direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D14⋊3Q8, D14⋊4(C2×Q8), (C2×Q8)⋊28D14, (C22×Q8)⋊5D7, (C22×D7)⋊7Q8, C28.258(C2×D4), (C2×C28).214D4, C14⋊5(C22⋊Q8), C22.37(Q8×D7), C4⋊Dic7⋊79C22, (Q8×C14)⋊35C22, C14.53(C22×Q8), (C2×C14).305C24, (C2×C28).552C23, Dic7⋊C4⋊75C22, C14.153(C22×D4), (C22×C4).384D14, D14⋊C4.157C22, C22.316(C23×D7), C23.341(C22×D7), (C22×C14).423C23, (C22×C28).285C22, C22.39(Q8⋊2D7), (C2×Dic7).157C23, (C22×D7).241C23, (C23×D7).114C22, (C22×Dic7).164C22, (Q8×C2×C14)⋊4C2, C7⋊6(C2×C22⋊Q8), C2.35(C2×Q8×D7), C4.98(C2×C7⋊D4), (D7×C22×C4).9C2, (C2×C4⋊Dic7)⋊46C2, (C2×C14).98(C2×Q8), (C2×Dic7⋊C4)⋊49C2, (C2×D14⋊C4).27C2, C14.127(C2×C4○D4), (C2×C14).588(C2×D4), C2.34(C2×Q8⋊2D7), (C2×C4×D7).262C22, C2.26(C22×C7⋊D4), (C2×C4).202(C7⋊D4), (C2×C4).242(C22×D7), C22.116(C2×C7⋊D4), (C2×C14).200(C4○D4), SmallGroup(448,1266)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D14⋊3Q8
G = < a,b,c,d,e | a2=b14=c2=d4=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, dcd-1=b7c, ce=ec, ede-1=d-1 >
Subgroups: 1332 in 322 conjugacy classes, 135 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×Q8, C2×Q8, C24, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C22⋊C4, C2×C4⋊C4, C22⋊Q8, C23×C4, C22×Q8, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C22×C14, C2×C22⋊Q8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C2×C4×D7, C2×C4×D7, C22×Dic7, C22×Dic7, C22×C28, C22×C28, Q8×C14, Q8×C14, C23×D7, C2×Dic7⋊C4, C2×C4⋊Dic7, C2×D14⋊C4, D14⋊3Q8, D7×C22×C4, Q8×C2×C14, C2×D14⋊3Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, C24, D14, C22⋊Q8, C22×D4, C22×Q8, C2×C4○D4, C7⋊D4, C22×D7, C2×C22⋊Q8, Q8×D7, Q8⋊2D7, C2×C7⋊D4, C23×D7, D14⋊3Q8, C2×Q8×D7, C2×Q8⋊2D7, C22×C7⋊D4, C2×D14⋊3Q8
►On 224 points
Generators in S224
(1 69)(2 70)(3 57)(4 58)(5 59)(6 60)(7 61)(8 62)(9 63)(10 64)(11 65)(12 66)(13 67)(14 68)(15 54)(16 55)(17 56)(18 43)(19 44)(20 45)(21 46)(22 47)(23 48)(24 49)(25 50)(26 51)(27 52)(28 53)(29 79)(30 80)(31 81)(32 82)(33 83)(34 84)(35 71)(36 72)(37 73)(38 74)(39 75)(40 76)(41 77)(42 78)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 99)(94 100)(95 101)(96 102)(97 103)(98 104)(113 187)(114 188)(115 189)(116 190)(117 191)(118 192)(119 193)(120 194)(121 195)(122 196)(123 183)(124 184)(125 185)(126 186)(127 173)(128 174)(129 175)(130 176)(131 177)(132 178)(133 179)(134 180)(135 181)(136 182)(137 169)(138 170)(139 171)(140 172)(141 204)(142 205)(143 206)(144 207)(145 208)(146 209)(147 210)(148 197)(149 198)(150 199)(151 200)(152 201)(153 202)(154 203)(155 221)(156 222)(157 223)(158 224)(159 211)(160 212)(161 213)(162 214)(163 215)(164 216)(165 217)(166 218)(167 219)(168 220)
(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)
(1 102)(2 101)(3 100)(4 99)(5 112)(6 111)(7 110)(8 109)(9 108)(10 107)(11 106)(12 105)(13 104)(14 103)(15 35)(16 34)(17 33)(18 32)(19 31)(20 30)(21 29)(22 42)(23 41)(24 40)(25 39)(26 38)(27 37)(28 36)(43 82)(44 81)(45 80)(46 79)(47 78)(48 77)(49 76)(50 75)(51 74)(52 73)(53 72)(54 71)(55 84)(56 83)(57 94)(58 93)(59 92)(60 91)(61 90)(62 89)(63 88)(64 87)(65 86)(66 85)(67 98)(68 97)(69 96)(70 95)(113 202)(114 201)(115 200)(116 199)(117 198)(118 197)(119 210)(120 209)(121 208)(122 207)(123 206)(124 205)(125 204)(126 203)(127 167)(128 166)(129 165)(130 164)(131 163)(132 162)(133 161)(134 160)(135 159)(136 158)(137 157)(138 156)(139 155)(140 168)(141 185)(142 184)(143 183)(144 196)(145 195)(146 194)(147 193)(148 192)(149 191)(150 190)(151 189)(152 188)(153 187)(154 186)(169 223)(170 222)(171 221)(172 220)(173 219)(174 218)(175 217)(176 216)(177 215)(178 214)(179 213)(180 212)(181 211)(182 224)
(1 212 103 174)(2 213 104 175)(3 214 105 176)(4 215 106 177)(5 216 107 178)(6 217 108 179)(7 218 109 180)(8 219 110 181)(9 220 111 182)(10 221 112 169)(11 222 99 170)(12 223 100 171)(13 224 101 172)(14 211 102 173)(15 184 41 141)(16 185 42 142)(17 186 29 143)(18 187 30 144)(19 188 31 145)(20 189 32 146)(21 190 33 147)(22 191 34 148)(23 192 35 149)(24 193 36 150)(25 194 37 151)(26 195 38 152)(27 196 39 153)(28 183 40 154)(43 113 80 207)(44 114 81 208)(45 115 82 209)(46 116 83 210)(47 117 84 197)(48 118 71 198)(49 119 72 199)(50 120 73 200)(51 121 74 201)(52 122 75 202)(53 123 76 203)(54 124 77 204)(55 125 78 205)(56 126 79 206)(57 162 85 130)(58 163 86 131)(59 164 87 132)(60 165 88 133)(61 166 89 134)(62 167 90 135)(63 168 91 136)(64 155 92 137)(65 156 93 138)(66 157 94 139)(67 158 95 140)(68 159 96 127)(69 160 97 128)(70 161 98 129)
(1 185 103 142)(2 186 104 143)(3 187 105 144)(4 188 106 145)(5 189 107 146)(6 190 108 147)(7 191 109 148)(8 192 110 149)(9 193 111 150)(10 194 112 151)(11 195 99 152)(12 196 100 153)(13 183 101 154)(14 184 102 141)(15 173 41 211)(16 174 42 212)(17 175 29 213)(18 176 30 214)(19 177 31 215)(20 178 32 216)(21 179 33 217)(22 180 34 218)(23 181 35 219)(24 182 36 220)(25 169 37 221)(26 170 38 222)(27 171 39 223)(28 172 40 224)(43 130 80 162)(44 131 81 163)(45 132 82 164)(46 133 83 165)(47 134 84 166)(48 135 71 167)(49 136 72 168)(50 137 73 155)(51 138 74 156)(52 139 75 157)(53 140 76 158)(54 127 77 159)(55 128 78 160)(56 129 79 161)(57 113 85 207)(58 114 86 208)(59 115 87 209)(60 116 88 210)(61 117 89 197)(62 118 90 198)(63 119 91 199)(64 120 92 200)(65 121 93 201)(66 122 94 202)(67 123 95 203)(68 124 96 204)(69 125 97 205)(70 126 98 206)
G:=sub<Sym(224)| (1,69)(2,70)(3,57)(4,58)(5,59)(6,60)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,54)(16,55)(17,56)(18,43)(19,44)(20,45)(21,46)(22,47)(23,48)(24,49)(25,50)(26,51)(27,52)(28,53)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,71)(36,72)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,99)(94,100)(95,101)(96,102)(97,103)(98,104)(113,187)(114,188)(115,189)(116,190)(117,191)(118,192)(119,193)(120,194)(121,195)(122,196)(123,183)(124,184)(125,185)(126,186)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)(134,180)(135,181)(136,182)(137,169)(138,170)(139,171)(140,172)(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(148,197)(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,221)(156,222)(157,223)(158,224)(159,211)(160,212)(161,213)(162,214)(163,215)(164,216)(165,217)(166,218)(167,219)(168,220), (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), (1,102)(2,101)(3,100)(4,99)(5,112)(6,111)(7,110)(8,109)(9,108)(10,107)(11,106)(12,105)(13,104)(14,103)(15,35)(16,34)(17,33)(18,32)(19,31)(20,30)(21,29)(22,42)(23,41)(24,40)(25,39)(26,38)(27,37)(28,36)(43,82)(44,81)(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,84)(56,83)(57,94)(58,93)(59,92)(60,91)(61,90)(62,89)(63,88)(64,87)(65,86)(66,85)(67,98)(68,97)(69,96)(70,95)(113,202)(114,201)(115,200)(116,199)(117,198)(118,197)(119,210)(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,167)(128,166)(129,165)(130,164)(131,163)(132,162)(133,161)(134,160)(135,159)(136,158)(137,157)(138,156)(139,155)(140,168)(141,185)(142,184)(143,183)(144,196)(145,195)(146,194)(147,193)(148,192)(149,191)(150,190)(151,189)(152,188)(153,187)(154,186)(169,223)(170,222)(171,221)(172,220)(173,219)(174,218)(175,217)(176,216)(177,215)(178,214)(179,213)(180,212)(181,211)(182,224), (1,212,103,174)(2,213,104,175)(3,214,105,176)(4,215,106,177)(5,216,107,178)(6,217,108,179)(7,218,109,180)(8,219,110,181)(9,220,111,182)(10,221,112,169)(11,222,99,170)(12,223,100,171)(13,224,101,172)(14,211,102,173)(15,184,41,141)(16,185,42,142)(17,186,29,143)(18,187,30,144)(19,188,31,145)(20,189,32,146)(21,190,33,147)(22,191,34,148)(23,192,35,149)(24,193,36,150)(25,194,37,151)(26,195,38,152)(27,196,39,153)(28,183,40,154)(43,113,80,207)(44,114,81,208)(45,115,82,209)(46,116,83,210)(47,117,84,197)(48,118,71,198)(49,119,72,199)(50,120,73,200)(51,121,74,201)(52,122,75,202)(53,123,76,203)(54,124,77,204)(55,125,78,205)(56,126,79,206)(57,162,85,130)(58,163,86,131)(59,164,87,132)(60,165,88,133)(61,166,89,134)(62,167,90,135)(63,168,91,136)(64,155,92,137)(65,156,93,138)(66,157,94,139)(67,158,95,140)(68,159,96,127)(69,160,97,128)(70,161,98,129), (1,185,103,142)(2,186,104,143)(3,187,105,144)(4,188,106,145)(5,189,107,146)(6,190,108,147)(7,191,109,148)(8,192,110,149)(9,193,111,150)(10,194,112,151)(11,195,99,152)(12,196,100,153)(13,183,101,154)(14,184,102,141)(15,173,41,211)(16,174,42,212)(17,175,29,213)(18,176,30,214)(19,177,31,215)(20,178,32,216)(21,179,33,217)(22,180,34,218)(23,181,35,219)(24,182,36,220)(25,169,37,221)(26,170,38,222)(27,171,39,223)(28,172,40,224)(43,130,80,162)(44,131,81,163)(45,132,82,164)(46,133,83,165)(47,134,84,166)(48,135,71,167)(49,136,72,168)(50,137,73,155)(51,138,74,156)(52,139,75,157)(53,140,76,158)(54,127,77,159)(55,128,78,160)(56,129,79,161)(57,113,85,207)(58,114,86,208)(59,115,87,209)(60,116,88,210)(61,117,89,197)(62,118,90,198)(63,119,91,199)(64,120,92,200)(65,121,93,201)(66,122,94,202)(67,123,95,203)(68,124,96,204)(69,125,97,205)(70,126,98,206)>;
G:=Group( (1,69)(2,70)(3,57)(4,58)(5,59)(6,60)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,54)(16,55)(17,56)(18,43)(19,44)(20,45)(21,46)(22,47)(23,48)(24,49)(25,50)(26,51)(27,52)(28,53)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,71)(36,72)(37,73)(38,74)(39,75)(40,76)(41,77)(42,78)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,99)(94,100)(95,101)(96,102)(97,103)(98,104)(113,187)(114,188)(115,189)(116,190)(117,191)(118,192)(119,193)(120,194)(121,195)(122,196)(123,183)(124,184)(125,185)(126,186)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)(134,180)(135,181)(136,182)(137,169)(138,170)(139,171)(140,172)(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(148,197)(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,221)(156,222)(157,223)(158,224)(159,211)(160,212)(161,213)(162,214)(163,215)(164,216)(165,217)(166,218)(167,219)(168,220), (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), (1,102)(2,101)(3,100)(4,99)(5,112)(6,111)(7,110)(8,109)(9,108)(10,107)(11,106)(12,105)(13,104)(14,103)(15,35)(16,34)(17,33)(18,32)(19,31)(20,30)(21,29)(22,42)(23,41)(24,40)(25,39)(26,38)(27,37)(28,36)(43,82)(44,81)(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,84)(56,83)(57,94)(58,93)(59,92)(60,91)(61,90)(62,89)(63,88)(64,87)(65,86)(66,85)(67,98)(68,97)(69,96)(70,95)(113,202)(114,201)(115,200)(116,199)(117,198)(118,197)(119,210)(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,167)(128,166)(129,165)(130,164)(131,163)(132,162)(133,161)(134,160)(135,159)(136,158)(137,157)(138,156)(139,155)(140,168)(141,185)(142,184)(143,183)(144,196)(145,195)(146,194)(147,193)(148,192)(149,191)(150,190)(151,189)(152,188)(153,187)(154,186)(169,223)(170,222)(171,221)(172,220)(173,219)(174,218)(175,217)(176,216)(177,215)(178,214)(179,213)(180,212)(181,211)(182,224), (1,212,103,174)(2,213,104,175)(3,214,105,176)(4,215,106,177)(5,216,107,178)(6,217,108,179)(7,218,109,180)(8,219,110,181)(9,220,111,182)(10,221,112,169)(11,222,99,170)(12,223,100,171)(13,224,101,172)(14,211,102,173)(15,184,41,141)(16,185,42,142)(17,186,29,143)(18,187,30,144)(19,188,31,145)(20,189,32,146)(21,190,33,147)(22,191,34,148)(23,192,35,149)(24,193,36,150)(25,194,37,151)(26,195,38,152)(27,196,39,153)(28,183,40,154)(43,113,80,207)(44,114,81,208)(45,115,82,209)(46,116,83,210)(47,117,84,197)(48,118,71,198)(49,119,72,199)(50,120,73,200)(51,121,74,201)(52,122,75,202)(53,123,76,203)(54,124,77,204)(55,125,78,205)(56,126,79,206)(57,162,85,130)(58,163,86,131)(59,164,87,132)(60,165,88,133)(61,166,89,134)(62,167,90,135)(63,168,91,136)(64,155,92,137)(65,156,93,138)(66,157,94,139)(67,158,95,140)(68,159,96,127)(69,160,97,128)(70,161,98,129), (1,185,103,142)(2,186,104,143)(3,187,105,144)(4,188,106,145)(5,189,107,146)(6,190,108,147)(7,191,109,148)(8,192,110,149)(9,193,111,150)