direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C14×C4○D8, C56.79C23, C28.81C24, D8⋊6(C2×C14), (C2×D8)⋊13C14, (C14×D8)⋊27C2, (C22×C8)⋊8C14, Q16⋊6(C2×C14), C4.84(D4×C14), (C22×C56)⋊22C2, (C2×C56)⋊51C22, (C2×Q16)⋊13C14, (C14×Q16)⋊27C2, SD16⋊5(C2×C14), C28.328(C2×D4), (C2×C28).539D4, (C7×D8)⋊23C22, C4.4(C23×C14), C23.28(C7×D4), C22.4(D4×C14), (C14×SD16)⋊33C2, (C2×SD16)⋊16C14, C8.12(C22×C14), (C7×Q16)⋊20C22, (C7×D4).35C23, D4.2(C22×C14), (C7×Q8).36C23, Q8.2(C22×C14), (C2×C28).974C23, (C7×SD16)⋊22C22, (C22×C14).132D4, C14.202(C22×D4), (D4×C14).328C22, (Q8×C14).281C22, (C22×C28).604C22, C2.26(D4×C2×C14), (C2×C8)⋊13(C2×C14), C4○D4⋊3(C2×C14), (C2×C4○D4)⋊10C14, (C14×C4○D4)⋊26C2, (C2×C4).148(C7×D4), (C2×D4).74(C2×C14), (C2×C14).689(C2×D4), (C7×C4○D4)⋊23C22, (C2×Q8).69(C2×C14), (C22×C4).131(C2×C14), (C2×C4).144(C22×C14), SmallGroup(448,1355)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×C4○D8
G = < a,b,c,d | a14=b4=d2=1, c4=b2, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=b2c3 >
Subgroups: 402 in 266 conjugacy classes, 162 normal (30 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, C23, C14, C14, C14, C2×C8, C2×C8, D8, SD16, Q16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, C4○D4, C28, C28, C28, C2×C14, C2×C14, C2×C14, C22×C8, C2×D8, C2×SD16, C2×Q16, C4○D8, C2×C4○D4, C56, C2×C28, C2×C28, C2×C28, C7×D4, C7×D4, C7×Q8, C7×Q8, C22×C14, C22×C14, C2×C4○D8, C2×C56, C2×C56, C7×D8, C7×SD16, C7×Q16, C22×C28, C22×C28, D4×C14, D4×C14, Q8×C14, C7×C4○D4, C7×C4○D4, C22×C56, C14×D8, C14×SD16, C14×Q16, C7×C4○D8, C14×C4○D4, C14×C4○D8
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C24, C2×C14, C4○D8, C22×D4, C7×D4, C22×C14, C2×C4○D8, D4×C14, C23×C14, C7×C4○D8, D4×C2×C14, C14×C4○D8
►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 56 92)(2 74 43 93)(3 75 44 94)(4 76 45 95)(5 77 46 96)(6 78 47 97)(7 79 48 98)(8 80 49 85)(9 81 50 86)(10 82 51 87)(11 83 52 88)(12 84 53 89)(13 71 54 90)(14 72 55 91)(15 39 160 114)(16 40 161 115)(17 41 162 116)(18 42 163 117)(19 29 164 118)(20 30 165 119)(21 31 166 120)(22 32 167 121)(23 33 168 122)(24 34 155 123)(25 35 156 124)(26 36 157 125)(27 37 158 126)(28 38 159 113)(57 108 140 194)(58 109 127 195)(59 110 128 196)(60 111 129 183)(61 112 130 184)(62 99 131 185)(63 100 132 186)(64 101 133 187)(65 102 134 188)(66 103 135 189)(67 104 136 190)(68 105 137 191)(69 106 138 192)(70 107 139 193)(141 176 217 203)(142 177 218 204)(143 178 219 205)(144 179 220 206)(145 180 221 207)(146 181 222 208)(147 182 223 209)(148 169 224 210)(149 170 211 197)(150 171 212 198)(151 172 213 199)(152 173 214 200)(153 174 215 201)(154 175 216 202)
(1 157 73 125 56 26 92 36)(2 158 74 126 43 27 93 37)(3 159 75 113 44 28 94 38)(4 160 76 114 45 15 95 39)(5 161 77 115 46 16 96 40)(6 162 78 116 47 17 97 41)(7 163 79 117 48 18 98 42)(8 164 80 118 49 19 85 29)(9 165 81 119 50 20 86 30)(10 166 82 120 51 21 87 31)(11 167 83 121 52 22 88 32)(12 168 84 122 53 23 89 33)(13 155 71 123 54 24 90 34)(14 156 72 124 55 25 91 35)(57 148 194 210 140 224 108 169)(58 149 195 197 127 211 109 170)(59 150 196 198 128 212 110 171)(60 151 183 199 129 213 111 172)(61 152 184 200 130 214 112 173)(62 153 185 201 131 215 99 174)(63 154 186 202 132 216 100 175)(64 141 187 203 133 217 101 176)(65 142 188 204 134 218 102 177)(66 143 189 205 135 219 103 178)(67 144 190 206 136 220 104 179)(68 145 191 207 137 221 105 180)(69 146 192 208 138 222 106 181)(70 147 193 209 139 223 107 182)
(1 183)(2 184)(3 185)(4 186)(5 187)(6 188)(7 189)(8 190)(9 191)(10 192)(11 193)(12 194)(13 195)(14 196)(15 216)(16 217)(17 218)(18 219)(19 220)(20 221)(21 222)(22 223)(23 224)(24 211)(25 212)(26 213)(27 214)(28 215)(29 206)(30 207)(31 208)(32 209)(33 210)(34 197)(35 198)(36 199)(37 200)(38 201)(39 202)(40 203)(41 204)(42 205)(43 112)(44 99)(45 100)(46 101)(47 102)(48 103)(49 104)(50 105)(51 106)(52 107)(53 108)(54 109)(55 110)(56 111)(57 84)(58 71)(59 72)(60 73)(61 74)(62 75)(63 76)(64 77)(65 78)(66 79)(67 80)(68 81)(69 82)(70 83)(85 136)(86 137)(87 138)(88 139)(89 140)(90 127)(91 128)(92 129)(93 130)(94 131)(95 132)(96 133)(97 134)(98 135)(113 174)(114 175)(115 176)(116 177)(117 178)(118 179)(119 180)(120 181)(121 182)(122 169)(123 170)(124 171)(125 172)(126 173)(141 161)(142 162)(143 163)(144 164)(145 165)(146 166)(147 167)(148 168)(149 155)(150 156)(151 157)(152 158)(153 159)(154 160)
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), (1,73,56,92)(2,74,43,93)(3,75,44,94)(4,76,45,95)(5,77,46,96)(6,78,47,97)(7,79,48,98)(8,80,49,85)(9,81,50,86)(10,82,51,87)(11,83,52,88)(12,84,53,89)(13,71,54,90)(14,72,55,91)(15,39,160,114)(16,40,161,115)(17,41,162,116)(18,42,163,117)(19,29,164,118)(20,30,165,119)(21,31,166,120)(22,32,167,121)(23,33,168,122)(24,34,155,123)(25,35,156,124)(26,36,157,125)(27,37,158,126)(28,38,159,113)(57,108,140,194)(58,109,127,195)(59,110,128,196)(60,111,129,183)(61,112,130,184)(62,99,131,185)(63,100,132,186)(64,101,133,187)(65,102,134,188)(66,103,135,189)(67,104,136,190)(68,105,137,191)(69,106,138,192)(70,107,139,193)(141,176,217,203)(142,177,218,204)(143,178,219,205)(144,179,220,206)(145,180,221,207)(146,181,222,208)(147,182,223,209)(148,169,224,210)(149,170,211,197)(150,171,212,198)(151,172,213,199)(152,173,214,200)(153,174,215,201)(154,175,216,202), (1,157,73,125,56,26,92,36)(2,158,74,126,43,27,93,37)(3,159,75,113,44,28,94,38)(4,160,76,114,45,15,95,39)(5,161,77,115,46,16,96,40)(6,162,78,116,47,17,97,41)(7,163,79,117,48,18,98,42)(8,164,80,118,49,19,85,29)(9,165,81,119,50,20,86,30)(10,166,82,120,51,21,87,31)(11,167,83,121,52,22,88,32)(12,168,84,122,53