direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×SD16⋊3D7, C28.8C24, SD16⋊12D14, C56.44C23, D28.4C23, Dic14.4C23, C4.45(D4×D7), C14⋊3(C4○D8), (C4×D7).29D4, C28.83(C2×D4), C7⋊C8.21C23, C4.8(C23×D7), D4⋊D7⋊11C22, (C2×SD16)⋊16D7, D14.10(C2×D4), (C2×C8).265D14, (C8×D7)⋊18C22, D4.6(C22×D7), (C7×D4).6C23, C7⋊Q16⋊7C22, C8.41(C22×D7), (C14×SD16)⋊11C2, (C2×D4).184D14, (C7×Q8).2C23, Q8.2(C22×D7), D4⋊2D7⋊7C22, C56⋊C2⋊18C22, (C2×Q8).151D14, Dic7.69(C2×D4), Q8⋊2D7⋊6C22, (C4×D7).26C23, (C22×D7).62D4, C22.141(D4×D7), (C2×C28).525C23, (C2×C56).166C22, (C2×Dic7).216D4, (C7×SD16)⋊13C22, C14.109(C22×D4), (D4×C14).166C22, (C2×D28).178C22, (Q8×C14).148C22, (C2×Dic14).197C22, C7⋊3(C2×C4○D8), (D7×C2×C8)⋊10C2, C2.82(C2×D4×D7), (C2×D4⋊D7)⋊28C2, (C2×C56⋊C2)⋊32C2, (C2×C7⋊Q16)⋊26C2, (C2×D4⋊2D7)⋊25C2, (C2×Q8⋊2D7)⋊15C2, (C2×C14).398(C2×D4), (C2×C7⋊C8).284C22, (C2×C4×D7).258C22, (C2×C4).614(C22×D7), SmallGroup(448,1214)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×SD16⋊3D7
G = < a,b,c,d,e | a2=b8=c2=d7=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b3, bd=db, be=eb, cd=dc, ece=b4c, ede=d-1 >
Subgroups: 1284 in 266 conjugacy classes, 103 normal (33 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C8, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, D7, C14, C14, C14, C2×C8, C2×C8, D8, SD16, SD16, Q16, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C22×C8, C2×D8, C2×SD16, C2×SD16, C2×Q16, C4○D8, C2×C4○D4, C7⋊C8, C56, Dic14, Dic14, C4×D7, C4×D7, D28, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×D4, C7×Q8, C7×Q8, C22×D7, C22×D7, C22×C14, C2×C4○D8, C8×D7, C56⋊C2, C2×C7⋊C8, D4⋊D7, C7⋊Q16, C2×C56, C7×SD16, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, D4⋊2D7, D4⋊2D7, Q8⋊2D7, Q8⋊2D7, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, D7×C2×C8, C2×C56⋊C2, SD16⋊3D7, C2×D4⋊D7, C2×C7⋊Q16, C14×SD16, C2×D4⋊2D7, C2×Q8⋊2D7, C2×SD16⋊3D7
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C4○D8, C22×D4, C22×D7, C2×C4○D8, D4×D7, C23×D7, SD16⋊3D7, C2×D4×D7, C2×SD16⋊3D7
►On 224 points
Generators in S224
(1 196)(2 197)(3 198)(4 199)(5 200)(6 193)(7 194)(8 195)(9 159)(10 160)(11 153)(12 154)(13 155)(14 156)(15 157)(16 158)(17 181)(18 182)(19 183)(20 184)(21 177)(22 178)(23 179)(24 180)(25 221)(26 222)(27 223)(28 224)(29 217)(30 218)(31 219)(32 220)(33 121)(34 122)(35 123)(36 124)(37 125)(38 126)(39 127)(40 128)(41 207)(42 208)(43 201)(44 202)(45 203)(46 204)(47 205)(48 206)(49 130)(50 131)(51 132)(52 133)(53 134)(54 135)(55 136)(56 129)(57 117)(58 118)(59 119)(60 120)(61 113)(62 114)(63 115)(64 116)(65 209)(66 210)(67 211)(68 212)(69 213)(70 214)(71 215)(72 216)(73 141)(74 142)(75 143)(76 144)(77 137)(78 138)(79 139)(80 140)(81 175)(82 176)(83 169)(84 170)(85 171)(86 172)(87 173)(88 174)(89 147)(90 148)(91 149)(92 150)(93 151)(94 152)(95 145)(96 146)(97 162)(98 163)(99 164)(100 165)(101 166)(102 167)(103 168)(104 161)(105 191)(106 192)(107 185)(108 186)(109 187)(110 188)(111 189)(112 190)
(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)
(1 218)(2 221)(3 224)(4 219)(5 222)(6 217)(7 220)(8 223)(9 41)(10 44)(11 47)(12 42)(13 45)(14 48)(15 43)(16 46)(17 65)(18 68)(19 71)(20 66)(21 69)(22 72)(23 67)(24 70)(25 197)(26 200)(27 195)(28 198)(29 193)(30 196)(31 199)(32 194)(33 91)(34 94)(35 89)(36 92)(37 95)(38 90)(39 93)(40 96)(49 104)(50 99)(51 102)(52 97)(53 100)(54 103)(55 98)(56 101)(57 85)(58 88)(59 83)(60 86)(61 81)(62 84)(63 87)(64 82)(73 107)(74 110)(75 105)(76 108)(77 111)(78 106)(79 109)(80 112)(113 175)(114 170)(115 173)(116 176)(117 171)(118 174)(119 169)(120 172)(121 149)(122 152)(123 147)(124 150)(125 145)(126 148)(127 151)(128 146)(129 166)(130 161)(131 164)(132 167)(133 162)(134 165)(135 168)(136 163)(137 189)(138 192)(139 187)(140 190)(141 185)(142 188)(143 191)(144 186)(153 205)(154 208)(155 203)(156 206)(157 201)(158 204)(159 207)(160 202)(177 213)(178 216)(179 211)(180 214)(181 209)(182 212)(183 215)(184 210)
(1 54 36 172 183 160 191)(2 55 37 173 184 153 192)(3 56 38 174 177 154 185)(4 49 39 175 178 155 186)(5 50 40 176 179 156 187)(6 51 33 169 180 157 188)(7 52 34 170 181 158 189)(8 53 35 171 182 159 190)(9 112 195 134 123 85 18)(10 105 196 135 124 86 19)(11 106 197 136 125 87 20)(12 107 198 129 126 88 21)(13 108 199 130 127 81 22)(14 109 200 131 128 82 23)(15 110 193 132 121 83 24)(16 111 194 133 122 84 17)(25 163 145 63 66 47 78)(26 164 146 64 67 48 79)(27 165 147 57 68 41 80)(28 166 148 58 69 42 73)(29 167 149 59 70 43 74)(30 168 150 60 71 44 75)(31 161 151 61 72 45 76)(32 162 152 62 65 46 77)(89 117 212 207 140 223 100)(90 118 213 208 141 224 101)(91 119 214 201 142 217 102)(92 120 215 202 143 218 103)(93 113 216 203 144 219 104)(94 114 209 204 137 220 97)(95 115 210 205 138 221 98)(96 116 211 206 139 222 99)
(1 191)(2 192)(3 185)(4 186)(5 187)(6 188)(7 189)(8 190)(9 134)(10 135)(11 136)(12 129)(13 130)(14 131)(15 132)(16 133)(17 122)(18 123)(19 124)(20 125)(21 126)(22 127)(23 128)(24 121)(25 74)(26 75)(27 76)(28 77)(29 78)(30 79)(31 80)(32 73)(33 180)(34 181)(35 182)(36 183)(37 184)(38 177)(39 178)(40 179)(41 161)(42 162)(43 163)(44 164)(45 165)(46 166)(47 167)(48 168)(49 155)(50 156)(51 157)(52 158)(53 159)(54 160)(55 153)(56 154)(57 61)(58 62)(59 63)(60 64)(65 148)(66 149)(67 150)(68 151)(69 152)(70 145)(71 146)(72 147)(89 216)(90 209)(91 210)(92 211)(93 212)(94 213)(95 214)(96 215)(97 208)(98 201)(99 202)(100 203)(101 204)(102 205)(103 206)(104 207)(105 196)(106 197)(107 198)(108 199)(109 200)(110 193)(111 194)(112 195)(113 117)(114 118)(115 119)(116 120)(137 224)(138 217)(139 218)(140 219)(141 220)(142 221)(143 222)(144 223)
G:=sub<Sym(224)| (1,196)(2,197)(3,198)(4,199)(5,200)(6,193)(7,194)(8,195)(9,159)(10,160)(11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,181)(18,182)(19,183)(20,184)(21,177)(22,178)(23,179)(24,180)(25,221)(26,222)(27,223)(28,224)(29,217)(30,218)(31,219)(32,220)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,207)(42,208)(43,201)(44,202)(45,203)(46,204)(47,205)(48,206)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,129)(57,117)(58,118)(59,119)(60,120)(61,113)(62,114)(63,115)(64,116)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,141)(74,142)(75,143)(76,144)(77,137)(78,138)(79,139)(80,140)(81,175)(82,176)(83,169)(84,170)(85,171)(86,172)(87,173)(88,174)(89,147)(90,148)(91,149)(92,150)(93,151)(94,152)(95,145)(96,146)(97,162)(98,163)(99,164)(100,165)(101,166)(102,167)(103,168)(104,161)(105,191)(106,192)(107,185)(108,186)(109,187)(110,188)(111,189)(112,190), (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), (1,218)(2,221)(3,224)(4,219)(5,222)(6,217)(7,220)(8,223)(9,41)(10,44)(11,47)(12,42)(13,45)(14,48)(15,43)(16,46)(17,65)(18,68)(19,71)(20,66)(21,69)(22,72)(23,67)(24,70)(25,197)(26,200)(27,195)(28,198)(29,193)(30,196)(31,199)(32,194)(33,91)(34,94)(35,89)(36,92)(37,95)(38,90)(39,93)(40,96)(49,104)(50,99)(51,102)(52,97)(53,100)(54,103)(55,98)(56,101)(57,85)(58,88)(59,83)(60,86)(61,81)(62,84)(63,87)(64,82)(73,107)(74,110)(75,105)(76,108)(77,111)(78,106)(79,109)(80,112)(113,175)(114,170)(115,173)(116,176)(117,171)(118,174)(119,169)(120,172)(121,149)(122,152)(123,147)(124,150)(125,145)(126,148)(127,151)(128,146)(129,166)(130,161)(131,164)(132,167)(133,162)(134,165)(135,168)(136,163)(137,189)(138,192)(139,187)(140,190)(141,185)(142,188)(143,191)(144,186)(153,205)(154,208)(155,203)(156,206)(157,201)(158,204)(159,207)(160,202)(177,213)(178,216)(179,211)(180,214)(181,209)(182,212)(183,215)(184,210), (1,54,36,172,183,160,191)(2,55,37,173,184,153,192)(3,56,38,174,177,154,185)(4,49,39,175,178,155,186)(5,50,40,176,179,156,187)(6,51,33,169,180,157,188)(7,52,34,170,181,158,189)(8,53,35,171,182,159,190)(9,112,195,134,123,85,18)(10,105,196,135,124,86,19)(11,106,197,136,125,87,20)(12,107,198,129,126,88,21)(13,108,199,130,127,81,22)(14,109,200,131,128,82,23)(15,110,193,132,121,83,24)(16,111,194,133,122,84,17)(25,163,145,63,66,47,78)(26,164,146,64,67,48,79)(27,165,147,57,68,41,80)(28,166,148,58,69,42,73)(29,167,149,59,70,43,74)(30,168,150,60,71,44,75)(31,161,151,61,72,45,76)(32,162,152,62,65,46,77)(89,117,212,207,140,223,100)(90,118,213,208,141,224,101)(91,119,214,201,142,217,102)(92,120,215,202,143,218,103)(93,113,216,203,144,219,104)(94,114,209,204,137,220,97)(95,115,210,205,138,221,98)(96,116,211,206,139,222,99), (1,191)(2,192)(3,185)(4,186)(5,187)(6,188)(7,189)(8,190)(9,134)(10,135)(11,136)(12,129)(13,130)(14,131)(15,132)(16,133)(17,122)(18,123)(19,124)(20,125)(21,126)(22,127)(23,128)(24,121)(25,74)(26,75)(27,76)(28,77)(29,78)(30,79)(31,80)(32,73)(33,180)(34,181)(35,182)(36,183)(37,184)(38,177)(39,178)(40,179)(41,161)(42,162)(43,163)(44,164)(45,165)(46,166)(47,167)(48,168)(49,155)(50,156)(51,157)(52,158)(53,159)(54,160)(55,153)(56,154)(57,61)(58,62)(59,63)(60,64)(65,148)(66,149)(67,150)(68,151)(69,152)(70,145)(71,146)(72,147)(89,216)(90,209)(91,210)(92,211)(93,212)(94,213)(95,214)(96,215)(97,208)(98,201)(99,202)(100,203)(101,204)(102,205)(103,206)(104,207)(105,196)(106,197)(107,198)(108,199)(109,200)(110,193)(111,194)(112,195)(113,117)(114,118)(115,119)(116,120)(137,224)(138,217)(139,218)(140,219)(141,220)(142,221)(143,222)(144,223)>;
G:=Group( (1,196)(2,197)(3,198)(4,199)(5,200)(6,193)(7,194)(8,195)(9,159)(10,160)(11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,181)(18,182)(19,183)(20,184)(21,177)(22,178)(23,179)(24,180)(25,221)(26,222)(27,223)(28,224)(29,217)(30,218)(31,219)(32,220)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,207)(42,208)(43,201)(44,202)(45,203)(46,204)(47,205)(48,206)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,129)(57,117)(58,118)(59,119)(60,120)(61,113)(62,114)(63,115)(64,116)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,141)(74,142)(75,143)(76,144)(77,137)(78,138)(79,139)(80,140)(81,175)(82,176)(83,169)(84,170)(85,171)(86,172)(87,173)(88,174)(89,147)(90,148)(91,149)(92,150)(93,151)(94,152)(95,145)(96,146)(97,162)(98,163)(99,164)(100,165)(101,166)(102,167)(103,168)(104,161)(105,191)(106,192)(107,185)(108,186)(109,187)(110,188)(111,189)(112,190), (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), (1,218)(2,221)(3,224)(4,219)(5,222)(6,217)(7,220)(8,223)(9,41)(10,44)(11,47)(12,42)(13,45)(14,48)(15,43)(16,46)(17,65)(18,68)(19,71)(20,66)(21,69)(22,72)(23,67)(24,70)(25,197)(26,200)(27,195)(28,198)(29,193)(30,196)(31,199)(32,194)(33,91)(34,94)(35,89)(36,92)(37,95)(38,90)(39,93)(40,96)(49,104)(50,99)(51,102)(52,97)(53,100)(54,103)(55,98)(56,101)(57,85)(58,88)(59,83)(60,86)(61,81)(62,84)(63,87)(64,82)(73,107)(74,110)(75,105)(76,108)(77,111)(78,106)(79,109)(80,112)(113,175)(114,170)(115,173)(116,176)(117,171)(118,174)(119,169)(120,172)(121,149)(122,152)(123,147)(124,150)(125,145)(126,148)(127,151)(128,146)(129,166)(130,161)(131,164)(132,167)(133,162)(134,165)(135,168)(136,163)(137,189)(138,192)(139,187)(140,190)(141,185)(142,188)(143,191)(144,186)(153,205)(154,208)(155,203)(156,206)(157,201)(158,204)(159,207)(160,202)(177,213)(178,216)(179,211)(180,214)(181,209)(182,212)(183,215)(184,210), (1,54,36,172,183,160,191)(2,55,37,173,184,153,192)(3,56,38,174,177,154,185)(4,49,39,175,178,155,186)(5,50,40,176,179,156,187)(6,51,33,169,180,157,188)(7,52,34,170,181,158,189)(8,53,35,171,182,159,190)(9,112,195,134,123,85,18)(10,105,196,135,124,86,19)(11,106,197,136,125,87,20)(12,107,198,129,126,88,21)(13,108,199,130,127,81,22)(14,109,200,131,128,82,23)(15,110,193,132,121,83,24)(16,111,194,133,122,84,17)(25,163,145,63,66,47,78)(26,164,146,64,67,48,79)(27,165,147,57,68,41,80)(28,166,148,58,69,42,73)(29,167,149,59,70,43,74)(30,168,150,60,71,44,75)(31,161,151,61,72,45,76)(32,162,152,62,65,46,77)(89,117,212,207,140,223,100)(90,118,213,208,141,224,101)(91,119,214,201,142,217,102)(92,120,215,202,143,218,103)(93,113,216,203,144,219,104)(94,114,209,204,137,220,97)(95,115,210,205,138,221,98)(96,116,211,206,139,222,99), (1,191)(2,192)(3,185)(4,186)(5,187)(6,188)(7,189)(8,190)(9,134)(10,135)(11,136)(12,129)(13,130)(14,131)(15,132)(16,133)(17,122)(18,123)(19,124)(20,125)(21,126)(22,127)(23,128)(24,121)(25,74)(26,75)(27,76)(28,77)(29,78)(30,79)(31,80)(32,73)(33,180)(34,181)(35,182)(36,183)(37,184)(38,177)(39,178)(40,179)(41,161)(42,162)(43,163)(44,164)(45,165)(46,166)(47,167)(48,168)(49,155)(50,156)(51,157)(52,158)(53,159)(54,160)(55,153)(56,154)(57,61)(58,62)(59,63)(60,64)(65,148)(66,149)(67,150)(68,151)(69,152)(70,145)(71,146)(72,147)(89,216)(90,209)(91,210)(92,211)(93,212)(94,213)(95,214)(96,215)(97,208)(98,201)(99,202)(100,203)(101,204)(102,205)(103,206)(104,207)(105,196)(106,197)(107,198)(108,199)(109,200)(110,193)(111,194)(112,195)(113,117)(114,118)(115,119)(116,120)(137,224)(138,217)(139,218)(140,219)(141,220)(142,221)(143,222)(144,223) );
G=PermutationGroup([[(1,196),(2,197),(3,198),(4,199),(5,200),(6,193),(7,194),(8,195),(9,159),(10,160),(11,153),(12,154),(13,155),(14,156),(15,157),(16,158),(17,181),(18,182),(19,183),(20,184),(21,177),(22,178),(23,179),(24,180),(25,221),(26,222),(27,223),(28,224),(29,217),(30,218),(31,219),(32,220),(33,121),(34,122),(35,123),(36,124),(37,125),(38,126),(39,127),(40,128),(41,207),(42,208),(43,201),(44,202),(45,203),(46,204),(47,205),(48,206),(49,130),(50,131),(51,132),(52,133),(53,134),(54,135),(55,136),(56,129),(57,117),(58,118),(59,119),(60,120),(61,113),(62,114),(63,115),(64,116),(65,209),(66,210),(67,211),(68,212),(69,213),(70,214),(71,215),(72,216),(73,141),(74,142),(75,143),(76,144),(77,137),(78,138),(79,139),(80,140),(81,175),(82,176),(83,169),(84,170),(85,171),(86,172),(87,173),(88,174),(89,147),(90,148),(91,149),(92,150),(93,151),(94,152),(95,145),(96,146),(97,162),(98,163),(99,164),(100,165),(101,166),(102,167),(103,168),(104,161),(105,191),(106,192),(107,185),(108,186),(109,187),(110,188),(111,189),(112,190)], [(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)], [(1,218),(2,221),(3,224),(4,219),(5,222),(6,217),(7,220),(8,223),(9,41),(10,44),(11,47),(12,42),(13,45),(14,48),(15,43),(16,46),(17,65),(18,68),(19,71),(20,66),(21,69),(22,72),(23,67),(24,70),(25,197),(26,200),(27,195),(28,198),(29,193),(30,196),(31,199),(32,194),(33,91),(34,94),(35,89),(36,92),(37,95),(38,90),(39,93),(40,96),(49,104),(50,99),(51,102),(52,97),(53,100),(54,103),(55,98),(56,101),(57,85),(58,88),(59,83),(60,86),(61,81),(62,84),(63,87),(64,82),(73,107),(74,110),(75,105),(76,108),(77,111),(78,106),(79,109),(80,112),(113,175),(114,170),(115,173),(116,176),(117,171),(118,174),(119,169),(120,172),(121,149),(122,152),(123,147),(124,150),(125,145),(126,148),(127,151),(128,146),(129,166),(130,161),(131,164),(132,167),(133,162),(134,165),(135,168),(136,163),(137,189),(138,192),(139,187),(140,190),(141,185),(142,188),(143,191),(144,186),(153,205),(154,208),(155,203),(156,206),(157,201),(158,204),(159,207),(160,202),(177,213),(178,216),(179,211),(180,214),(181,209),(182,212),(183,215),(184,210)], [(1,54,36,172,183,160,191),(2,55,37,173,184,153,192),(3,56,38,174,177,154,185),(4,49,39,175,178,155,186),(5,50,40,176,179,156,187),(6,51,33,169,180,157,188),(7,52,34,170,181,158,189),(8,53,35,171,182,159,190),(9,112,195,134,123,85,18),(10,105,196,135,124,86,19),(11,106,197,136,125,87,20),(12,107,198,129,126,88,21),(13,108,199,130,127,81,22),(14,109,200,131,128,82,23),(15,110,193,132,121,83,24),(16,111,194,133,122,84,17),(25,163,145,63,66,47,78),(26,164,146,64,67,48,79),(27,165,147,57,68,41,80),(28,166,148,58,69,42,73),(29,167,149,59,70,43,74),(30,168,150,60,71,44,75),(31,161,151,61,72,45,76),(32,162,152,62,65,46,77),(89,117,212,207,140,223,100),(90,118,213,208,141,224,101),(91,119,214,201,142,217,102),(92,120,215,202,143,218,103),(93,113,216,203,144,219,104),(94,114,209,204,137,220,97),(95,115,210,205,138,221,98),(96,116,211,206,139,222,99)], [(1,191),(2,192),(3,185),(4,186),(5,187),(6,188),(7,189),(8,190),(9,134),(10,135),(11,136),(12,129),(13,130),(14,131),(15,132),(16,133),(17,122),(18,123),(19,124),(20,125),(21,126),(22,127),(23,128),(24,121),(25,74),(26,75),(27,76),(28,77),(29,78),(30,79),(31,80),(32,73),(33,180),(34,181),(35,182),(36,183),(37,184),(38,177),(39,178),(40,179),(41,161),(42,162),(43,163),(44,164),(45,165),(46,166),(47,167),(48,168),(49,155),(50,156),(51,157),(52,158),(53,159),(54,160),(55,153),(56,154),(57,61),(58,62),(59,63),(60,64),(65,148),(66,149),(67,150),(68,151),(69,152),(70,145),(71,146),(72,147),(89,216),(90,209),(91,210),(92,211),(93,212),(94,213),(95,214),(96,215),(97,208),(98,201),(99,202),(100,203),(101,204),(102,205),(103,206),(104,207),(105,196),(106,197),(107,198),(108,199),(109,200),(110,193),(111,194),(112,195),(113,117),(114,118),(115,119),(116,120),(137,224),(138,217),(139,218),(140,219),(141,220),(142,221),(143,222),(144,223)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 14 | 14 | 28 | 28 | 2 | 2 | 4 | 4 | 7 | 7 | 7 | 7 | 28 | 28 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | D14 | D14 | D14 | D14 | C4○D8 | D4×D7 | D4×D7 | SD16⋊3D7 |
| kernel | C2×SD16⋊3D7 | D7×C2×C8 | C2×C56⋊C2 | SD16⋊3D7 | C2×D4⋊D7 | C2×C7⋊Q16 | C14×SD16 | C2×D4⋊2D7 | C2×Q8⋊2D7 | C4×D7 | C2×Dic7 | C22×D7 | C2×SD16 | C2×C8 | SD16 | C2×D4 | C2×Q8 | C14 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 8 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 3 | 12 | 3 | 3 | 8 | 3 | 3 | 12 |
Matrix representation of C2×SD16⋊3D7 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 69 | 0 | 0 | 0 |
| 0 | 18 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 0 | 69 | 0 | 0 |
| 95 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 79 | 112 |
| 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 79 | 112 |
| 0 | 0 | 25 | 34 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,112,0,0,0,0,112],[69,0,0,0,0,18,0,0,0,0,112,0,0,0,0,112],[0,95,0,0,69,0,0,0,0,0,112,0,0,0,0,112],[1,0,0,0,0,1,0,0,0,0,79,1,0,0,112,0],[1,0,0,0,0,112,0,0,0,0,79,25,0,0,112,34] >;
C2×SD16⋊3D7 in GAP, Magma, Sage, TeX
C_2\times {\rm SD}_{16}\rtimes_3D_7 % in TeX
G:=Group("C2xSD16:3D7"); // GroupNames label
G:=SmallGroup(448,1214);
// by ID
G=gap.SmallGroup(448,1214);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,1123,185,136,438,235,102,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^8=c^2=d^7=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^3,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=b^4*c,e*d*e=d^-1>;
// generators/relations