(10,194,112,151)(11,195,99,152)(12,196,100,153)(13,183,101,154)(14,184,102,141)(15,173,41,211)(16,174,42,212)(17,175,29,213)(18,176,30,214)(19,177,31,215)(20,178,32,216)(21,179,33,217)(22,180,34,218)(23,181,35,219)(24,182,36,220)(25,169,37,221)(26,170,38,222)(27,171,39,223)(28,172,40,224)(43,130,80,162)(44,131,81,163)(45,132,82,164)(46,133,83,165)(47,134,84,166)(48,135,71,167)(49,136,72,168)(50,137,73,155)(51,138,74,156)(52,139,75,157)(53,140,76,158)(54,127,77,159)(55,128,78,160)(56,129,79,161)(57,113,85,207)(58,114,86,208)(59,115,87,209)(60,116,88,210)(61,117,89,197)(62,118,90,198)(63,119,91,199)(64,120,92,200)(65,121,93,201)(66,122,94,202)(67,123,95,203)(68,124,96,204)(69,125,97,205)(70,126,98,206) );
G=PermutationGroup([[(1,69),(2,70),(3,57),(4,58),(5,59),(6,60),(7,61),(8,62),(9,63),(10,64),(11,65),(12,66),(13,67),(14,68),(15,54),(16,55),(17,56),(18,43),(19,44),(20,45),(21,46),(22,47),(23,48),(24,49),(25,50),(26,51),(27,52),(28,53),(29,79),(30,80),(31,81),(32,82),(33,83),(34,84),(35,71),(36,72),(37,73),(38,74),(39,75),(40,76),(41,77),(42,78),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110),(91,111),(92,112),(93,99),(94,100),(95,101),(96,102),(97,103),(98,104),(113,187),(114,188),(115,189),(116,190),(117,191),(118,192),(119,193),(120,194),(121,195),(122,196),(123,183),(124,184),(125,185),(126,186),(127,173),(128,174),(129,175),(130,176),(131,177),(132,178),(133,179),(134,180),(135,181),(136,182),(137,169),(138,170),(139,171),(140,172),(141,204),(142,205),(143,206),(144,207),(145,208),(146,209),(147,210),(148,197),(149,198),(150,199),(151,200),(152,201),(153,202),(154,203),(155,221),(156,222),(157,223),(158,224),(159,211),(160,212),(161,213),(162,214),(163,215),(164,216),(165,217),(166,218),(167,219),(168,220)], [(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)], [(1,102),(2,101),(3,100),(4,99),(5,112),(6,111),(7,110),(8,109),(9,108),(10,107),(11,106),(12,105),(13,104),(14,103),(15,35),(16,34),(17,33),(18,32),(19,31),(20,30),(21,29),(22,42),(23,41),(24,40),(25,39),(26,38),(27,37),(28,36),(43,82),(44,81),(45,80),(46,79),(47,78),(48,77),(49,76),(50,75),(51,74),(52,73),(53,72),(54,71),(55,84),(56,83),(57,94),(58,93),(59,92),(60,91),(61,90),(62,89),(63,88),(64,87),(65,86),(66,85),(67,98),(68,97),(69,96),(70,95),(113,202),(114,201),(115,200),(116,199),(117,198),(118,197),(119,210),(120,209),(121,208),(122,207),(123,206),(124,205),(125,204),(126,203),(127,167),(128,166),(129,165),(130,164),(131,163),(132,162),(133,161),(134,160),(135,159),(136,158),(137,157),(138,156),(139,155),(140,168),(141,185),(142,184),(143,183),(144,196),(145,195),(146,194),(147,193),(148,192),(149,191),(150,190),(151,189),(152,188),(153,187),(154,186),(169,223),(170,222),(171,221),(172,220),(173,219),(174,218),(175,217),(176,216),(177,215),(178,214),(179,213),(180,212),(181,211),(182,224)], [(1,212,103,174),(2,213,104,175),(3,214,105,176),(4,215,106,