,23,89,33)(13,155,71,123,54,24,90,34)(14,156,72,124,55,25,91,35)(57,148,194,210,140,224,108,169)(58,149,195,197,127,211,109,170)(59,150,196,198,128,212,110,171)(60,151,183,199,129,213,111,172)(61,152,184,200,130,214,112,173)(62,153,185,201,131,215,99,174)(63,154,186,202,132,216,100,175)(64,141,187,203,133,217,101,176)(65,142,188,204,134,218,102,177)(66,143,189,205,135,219,103,178)(67,144,190,206,136,220,104,179)(68,145,191,207,137,221,105,180)(69,146,192,208,138,222,106,181)(70,147,193,209,139,223,107,182), (1,183)(2,184)(3,185)(4,186)(5,187)(6,188)(7,189)(8,190)(9,191)(10,192)(11,193)(12,194)(13,195)(14,196)(15,216)(16,217)(17,218)(18,219)(19,220)(20,221)(21,222)(22,223)(23,224)(24,211)(25,212)(26,213)(27,214)(28,215)(29,206)(30,207)(31,208)(32,209)(33,210)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,112)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,84)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)(64,77)(65,78)(66,79)(67,80)(68,81)(69,82)(70,83)(85,136)(86,137)(87,138)(88,139)(89,140)(90,127)(91,128)(92,129)(93,130)(94,131)(95,132)(96,133)(97,134)(98,135)(113,174)(114,175)(115,176)(116,177)(117,178)(118,179)(119,180)(120,181)(121,182)(122,169)(123,170)(124,171)(125,172)(126,173)(141,161)(142,162)(143,163)(144,164)(145,165)(146,166)(147,167)(148,168)(149,155)(150,156)(151,157)(152,158)(153,159)(154,160)>;
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), (1,73,56,92)(2,74,43,93)(3,75,44,94)(4,76,45,95)(5,77,46,96)(6,78,47,97)(7,79,48,98)(8,80,49,85)(9,81,50,86)(10,82,51,87)(11,83,52,88)(12,84,53,89)(13,71,54,90)(14,72,55,91)(15,39,160,114)(16,40,161,115)(17,41,162,116)(18,42,163,117)(19,29,164,118)(20,30,165,119)(21,31,166,120)(22,32,167,121)(23,33,168,122)(24,34,155,123)(25,35,156,124)(26,36,157,125)(27,37,158,126)(28,38,159,113)(57,108,140,194)(58,109,127,195)(59,110,128,196)(60,111,129,183)(61,112,130,184)(62,99,131,185)(63,100,132,186)(64,101,133,187)(65,102,134,188)(66,103,135,189)(67,104,136,190)(68,105,137,191)(69,106,138,192)(70,107,139,193)(141,176,217,203)(142,177,218,204)(143,178,219,205)(144,179,220,206)(145,180,221,207)(146,181,222,208)(147,182,223,209)(148,169,224,210)(149,170,211,197)(150,171,212,198)(151,172,213,199)(152,173,214,200)(153,174,215,201)(154,175,216,202), (1,157,73,125,56,26,92,36)(2,158,74,126,43,27,93,37)(3,159,75,113,44,28,94,38)(4,160,76,114,45,15,95,39)(5,161,77,115,46,16,96,40)(6,162,78,116,47,17,97,41)(7,163,79,117,48,18,98,42)(8,164,80,118,49,19,85,29)(9,165,81,119,50,20,86,30)(10,166,82,120,51,21,87,31)(11,167,83,121,52,22,88,32)(12,168,84,122,53,23,89,33)(13,155,71,123,54,24,90,34)(14,156,72,124,55,25,91,35)(57,148,194,210,140,224,108,169)(58,149,195,197,127,211,109,170)(59,150,196,198,128,212,110,171)(60,151,183,199,129,213,111,172)(61,152,184,200,130,214,112,173)(62,153,185,201,131,215,99,174)(63,154,186,202,132,216,100,175)(64,141,187,203,133,217,101,176)(65,142,188,204,134,218,102,177)(66,143,189,205,135,219,103,178)(67,144,190,206,136,220,104,179)(68,145,191,207,137,221,105,180)(69,146,192,208,138,222,106,181)(70,147,193,209,139,223,107,182), (1,183)(2,184)(3,185)(4,186)(5,187)(6,188)(7,189)(8,190)(9,191)(10,192)(11,193)(12,194)(13,195)(14,196)(15,216)(16,217)(17,218)(18,219)(19,220)(20,221)(21,222)(22,223)(23,224)(24,211)(25,212)(26,213)(27,214)(28,215)(29,206)(30,207)(31,208)(32,209)(33,210)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,112)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,84)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)(64,77)(65,78)(66,79)(67,80)(68,81)(69,82)(70,83)(85,136)(86,137)(87,138)(88,139)(89,140)(90,127)(91,128)(92,129)(93,130)(94,131)(95,132)(96,133)(97,134)(98,135)(113,174)(114,175)(115,176)(116,177)(117,178)(118,179)(119,180)(120,181)(121,182)(122,169)(123,170)(124,171)(125,172)(126,173)(141,161)(142,162)(143,163)(144,164)(145,165)(146,166)(147,167)(148,168)(149,155)(150,156)(151,157)(152,158)(153,159)(154,160) );
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)], [(1,73,56,92),(2,74,43,93),(3,75,44,94),(4,76,45,95),(5,77,46,96),(6,78,47,97),(7,79,48,98),(8,80,49,85),(9,81,50,86),(10,82,51,87),(11,83,52,88),(12,84,53,89),(13,71,54,90),(14,72,55,91),(15,39,160,114),(16,40,161,115),(17,41,162,116),(18,42,163,117),(19,29,164,118),(20,30,165,119),(21,31,166,120),(22,32,167,121),(23,33,168,122),(24,34,155,123),(25,35,156,124),(26,36,157,125),(27,37,158,126),(28,38,159,113),(57,108,140,194),(58,109,127,195),(59,110,128,196),(60,111,129,183),(61,112,130,184),(62,99,131,185),(63,100,132,186),(64,101,133,187),(65,102,134,188),(66,103,135,189),(67,104,136,190),(68,105,137,191),(69,106,138,192),(70,107,139,193),(141,176,217,203),(142,177,218,204),(143,178,219,205),(144,179,220,206),(145,180,221,207),(146,181,222,208),(147,182,223,209),(148,169,224,210),(149,170,211,197),(150,171,212,198),(151,172,213,199),(152,173,214,200),(153,174,215,201),(154,175,216,202)], [(1,157,73,125,56,26,92,36),(2,158,74,126,43,27,93,37),(3,159,75,113,44,28,94,38),(4,160,76,114,45,15,95,39),(5,161,77,115,46,16,96,40),(6,162,78,116,47,17,97,41),(7,163,79,117,48,18,98,42),(8,164,80,118,49,19,85,29),(9,165,81,119,50,20,86,30),(10,166,82,120,51,21,87,31),(11,167,83,121,52,22,88,32),(12,168,84,122,53,23,89,33),(13,155,71,123,54,24,90,34),(14,156,72,124,55,25,91,35),(57,148,194,210,140,224,108,169),(58,149,195,197,127,211,109,170),(59,150,196,198,128,212,110,171),(60,151,183,199,129,213,111,172),(61,152,184,200,130,214,112,173),(62,153,185,201,131,215,99,174),(63,154,186,202,132,216,100,175),(64,141,187,203,133,217,101,176),(65,142,188,204,134,218,102,177),(66,143,189,205,135,219,103,178),(67,144,190,206,136,220,104,179),(68,145,191,207,137,221,105,180),(69,146,192,208,138,222,106,181),(70,147,193,209,139,223,107,182)], [(1,183),(2,184),(3,185),(4,186),(5,187),(6,188),(7,189),(8,190),(9,191),(10,192),(11,193),(12,194),(13,195),(14,196),(15,216),(16,217),(17,218),(18,219),(19,220),(20,221),(21,222),(22,223),(23,224),(24,211),(25,212),(26,213),(27,214),(28,215),(29,206),(30,207),(31,208),(32,209),(33,210),(34,197),(35,198),(36,199),(37,200),(38,201),(39,202),(40,203),(41,204),(42,205),(43,112),(44,99),(45,100),(46,101),(47,102),(48,103),(49,104),(50,105),(51,106),(52,107),(53,108),(54,109),(55,110),(56,111),(57,84),(58,71),(59,72),(60,73),(61,74),(62,75),(63,76),(64,77),(65,78),(66,79),(67,80),(68,81),(69,82),(70,83),(85,136),(86,137),(87,138),(88,139),(89,140),(90,127),(91,128),(92,129),(93,130),(94,131),(95,132),(96,133),(97,134),(98,135),(113,174),(114,175),(115,176),(116,177),(117,178),(118,179),(119,180),(120,181),(121,182),(122,169),(123,170),(124,171),(125,172),(126,173),(141,161),(142,162),(143,163),(144,164),(145,165),(146,166),(147,167),(148,168),(149,155),(150,156),(151,157),(152,158),(153,159),(154,160)]])
196 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | ··· | 7F | 8A | ··· | 8H | 14A | ··· | 14R | 14S | ··· | 14AD | 14AE | ··· | 14BB | 28A | ··· | 28X | 28Y | ··· | 28AJ | 28AK | ··· | 28BH | 56A | ··· | 56AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | |||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | C4○D8 | C7×D4 | C7×D4 | C7×C4○D8 |
| kernel | C14×C4○D8 | C22×C56 | C14×D8 | C14×SD16 | C14×Q16 | C7×C4○D8 | C14×C4○D4 | C2×C4○D8 | C22×C8 | C2×D8 | C2×SD16 | C2×Q16 | C4○D8 | C2×C4○D4 | C2×C28 | C22×C14 | C14 | C2×C4 | C23 | C2 |
| # reps | 1 | 1 | 1 | 2 | 1 | 8 | 2 | 6 | 6 | 6 | 12 | 6 | 48 | 12 | 3 | 1 | 8 | 18 | 6 | 48 |
Matrix representation of C14×C4○D8 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 16 | 0 |
| 0 | 0 | 0 | 16 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 5 | 27 | 0 | 0 |
| 66 | 108 | 0 | 0 |
| 0 | 0 | 44 | 0 |
| 0 | 0 | 13 | 18 |
| 43 | 29 | 0 | 0 |
| 22 | 70 | 0 | 0 |
| 0 | 0 | 95 | 36 |
| 0 | 0 | 13 | 18 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,16,0,0,0,0,16],[112,0,0,0,0,112,0,0,0,0,15,0,0,0,0,15],[5,66,0,0,27,108,0,0,0,0,44,13,0,0,0,18],[43,22,0,0,29,70,0,0,0,0,95,13,0,0,36,18] >;
C14×C4○D8 in GAP, Magma, Sage, TeX
C_{14}\times C_4\circ D_8 % in TeX
G:=Group("C14xC4oD8"); // GroupNames label
G:=SmallGroup(448,1355);
// by ID
G=gap.SmallGroup(448,1355);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,1192,14117,7068,124]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^4=d^2=1,c^4=b^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=b^2*c^3>;
// generators/relations