,223,206,98,81,191,167,59),(37,222,207,97,82,190,168,58),(38,221,208,96,83,189,155,57),(39,220,209,95,84,188,156,70),(40,219,210,94,71,187,157,69),(41,218,197,93,72,186,158,68),(42,217,198,92,73,185,159,67)], [(1,75),(2,74),(3,73),(4,72),(5,71),(6,84),(7,83),(8,82),(9,81),(10,80),(11,79),(12,78),(13,77),(14,76),(15,187),(16,186),(17,185),(18,184),(19,183),(20,196),(21,195),(22,194),(23,193),(24,192),(25,191),(26,190),(27,189),(28,188),(29,130),(30,129),(31,128),(32,127),(33,140),(34,139),(35,138),(36,137),(37,136),(38,135),(39,134),(40,133),(41,132),(42,131),(43,220),(44,219),(45,218),(46,217),(47,216),(48,215),(49,214),(50,213),(51,212),(52,211),(53,224),(54,223),(55,222),(56,221),(57,180),(58,179),(59,178),(60,177),(61,176),(62,175),(63,174),(64,173),(65,172),(66,171),(67,170),(68,169),(69,182),(70,181),(85,104),(86,103),(87,102),(88,101),(89,100),(90,99),(91,112),(92,111),(93,110),(94,109),(95,108),(96,107),(97,106),(98,105),(113,203),(114,202),(115,201),(116,200),(117,199),(118,198),(119,197),(120,210),(121,209),(122,208),(123,207),(124,206),(125,205),(126,204),(141,155),(142,168),(143,167),(144,166),(145,165),(146,164),(147,163),(148,162),(149,161),(150,160),(151,159),(152,158),(153,157),(154,156)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | D8 | SD16 | D14 | D14 | C4×D7 | D28 | C7⋊D4 | C7⋊D4 | D4⋊D7 | Q8⋊D7 |
| kernel | C2×C14.D8 | C14.D8 | C22×C7⋊C8 | C14×C4⋊C4 | C22×D28 | C2×D28 | C2×C28 | C22×C14 | C2×C4⋊C4 | C2×C14 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 3 | 1 | 3 | 4 | 4 | 6 | 3 | 12 | 12 | 6 | 6 | 6 | 6 |
Matrix representation of C2×C14.D8 ►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 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 9 | 33 | 0 | 0 | 0 | 0 |
| 80 | 80 | 0 | 0 | 0 | 0 |
| 0 | 0 | 81 | 33 | 0 | 0 |
| 0 | 0 | 47 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 55 | 38 | 0 | 0 | 0 | 0 |
| 81 | 58 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 109 | 0 | 0 |
| 0 | 0 | 56 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 100 | 13 |
| 0 | 0 | 0 | 0 | 100 | 100 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 9 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 80 | 0 | 0 |
| 0 | 0 | 43 | 105 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[9,80,0,0,0,0,33,80,0,0,0,0,0,0,81,47,0,0,0,0,33,8,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[55,81,0,0,0,0,38,58,0,0,0,0,0,0,98,56,0,0,0,0,109,15,0,0,0,0,0,0,100,100,0,0,0,0,13,100],[1,9,0,0,0,0,0,112,0,0,0,0,0,0,8,43,0,0,0,0,80,105,0,0,0,0,0,0,112,0,0,0,0,0,0,1] >;
C2×C14.D8 in GAP, Magma, Sage, TeX
C_2\times C_{14}.D_8 % in TeX
G:=Group("C2xC14.D8"); // GroupNames label
G:=SmallGroup(448,499);
// by ID
G=gap.SmallGroup(448,499);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,422,58,1684,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^14=c^8=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=b^7*c^-1>;
// generators/relations