177),(5,216,107,178),(6,217,108,179),(7,218,109,180),(8,219,110,181),(9,220,111,182),(10,221,112,169),(11,222,99,170),(12,223,100,171),(13,224,101,172),(14,211,102,173),(15,184,41,141),(16,185,42,142),(17,186,29,143),(18,187,30,144),(19,188,31,145),(20,189,32,146),(21,190,33,147),(22,191,34,148),(23,192,35,149),(24,193,36,150),(25,194,37,151),(26,195,38,152),(27,196,39,153),(28,183,40,154),(43,113,80,207),(44,114,81,208),(45,115,82,209),(46,116,83,210),(47,117,84,197),(48,118,71,198),(49,119,72,199),(50,120,73,200),(51,121,74,201),(52,122,75,202),(53,123,76,203),(54,124,77,204),(55,125,78,205),(56,126,79,206),(57,162,85,130),(58,163,86,131),(59,164,87,132),(60,165,88,133),(61,166,89,134),(62,167,90,135),(63,168,91,136),(64,155,92,137),(65,156,93,138),(66,157,94,139),(67,158,95,140),(68,159,96,127),(69,160,97,128),(70,161,98,129)], [(1,185,103,142),(2,186,104,143),(3,187,105,144),(4,188,106,145),(5,189,107,146),(6,190,108,147),(7,191,109,148),(8,192,110,149),(9,193,111,150),(10,194,112,151),(11,195,99,152),(12,196,100,153),(13,183,101,154),(14,184,102,141),(15,173,41,211),(16,174,42,212),(17,175,29,213),(18,176,30,214),(19,177,31,215),(20,178,32,216),(21,179,33,217),(22,180,34,218),(23,181,35,219),(24,182,36,220),(25,169,37,221),(26,170,38,222),(27,171,39,223),(28,172,40,224),(43,130,80,162),(44,131,81,163),(45,132,82,164),(46,133,83,165),(47,134,84,166),(48,135,71,167),(49,136,72,168),(50,137,73,155),(51,138,74,156),(52,139,75,157),(53,140,76,158),(54,127,77,159),(55,128,78,160),(56,129,79,161),(57,113,85,207),(58,114,86,208),(59,115,87,209),(60,116,88,210),(61,117,89,197),(62,118,90,198),(63,119,91,199),(64,120,92,200),(65,121,93,201),(66,122,94,202),(67,123,95,203),(68,124,96,204),(69,125,97,205),(70,126,98,206)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | Q8 | D7 | C4○D4 | D14 | D14 | C7⋊D4 | Q8×D7 | Q8⋊2D7 |
| kernel | C2×D14⋊3Q8 | C2×Dic7⋊C4 | C2×C4⋊Dic7 | C2×D14⋊C4 | D14⋊3Q8 | D7×C22×C4 | Q8×C2×C14 | C2×C28 | C22×D7 | C22×Q8 | C2×C14 | C22×C4 | C2×Q8 | C2×C4 | C22 | C22 |
| # reps | 1 | 2 | 1 | 2 | 8 | 1 | 1 | 4 | 4 | 3 | 4 | 9 | 12 | 24 | 6 | 6 |
Matrix representation of C2×D14⋊3Q8 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 4 |
| 0 | 0 | 0 | 0 | 21 | 12 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 3 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,24,21,0,0,0,0,4,12],[28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,3,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C2×D14⋊3Q8 in GAP, Magma, Sage, TeX
C_2\times D_{14}\rtimes_3Q_8 % in TeX
G:=Group("C2xD14:3Q8"); // GroupNames label
G:=SmallGroup(448,1266);
// by ID
G=gap.SmallGroup(448,1266);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,184,675,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^14=c^2=d^4=1,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=b^7*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations