direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C22⋊Dic14, C23⋊3Dic14, C24.51D14, (C22×C14)⋊4Q8, C14⋊1(C22⋊Q8), C14.5(C22×Q8), (C2×C14).25C24, C4⋊Dic7⋊49C22, C22⋊C4.84D14, Dic7.41(C2×D4), C22⋊2(C2×Dic14), C22.122(D4×D7), C14.32(C22×D4), (C2×C28).125C23, Dic7⋊C4⋊46C22, (C2×Dic7).189D4, (C22×Dic14)⋊5C2, (C22×C4).167D14, (C23×Dic7).8C2, C2.7(C22×Dic14), C22.67(C23×D7), (C2×Dic14)⋊47C22, (C23×C14).51C22, (C22×C28).70C22, C23.318(C22×D7), C23.D7.83C22, C22.64(D4⋊2D7), (C22×C14).117C23, (C2×Dic7).175C23, (C22×Dic7).202C22, C2.7(C2×D4×D7), C7⋊1(C2×C22⋊Q8), (C2×C14)⋊4(C2×Q8), (C2×C4⋊Dic7)⋊17C2, C14.66(C2×C4○D4), C2.7(C2×D4⋊2D7), (C2×Dic7⋊C4)⋊21C2, (C2×C14).378(C2×D4), (C2×C22⋊C4).16D7, (C14×C22⋊C4).17C2, (C2×C4).132(C22×D7), (C2×C23.D7).20C2, (C2×C14).166(C4○D4), (C7×C22⋊C4).96C22, SmallGroup(448,934)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C22⋊Dic14
G = < a,b,c,d,e | a2=b2=c2=d28=1, e2=d14, ab=ba, ac=ca, ad=da, ae=ea, dbd-1=bc=cb, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 1236 in 322 conjugacy classes, 135 normal (31 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C23, C23, C14, C14, C14, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Q8, C24, Dic7, Dic7, C28, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C22⋊Q8, C23×C4, C22×Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C2×C22⋊Q8, Dic7⋊C4, C4⋊Dic7, C23.D7, C7×C22⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×Dic7, C22×Dic7, C22×C28, C23×C14, C22⋊Dic14, C2×Dic7⋊C4, C2×C4⋊Dic7, C2×C23.D7, C14×C22⋊C4, C22×Dic14, C23×Dic7, C2×C22⋊Dic14
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, Dic14, C22×D7, C2×C22⋊Q8, C2×Dic14, D4×D7, D4⋊2D7, C23×D7, C22⋊Dic14, C22×Dic14, C2×D4×D7, C2×D4⋊2D7, C2×C22⋊Dic14
►On 224 points
Generators in S224
(1 215)(2 216)(3 217)(4 218)(5 219)(6 220)(7 221)(8 222)(9 223)(10 224)(11 197)(12 198)(13 199)(14 200)(15 201)(16 202)(17 203)(18 204)(19 205)(20 206)(21 207)(22 208)(23 209)(24 210)(25 211)(26 212)(27 213)(28 214)(29 112)(30 85)(31 86)(32 87)(33 88)(34 89)(35 90)(36 91)(37 92)(38 93)(39 94)(40 95)(41 96)(42 97)(43 98)(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)(57 191)(58 192)(59 193)(60 194)(61 195)(62 196)(63 169)(64 170)(65 171)(66 172)(67 173)(68 174)(69 175)(70 176)(71 177)(72 178)(73 179)(74 180)(75 181)(76 182)(77 183)(78 184)(79 185)(80 186)(81 187)(82 188)(83 189)(84 190)(113 165)(114 166)(115 167)(116 168)(117 141)(118 142)(119 143)(120 144)(121 145)(122 146)(123 147)(124 148)(125 149)(126 150)(127 151)(128 152)(129 153)(130 154)(131 155)(132 156)(133 157)(134 158)(135 159)(136 160)(137 161)(138 162)(139 163)(140 164)
(1 38)(2 202)(3 40)(4 204)(5 42)(6 206)(7 44)(8 208)(9 46)(10 210)(11 48)(12 212)(13 50)(14 214)(15 52)(16 216)(17 54)(18 218)(19 56)(20 220)(21 30)(22 222)(23 32)(24 224)(25 34)(26 198)(27 36)(28 200)(29 98)(31 100)(33 102)(35 104)(37 106)(39 108)(41 110)(43 112)(45 86)(47 88)(49 90)(51 92)(53 94)(55 96)(57 129)(58 178)(59 131)(60 180)(61 133)(62 182)(63 135)(64 184)(65 137)(66 186)(67 139)(68 188)(69 113)(70 190)(71 115)(72 192)(73 117)(74 194)(75 119)(76 196)(77 121)(78 170)(79 123)(80 172)(81 125)(82 174)(83 127)(84 176)(85 207)(87 209)(89 211)(91 213)(93 215)(95 217)(97 219)(99 221)(101 223)(103 197)(105 199)(107 201)(109 203)(111 205)(114 152)(116 154)(118 156)(120 158)(122 160)(124 162)(126 164)(128 166)(130 168)(132 142)(134 144)(136 146)(138 148)(140 150)(141 179)(143 181)(145 183)(147 185)(149 187)(151 189)(153 191)(155 193)(157 195)(159 169)(161 171)(163 173)(165 175)(167 177)
(1 107)(2 108)(3 109)(4 110)(5 111)(6 112)(7 85)(8 86)(9 87)(10 88)(11 89)(12 90)(13 91)(14 92)(15 93)(16 94)(17 95)(18 96)(19 97)(20 98)(21 99)(22 100)(23 101)(24 102)(25 103)(26 104)(27 105)(28 106)(29 220)(30 221)(31 222)(32 223)(33 224)(34 197)(35 198)(36 199)(37 200)(38 201)(39 202)(40 203)(41 204)(42 205)(43 206)(44 207)(45 208)(46 209)(47 210)(48 211)(49 212)(50 213)(51 214)(52 215)(53 216)(54 217)(55 218)(56 219)(57 167)(58 168)(59 141)(60 142)(61 143)(62 144)(63 145)(64 146)(65 147)(66 148)(67 149)(68 150)(69 151)(70 152)(71 153)(72 154)(73 155)(74 156)(75 157)(76 158)(77 159)(78 160)(79 161)(80 162)(81 163)(82 164)(83 165)(84 166)(113 189)(114 190)(115 191)(116 192)(117 193)(118 194)(119 195)(120 196)(121 169)(122 170)(123 171)(124 172)(125 173)(126 174)(127 175)(128 176)(129 177)(130 178)(131 179)(132 180)(133 181)(134 182)(135 183)(136 184)(137 185)(138 186)(139 187)(140 188)
(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 81 15 67)(2 80 16 66)(3 79 17 65)(4 78 18 64)(5 77 19 63)(6 76 20 62)(7 75 21 61)(8 74 22 60)(9 73 23 59)(10 72 24 58)(11 71 25 57)(12 70 26 84)(13 69 27 83)(14 68 28 82)(29 134 43 120)(30 133 44 119)(31 132 45 118)(32 131 46 117)(33 130 47 116)(34 129 48 115)(35 128 49 114)(36 127 50 113)(37 126 51 140)(38 125 52 139)(39 124 53 138)(40 123 54 137)(41 122 55 136)(42 121 56 135)(85 157 99 143)(86 156 100 142)(87 155 101 141)(88 154 102 168)(89 153 103 167)(90 152 104 166)(91 151 105 165)(92 150 106 164)(93 149 107 163)(94 148 108 162)(95 147 109 161)(96 146 110 160)(97 145 111 159)(98 144 112 158)(169 219 183 205)(170 218 184 204)(171 217 185 203)(172 216 186 202)(173 215 187 201)(174 214 188 200)(175 213 189 199)(176 212 190 198)(177 211 191 197)(178 210 192 224)(179 209 193 223)(180 208 194 222)(181 207 195 221)(182 206 196 220)
G:=sub<Sym(224)| (1,215)(2,216)(3,217)(4,218)(5,219)(6,220)(7,221)(8,222)(9,223)(10,224)(11,197)(12,198)(13,199)(14,200)(15,201)(16,202)(17,203)(18,204)(19,205)(20,206)(21,207)(22,208)(23,209)(24,210)(25,211)(26,212)(27,213)(28,214)(29,112)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(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)(57,191)(58,192)(59,193)(60,194)(61,195)(62,196)(63,169)(64,170)(65,171)(66,172)(67,173)(68,174)(69,175)(70,176)(71,177)(72,178)(73,179)(74,180)(75,181)(76,182)(77,183)(78,184)(79,185)(80,186)(81,187)(82,188)(83,189)(84,190)(113,165)(114,166)(115,167)(116,168)(117,141)(118,142)(119,143)(120,144)(121,145)(122,146)(123,147)(124,148)(125,149)(126,150)(127,151)(128,152)(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)(137,161)(138,162)(139,163)(140,164), (1,38)(2,202)(3,40)(4,204)(5,42)(6,206)(7,44)(8,208)(9,46)(10,210)(11,48)(12,212)(13,50)(14,214)(15,52)(16,216)(17,54)(18,218)(19,56)(20,220)(21,30)(22,222)(23,32)(24,224)(25,34)(26,198)(27,36)(28,200)(29,98)(31,100)(33,102)(35,104)(37,106)(39,108)(41,110)(43,112)(45,86)(47,88)(49,90)(51,92)(53,94)(55,96)(57,129)(58,178)(59,131)(60,180)(61,133)(62,182)(63,135)(64,184)(65,137)(66,186)(67,139)(68,188)(69,113)(70,190)(71,115)(72,192)(73,117)(74,194)(75,119)(76,196)(77,121)(78,170)(79,123)(80,172)(81,125)(82,174)(83,127)(84,176)(85,207)(87,209)(89,211)(91,213)(93,215)(95,217)(97,219)(99,221)(101,223)(103,197)(105,199)(107,201)(109,203)(111,205)(114,152)(116,154)(118,156)(120,158)(122,160)(124,162)(126,164)(128,166)(130,168)(132,142)(134,144)(136,146)(138,148)(140,150)(141,179)(143,181)(145,183)(147,185)(149,187)(151,189)(153,191)(155,193)(157,195)(159,169)(161,171)(163,173)(165,175)(167,177), (1,107)(2,108)(3,109)(4,110)(5,111)(6,112)(7,85)(8,86)(9,87)(10,88)(11,89)(12,90)(13,91)(14,92)(15,93)(16,94)(17,95)(18,96)(19,97)(20,98)(21,99)(22,100)(23,101)(24,102)(25,103)(26,104)(27,105)(28,106)(29,220)(30,221)(31,222)(32,223)(33,224)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,206)(44,207)(45,208)(46,209)(47,210)(48,211)(49,212)(50,213)(51,214)(52,215)(53,216)(54,217)(55,218)(56,219)(57,167)(58,168)(59,141)(60,142)(61,143)(62,144)(63,145)(64,146)(65,147)(66,148)(67,149)(68,150)(69,151)(70,152)(71,153)(72,154)(73,155)(74,156)(75,157)(76,158)(77,159)(78,160)(79,161)(80,162)(81,163)(82,164)(83,165)(84,166)(113,189)(114,190)(115,191)(116,192)(117,193)(118,194)(119,195)(120,196)(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)(136,184)(137,185)(138,186)(139,187)(140,188), (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), (1,81,15,67)(2,80,16,66)(3,79,17,65)(4,78,18,64)(5,77,19,63)(6,76,20,62)(7,75,21,61)(8,74,22,60)(9,73,23,59)(10,72,24,58)(11,71,25,57)(12,70,26,84)(13,69,27,83)(14,68,28,82)(29,134,43,120)(30,133,44,119)(31,132,45,118)(32,131,46,117)(33,130,47,116)(34,129,48,115)(35,128,49,114)(36,127,50,113)(37,126,51,140)(38,125,52,139)(39,124,53,138)(40,123,54,137)(41,122,55,136)(42,121,56,135)(85,157,99,143)(86,156,100,142)(87,155,101,141)(88,154,102,168)(89,153,103,167)(90,152,104,166)(91,151,105,165)(92,150,106,164)(93,149,107,163)(94,148,108,162)(95,147,109,161)(96,146,110,160)(97,145,111,159)(98,144,112,158)(169,219,183,205)(170,218,184,204)(171,217,185,203)(172,216,186,202)(173,215,187,201)(174,214,188,200)(175,213,189,199)(176,212,190,198)(177,211,191,197)(178,210,192,224)(179,209,193,223)(180,208,194,222)(181,207,195,221)(182,206,196,220)>;
G:=Group( (1,215)(2,216)(3,217)(4,218)(5,219)(6,220)(7,221)(8,222)(9,223)(10,224)(11,197)(12,198)(13,199)(14,200)(15,201)(16,202)(17,203)(18,204)(19,205)(20,206)(21,207)(22,208)(23,209)(24,210)(25,211)(26,212)(27,213)(28,214)(29,112)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(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)(57,191)(58,192)(59,193)(60,194)(61,195)(62,196)(63,169)(64,170)(65,171)(66,172)(67,173)(68,174)(69,175)(70,176)(71,177)(72,178)(73,179)(74,180)(75,181)(76,182)(77,183)(78,184)(79,185)(80,186)(81,187)(82,188)(83,189)(84,190)(113,165)(114,166)(115,167)(116,168)(117,141)(118,142)(119,143)(120,144)(121,145)(122,146)(123,147)(124,148)(125,149)(126,150)(127,151)(128,152)(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)(137,161)(138,162)(139,163)(140,164), (1,38)(2,202)(3,40)(4,204)(5,42)(6,206)(7,44)(8,208)(9,46)(10,210)(11,48)(12,212)(13,50)(14,214)(15,52)(16,216)(17,54)(18,218)(19,56)(20,220)(21,30)(22,222)(23,32)(24,224)(25,34)(26,198)(27,36)(28,200)(29,98)(31,100)(33,102)(35,104)(37,106)(39,108)(41,110)(43,112)(45,86)(47,88)(49,90)(51,92)(53,94)(55,96)(57,129)(58,178)(59,131)(60,180)(61,133)(62,182)(63,135)(64,184)(65,137)(66,186)(67,139)(68,188)(69,113)(70,190)(71,115)(72,192)(73,117)(74,194)(75,119)(76,196)(77,121)(78,170)(79,123)(80,172)(81,125)(82,174)(83,127)(84,176)(85,207)(87,209)(89,211)(91,213)(93,215)(95,217)(97,219)(99,221)(101,223)(103,197)(105,199)(107,201)(109,203)(111,205)(114,152)(116,154)(118,156)(120,158)(122,160)(124,162)(126,164)(128,166)(130,168)(132,142)(134,144)(136,146)(138,148)(140,150)(141,179)(143,181)(145,183)(147,185)(149,187)(151,189)(153,191)(155,193)(157,195)(159,169)(161,171)(163,173)(165,175)(167,177), (1,107)(2,108)(3,109)(4,110)(5,111)(6,112)(7,85)(8,86)(9,87)(10,88)(11,89)(12,90)(13,91)(14,92)(15,93)(16,94)(17,95)(18,96)(19,97)(20,98)(21,99)(22,100)(23,101)(24,102)(25,103)(26,104)(27,105)(28,106)(29,220)(30,221)(31,222)(32,223)(33,224)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,206)(44,207)(45,208)(46,209)(47,210)(48,211)(49,212)(50,213)(51,214)(52,215)(53,216)(54,217)(55,218)(56,219)(57,167)(58,168)(59,141)(60,142)(61,143)(62,144)(63,145)(64,146)(65,147)(66,148)(67,149)(68,150)(69,151)(70,152)(71,153)(72,154)(73,155)(74,156)(75,157)(76,158)(77,159)(78,160)(79,161)(80,162)(81,163)(82,164)(83,165)(84,166)(113,189)(114,190)(115,191)(116,192)(117,193)(118,194)(119,195)(120,196)(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)(136,184)(137,185)(138,186)(139,187)(140,188), (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), (1,81,15,67)(2,80,16,66)(3,79,17,65)(4,78,18,64)(5,77,19,63)(6,76,20,62)(7,75,21,61)(8,74,22,60)(9,73,23,59)(10,72,24,58)(11,71,25,57)(12,70,26,84)(13,69,27,83)(14,68,28,82)(29,134,43,120)(30,133,44,119)(31,132,45,118)(32,131,46,117)(33,130,47,116)(34,129,48,115)(35,128,49,114)(36,127,50,113)(37,126,51,140)(38,125,52,139)(39,124,53,138)(40,123,54,137)(41,122,55,136)(42,121,56,135)(85,157,99,143)(86,156,100,142)(87,155,101,141)(88,154,102,168)(89,153,103,167)(90,152,104,166)(91,151,105,165)(92,150,106,164)(93,149,107,163)(94,148,108,162)(95,147,109,161)(96,146,110,160)(97,145,111,159)(98,144,112,158)(169,219,183,205)(170,218,184,204)(171,217,185,203)(172,216,186,202)(173,215,187,201)(174,214,188,200)(175,213,189,199)(176,212,190,198)(177,211,191,197)(178,210,192,224)(179,209,193,223)(180,208,194,222)(181,207,195,221)(182,206,196,220) );
G=PermutationGroup([[(1,215),(2,216),(3,217),(4,218),(5,219),(6,220),(7,221),(8,222),(9,223),(10,224),(11,197),(12,198),(13,199),(14,200),(15,201),(16,202),(17,203),(18,204),(19,205),(20,206),(21,207),(22,208),(23,209),(24,210),(25,211),(26,212),(27,213),(28,214),(29,112),(30,85),(31,86),(32,87),(33,88),(34,89),(35,90),(36,91),(37,92),(38,93),(39,94),(40,95),(41,96),(42,97),(43,98),(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),(57,191),(58,192),(59,193),(60,194),(61,195),(62,196),(63,169),(64,170),(65,171),(66,172),(67,173),(68,174),(69,175),(70,176),(71,177),(72,178),(73,179),(74,180),(75,181),(76,182),(77,183),(78,184),(79,185),(80,186),(81,187),(82,188),(83,189),(84,190),(113,165),(114,166),(115,167),(116,168),(117,141),(118,142),(119,143),(120,144),(121,145),(122,146),(123,147),(124,148),(125,149),(126,150),(127,151),(128,152),(129,153),(130,154),(131,155),(132,156),(133,157),(134,158),(135,159),(136,160),(137,161),(138,162),(139,163),(140,164)], [(1,38),(2,202),(3,40),(4,204),(5,42),(6,206),(7,44),(8,208),(9,46),(10,210),(11,48),(12,212),(13,50),(14,214),(15,52),(16,216),(17,54),(18,218),(19,56),(20,220),(21,30),(22,222),(23,32),(24,224),(25,34),(26,198),(27,36),(28,200),(29,98),(31,100),(33,102),(35,104),(37,106),(39,108),(41,110),(43,112),(45,86),(47,88),(49,90),(51,92),(53,94),(55,96),(57,129),(58,178),(59,131),(60,180),(61,133),(62,182),(63,135),(64,184),(65,137),(66,186),(67,139),(68,188),(69,113),(70,190),(71,115),(72,192),(73,117),(74,194),(75,119),(76,196),(77,121),(78,170),(79,123),(80,172),(81,125),(82,174),(83,127),(84,176),(85,207),(87,209),(89,211),(91,213),(93,215),(95,217),(97,219),(99,221),(101,223),(103,197),(105,199),(107,201),(109,203),(111,205),(114,152),(116,154),(118,156),(120,158),(122,160),(124,162),(126,164),(128,166),(130,168),(132,142),(134,144),(136,146),(138,148),(140,150),(141,179),(143,181),(145,183),(147,185),(149,187),(151,189),(153,191),(155,193),(157,195),(159,169),(161,171),(163,173),(165,175),(167,177)], [(1,107),(2,108),(3,109),(4,110),(5,111),(6,112),(7,85),(8,86),(9,87),(10,88),(11,89),(12,90),(13,91),(14,92),(15,93),(16,94),(17,95),(18,96),(19,97),(20,98),(21,99),(22,100),(23,101),(24,102),(25,103),(26,104),(27,105),(28,106),(29,220),(30,221),(31,222),(32,223),(33,224),(34,197),(35,198),(36,199),(37,200),(38,201),(39,202),(40,203),(41,204),(42,205),(43,206),(44,207),(45,208),(46,209),(47,210),(48,211),(49,212),(50,213),(51,214),(52,215),(53,216),(54,217),(55,218),(56,219),(57,167),(58,168),(59,141),(60,142),(61,143),(62,144),(63,145),(64,146),(65,147),(66,148),(67,149),(68,150),(69,151),(70,152),(71,153),(72,154),(73,155),(74,156),(75,157),(76,158),(77,159),(78,160),(79,161),(80,162),(81,163),(82,164),(83,165),(84,166),(113,189),(114,190),(115,191),(116,192),(117,193),(118,194),(119,195),(120,196),(121,169),(122,170),(123,171),(124,172),(125,173),(126,174),(127,175),(128,176),(129,177),(130,178),(131,179),(132,180),(133,181),(134,182),(135,183),(136,184),(137,185),(138,186),(139,187),(140,188)], [(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)], [(1,81,15,67),(2,80,16,66),(3,79,17,65),(4,78,18,64),(5,77,19,63),(6,76,20,62),(7,75,21,61),(8,74,22,60),(9,73,23,59),(10,72,24,58),(11,71,25,57),(12,70,26,84),(13,69,27,83),(14,68,28,82),(29,134,43,120),(30,133,44,119),(31,132,45,118),(32,131,46,117),(33,130,47,116),(34,129,48,115),(35,128,49,114),(36,127,50,113),(37,126,51,140),(38,125,52,139),(39,124,53,138),(40,123,54,137),(41,122,55,136),(42,121,56,135),(85,157,99,143),(86,156,100,142),(87,155,101,141),(88,154,102,168),(89,153,103,167),(90,152,104,166),(91,151,105,165),(92,150,106,164),(93,149,107,163),(94,148,108,162),(95,147,109,161),(96,146,110,160),(97,145,111,159),(98,144,112,158),(169,219,183,205),(170,218,184,204),(171,217,185,203),(172,216,186,202),(173,215,187,201),(174,214,188,200),(175,213,189,199),(176,212,190,198),(177,211,191,197),(178,210,192,224),(179,209,193,223),(180,208,194,222),(181,207,195,221),(182,206,196,220)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 14V | ··· | 14AG | 28A | ··· | 28X |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | Q8 | D7 | C4○D4 | D14 | D14 | D14 | Dic14 | D4×D7 | D4⋊2D7 |
| kernel | C2×C22⋊Dic14 | C22⋊Dic14 | C2×Dic7⋊C4 | C2×C4⋊Dic7 | C2×C23.D7 | C14×C22⋊C4 | C22×Dic14 | C23×Dic7 | C2×Dic7 | C22×C14 | C2×C22⋊C4 | C2×C14 | C22⋊C4 | C22×C4 | C24 | C23 | C22 | C22 |
| # reps | 1 | 8 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 3 | 4 | 12 | 6 | 3 | 24 | 6 | 6 |
Matrix representation of C2×C22⋊Dic14 ►in GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 17 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 4 | 21 | 0 | 0 |
| 0 | 8 | 6 | 0 | 0 |
| 0 | 0 | 0 | 1 | 24 |
| 0 | 0 | 0 | 12 | 28 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 3 | 25 | 0 | 0 |
| 0 | 17 | 26 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 1 | 12 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,17,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[28,0,0,0,0,0,4,8,0,0,0,21,6,0,0,0,0,0,1,12,0,0,0,24,28],[1,0,0,0,0,0,3,17,0,0,0,25,26,0,0,0,0,0,17,1,0,0,0,0,12] >;
C2×C22⋊Dic14 in GAP, Magma, Sage, TeX
C_2\times C_2^2\rtimes {\rm Dic}_{14} % in TeX
G:=Group("C2xC2^2:Dic14"); // GroupNames label
G:=SmallGroup(448,934);
// by ID
G=gap.SmallGroup(448,934);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,675,297,80,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^28=1,e^2=d^14,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,d*b*d^-1=b*c=c*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations