direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×C23.46D4, C4.Q8⋊9C14, C22⋊C8⋊10C14, C4⋊D4.6C14, (C2×C28).337D4, D4⋊C4⋊12C14, C23.46(C7×D4), C2.12(C14×SD16), C14.92(C2×SD16), (C2×C14).36SD16, C28.318(C4○D4), C22.8(C7×SD16), (C2×C28).937C23, (C2×C56).305C22, (C22×C14).168D4, C22.102(D4×C14), C14.142(C8⋊C22), (D4×C14).196C22, (C22×C28).429C22, C14.96(C22.D4), (C2×C4⋊C4)⋊12C14, (C14×C4⋊C4)⋊39C2, (C7×C4.Q8)⋊24C2, C4.30(C7×C4○D4), (C2×C4).38(C7×D4), C4⋊C4.58(C2×C14), (C7×C22⋊C8)⋊27C2, (C2×C8).42(C2×C14), C2.17(C7×C8⋊C22), (C7×D4⋊C4)⋊36C2, (C2×D4).19(C2×C14), (C7×C4⋊D4).16C2, (C2×C14).658(C2×D4), (C7×C4⋊C4).381C22, (C22×C4).47(C2×C14), (C2×C4).112(C22×C14), C2.12(C7×C22.D4), SmallGroup(448,889)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C23.46D4
G = < a,b,c,d,e,f | a7=b2=c2=d2=f2=1, e4=d, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ebe-1=fbf=bc=cb, bd=db, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef=ce3 >
Subgroups: 226 in 114 conjugacy classes, 54 normal (30 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, C23, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×D4, C2×D4, C28, C28, C2×C14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, C4.Q8, C2×C4⋊C4, C4⋊D4, C56, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C23.46D4, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×C56, C22×C28, C22×C28, D4×C14, D4×C14, C7×C22⋊C8, C7×D4⋊C4, C7×C4.Q8, C14×C4⋊C4, C7×C4⋊D4, C7×C23.46D4
Quotients: C1, C2, C22, C7, D4, C23, C14, SD16, C2×D4, C4○D4, C2×C14, C22.D4, C2×SD16, C8⋊C22, C7×D4, C22×C14, C23.46D4, C7×SD16, D4×C14, C7×C4○D4, C7×C22.D4, C14×SD16, C7×C8⋊C22, C7×C23.46D4
►On 224 points
Generators in S224
(1 175 223 55 215 47 207)(2 176 224 56 216 48 208)(3 169 217 49 209 41 201)(4 170 218 50 210 42 202)(5 171 219 51 211 43 203)(6 172 220 52 212 44 204)(7 173 221 53 213 45 205)(8 174 222 54 214 46 206)(9 161 193 25 185 17 177)(10 162 194 26 186 18 178)(11 163 195 27 187 19 179)(12 164 196 28 188 20 180)(13 165 197 29 189 21 181)(14 166 198 30 190 22 182)(15 167 199 31 191 23 183)(16 168 200 32 192 24 184)(33 129 76 121 68 113 64)(34 130 77 122 69 114 57)(35 131 78 123 70 115 58)(36 132 79 124 71 116 59)(37 133 80 125 72 117 60)(38 134 73 126 65 118 61)(39 135 74 127 66 119 62)(40 136 75 128 67 120 63)(81 105 158 97 150 89 142)(82 106 159 98 151 90 143)(83 107 160 99 152 91 144)(84 108 153 100 145 92 137)(85 109 154 101 146 93 138)(86 110 155 102 147 94 139)(87 111 156 103 148 95 140)(88 112 157 104 149 96 141)
(2 120)(4 114)(6 116)(8 118)(10 141)(12 143)(14 137)(16 139)(18 149)(20 151)(22 145)(24 147)(26 157)(28 159)(30 153)(32 155)(34 218)(36 220)(38 222)(40 224)(42 122)(44 124)(46 126)(48 128)(50 130)(52 132)(54 134)(56 136)(57 170)(59 172)(61 174)(63 176)(65 206)(67 208)(69 202)(71 204)(73 214)(75 216)(77 210)(79 212)(82 164)(84 166)(86 168)(88 162)(90 180)(92 182)(94 184)(96 178)(98 188)(100 190)(102 192)(104 186)(106 196)(108 198)(110 200)(112 194)
(1 119)(2 120)(3 113)(4 114)(5 115)(6 116)(7 117)(8 118)(9 140)(10 141)(11 142)(12 143)(13 144)(14 137)(15 138)(16 139)(17 148)(18 149)(19 150)(20 151)(21 152)(22 145)(23 146)(24 147)(25 156)(26 157)(27 158)(28 159)(29 160)(30 153)(31 154)(32 155)(33 217)(34 218)(35 219)(36 220)(37 221)(38 222)(39 223)(40 224)(41 121)(42 122)(43 123)(44 124)(45 125)(46 126)(47 127)(48 128)(49 129)(50 130)(51 131)(52 132)(53 133)(54 134)(55 135)(56 136)(57 170)(58 171)(59 172)(60 173)(61 174)(62 175)(63 176)(64 169)(65 206)(66 207)(67 208)(68 201)(69 202)(70 203)(71 204)(72 205)(73 214)(74 215)(75 216)(76 209)(77 210)(78 211)(79 212)(80 213)(81 163)(82 164)(83 165)(84 166)(85 167)(86 168)(87 161)(88 162)(89 179)(90 180)(91 181)(92 182)(93 183)(94 184)(95 177)(96 178)(97 187)(98 188)(99 189)(100 190)(101 191)(102 192)(103 185)(104 186)(105 195)(106 196)(107 197)(108 198)(109 199)(110 200)(111 193)(112 194)
(1 5)(2 6)(3 7)(4 8)(9 13)(10 14)(11 15)(12 16)(17 21)(18 22)(19 23)(20 24)(25 29)(26 30)(27 31)(28 32)(33 37)(34 38)(35 39)(36 40)(41 45)(42 46)(43 47)(44 48)(49 53)(50 54)(51 55)(52 56)(57 61)(58 62)(59 63)(60 64)(65 69)(66 70)(67 71)(68 72)(73 77)(74 78)(75 79)(76 80)(81 85)(82 86)(83 87)(84 88)(89 93)(90 94)(91 95)(92 96)(97 101)(98 102)(99 103)(100 104)(105 109)(106 110)(107 111)(108 112)(113 117)(114 118)(115 119)(116 120)(121 125)(122 126)(123 127)(124 128)(129 133)(130 134)(131 135)(132 136)(137 141)(138 142)(139 143)(140 144)(145 149)(146 150)(147 151)(148 152)(153 157)(154 158)(155 159)(156 160)(161 165)(162 166)(163 167)(164 168)(169 173)(170 174)(171 175)(172 176)(177 181)(178 182)(179 183)(180 184)(185 189)(186 190)(187 191)(188 192)(193 197)(194 198)(195 199)(196 200)(201 205)(202 206)(203 207)(204 208)(209 213)(210 214)(211 215)(212 216)(217 221)(218 222)(219 223)(220 224)
(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)
(1 162)(2 83)(3 168)(4 81)(5 166)(6 87)(7 164)(8 85)(9 71)(10 207)(11 69)(12 205)(13 67)(14 203)(15 65)(16 201)(17 79)(18 215)(19 77)(20 213)(21 75)(22 211)(23 73)(24 209)(25 36)(26 223)(27 34)(28 221)(29 40)(30 219)(31 38)(32 217)(33 155)(35 153)(37 159)(39 157)(41 184)(42 89)(43 182)(44 95)(45 180)(46 93)(47 178)(48 91)(49 192)(50 97)(51 190)(52 103)(53 188)(54 101)(55 186)(56 99)(57 195)(58 108)(59 193)(60 106)(61 199)(62 112)(63 197)(64 110)(66 141)(68 139)(70 137)(72 143)(74 149)(76 147)(78 145)(80 151)(82 117)(84 115)(86 113)(88 119)(90 125)(92 123)(94 121)(96 127)(98 133)(100 131)(102 129)(104 135)(105 170)(107 176)(109 174)(111 172)(114 163)(116 161)(118 167)(120 165)(122 179)(124 177)(126 183)(128 181)(130 187)(132 185)(134 191)(136 189)(138 206)(140 204)(142 202)(144 208)(146 214)(148 212)(150 210)(152 216)(154 222)(156 220)(158 218)(160 224)(169 200)(171 198)(173 196)(175 194)
G:=sub<Sym(224)| (1,175,223,55,215,47,207)(2,176,224,56,216,48,208)(3,169,217,49,209,41,201)(4,170,218,50,210,42,202)(5,171,219,51,211,43,203)(6,172,220,52,212,44,204)(7,173,221,53,213,45,205)(8,174,222,54,214,46,206)(9,161,193,25,185,17,177)(10,162,194,26,186,18,178)(11,163,195,27,187,19,179)(12,164,196,28,188,20,180)(13,165,197,29,189,21,181)(14,166,198,30,190,22,182)(15,167,199,31,191,23,183)(16,168,200,32,192,24,184)(33,129,76,121,68,113,64)(34,130,77,122,69,114,57)(35,131,78,123,70,115,58)(36,132,79,124,71,116,59)(37,133,80,125,72,117,60)(38,134,73,126,65,118,61)(39,135,74,127,66,119,62)(40,136,75,128,67,120,63)(81,105,158,97,150,89,142)(82,106,159,98,151,90,143)(83,107,160,99,152,91,144)(84,108,153,100,145,92,137)(85,109,154,101,146,93,138)(86,110,155,102,147,94,139)(87,111,156,103,148,95,140)(88,112,157,104,149,96,141), (2,120)(4,114)(6,116)(8,118)(10,141)(12,143)(14,137)(16,139)(18,149)(20,151)(22,145)(24,147)(26,157)(28,159)(30,153)(32,155)(34,218)(36,220)(38,222)(40,224)(42,122)(44,124)(46,126)(48,128)(50,130)(52,132)(54,134)(56,136)(57,170)(59,172)(61,174)(63,176)(65,206)(67,208)(69,202)(71,204)(73,214)(75,216)(77,210)(79,212)(82,164)(84,166)(86,168)(88,162)(90,180)(92,182)(94,184)(96,178)(98,188)(100,190)(102,192)(104,186)(106,196)(108,198)(110,200)(112,194), (1,119)(2,120)(3,113)(4,114)(5,115)(6,116)(7,117)(8,118)(9,140)(10,141)(11,142)(12,143)(13,144)(14,137)(15,138)(16,139)(17,148)(18,149)(19,150)(20,151)(21,152)(22,145)(23,146)(24,147)(25,156)(26,157)(27,158)(28,159)(29,160)(30,153)(31,154)(32,155)(33,217)(34,218)(35,219)(36,220)(37,221)(38,222)(39,223)(40,224)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(51,131)(52,132)(53,133)(54,134)(55,135)(56,136)(57,170)(58,171)(59,172)(60,173)(61,174)(62,175)(63,176)(64,169)(65,206)(66,207)(67,208)(68,201)(69,202)(70,203)(71,204)(72,205)(73,214)(74,215)(75,216)(76,209)(77,210)(78,211)(79,212)(80,213)(81,163)(82,164)(83,165)(84,166)(85,167)(86,168)(87,161)(88,162)(89,179)(90,180)(91,181)(92,182)(93,183)(94,184)(95,177)(96,178)(97,187)(98,188)(99,189)(100,190)(101,191)(102,192)(103,185)(104,186)(105,195)(106,196)(107,197)(108,198)(109,199)(110,200)(111,193)(112,194), (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64)(65,69)(66,70)(67,71)(68,72)(73,77)(74,78)(75,79)(76,80)(81,85)(82,86)(83,87)(84,88)(89,93)(90,94)(91,95)(92,96)(97,101)(98,102)(99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224), (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), (1,162)(2,83)(3,168)(4,81)(5,166)(6,87)(7,164)(8,85)(9,71)(10,207)(11,69)(12,205)(13,67)(14,203)(15,65)(16,201)(17,79)(18,215)(19,77)(20,213)(21,75)(22,211)(23,73)(24,209)(25,36)(26,223)(27,34)(28,221)(29,40)(30,219)(31,38)(32,217)(33,155)(35,153)(37,159)(39,157)(41,184)(42,89)(43,182)(44,95)(45,180)(46,93)(47,178)(48,91)(49,192)(50,97)(51,190)(52,103)(53,188)(54,101)(55,186)(56,99)(57,195)(58,108)(59,193)(60,106)(61,199)(62,112)(63,197)(64,110)(66,141)(68,139)(70,137)(72,143)(74,149)(76,147)(78,145)(80,151)(82,117)(84,115)(86,113)(88,119)(90,125)(92,123)(94,121)(96,127)(98,133)(100,131)(102,129)(104,135)(105,170)(107,176)(109,174)(111,172)(114,163)(116,161)(118,167)(120,165)(122,179)(124,177)(126,183)(128,181)(130,187)(132,185)(134,191)(136,189)(138,206)(140,204)(142,202)(144,208)(146,214)(148,212)(150,210)(152,216)(154,222)(156,220)(158,218)(160,224)(169,200)(171,198)(173,196)(175,194)>;
G:=Group( (1,175,223,55,215,47,207)(2,176,224,56,216,48,208)(3,169,217,49,209,41,201)(4,170,218,50,210,42,202)(5,171,219,51,211,43,203)(6,172,220,52,212,44,204)(7,173,221,53,213,45,205)(8,174,222,54,214,46,206)(9,161,193,25,185,17,177)(10,162,194,26,186,18,178)(11,163,195,27,187,19,179)(12,164,196,28,188,20,180)(13,165,197,29,189,21,181)(14,166,198,30,190,22,182)(15,167,199,31,191,23,183)(16,168,200,32,192,24,184)(33,129,76,121,68,113,64)(34,130,77,122,69,114,57)(35,131,78,123,70,115,58)(36,132,79,124,71,116,59)(37,133,80,125,72,117,60)(38,134,73,126,65,118,61)(39,135,74,127,66,119,62)(40,136,75,128,67,120,63)(81,105,158,97,150,89,142)(82,106,159,98,151,90,143)(83,107,160,99,152,91,144)(84,108,153,100,145,92,137)(85,109,154,101,146,93,138)(86,110,155,102,147,94,139)(87,111,156,103,148,95,140)(88,112,157,104,149,96,141), (2,120)(4,114)(6,116)(8,118)(10,141)(12,143)(14,137)(16,139)(18,149)(20,151)(22,145)(24,147)(26,157)(28,159)(30,153)(32,155)(34,218)(36,220)(38,222)(40,224)(42,122)(44,124)(46,126)(48,128)(50,130)(52,132)(54,134)(56,136)(57,170)(59,172)(61,174)(63,176)(65,206)(67,208)(69,202)(71,204)(73,214)(75,216)(77,210)(79,212)(82,164)(84,166)(86,168)(88,162)(90,180)(92,182)(94,184)(96,178)(98,188)(100,190)(102,192)(104,186)(106,196)(108,198)(110,200)(112,194), (1,119)(2,120)(3,113)(4,114)(5,115)(6,116)(7,117)(8,118)(9,140)(10,141)(11,142)(12,143)(13,144)(14,137)(15,138)(16,139)(17,148)(18,149)(19,150)(20,151)(21,152)(22,145)(23,146)(24,147)(25,156)(26,157)(27,158)(28,159)(29,160)(30,153)(31,154)(32,155)(33,217)(34,218)(35,219)(36,220)(37,221)(38,222)(39,223)(40,224)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(51,131)(52,132)(53,133)(54,134)(55,135)(56,136)(57,170)(58,171)(59,172)(60,173)(61,174)(62,175)(63,176)(64,169)(65,206)(66,207)(67,208)(68,201)(69,202)(70,203)(71,204)(72,205)(73,214)(74,215)(75,216)(76,209)(77,210)(78,211)(79,212)(80,213)(81,163)(82,164)(83,165)(84,166)(85,167)(86,168)(87,161)(88,162)(89,179)(90,180)(91,181)(92,182)(93,183)(94,184)(95,177)(96,178)(97,187)(98,188)(99,189)(100,190)(101,191)(102,192)(103,185)(104,186)(105,195)(106,196)(107,197)(108,198)(109,199)(110,200)(111,193)(112,194), (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64)(65,69)(66,70)(67,71)(68,72)(73,77)(74,78)(75,79)(76,80)(81,85)(82,86)(83,87)(84,88)(89,93)(90,94)(91,95)(92,96)(97,101)(98,102)(99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224), (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), (1,162)(2,83)(3,168)(4,81)(5,166)(6,87)(7,164)(8,85)(9,71)(10,207)(11,69)(12,205)(13,67)(14,203)(15,65)(16,201)(17,79)(18,215)(19,77)(20,213)(21,75)(22,211)(23,73)(24,209)(25,36)(26,223)(27,34)(28,221)(29,40)(30,219)(31,38)(32,217)(33,155)(35,153)(37,159)(39,157)(41,184)(42,89)(43,182)(44,95)(45,180)(46,93)(47,178)(48,91)(49,192)(50,97)(51,190)(52,103)(53,188)(54,101)(55,186)(56,99)(57,195)(58,108)(59,193)(60,106)(61,199)(62,112)(63,197)(64,110)(66,141)(68,139)(70,137)(72,143)(74,149)(76,147)(78,145)(80,151)(82,117)(84,115)(86,113)(88,119)(90,125)(92,123)(94,121)(96,127)(98,133)(100,131)(102,129)(104,135)(105,170)(107,176)(109,174)(111,172)(114,163)(116,161)(118,167)(120,165)(122,179)(124,177)(126,183)(128,181)(130,187)(132,185)(134,191)(136,189)(138,206)(140,204)(142,202)(144,208)(146,214)(148,212)(150,210)(152,216)(154,222)(156,220)(158,218)(160,224)(169,200)(171,198)(173,196)(175,194) );
G=PermutationGroup([[(1,175,223,55,215,47,207),(2,176,224,56,216,48,208),(3,169,217,49,209,41,201),(4,170,218,50,210,42,202),(5,171,219,51,211,43,203),(6,172,220,52,212,44,204),(7,173,221,53,213,45,205),(8,174,222,54,214,46,206),(9,161,193,25,185,17,177),(10,162,194,26,186,18,178),(11,163,195,27,187,19,179),(12,164,196,28,188,20,180),(13,165,197,29,189,21,181),(14,166,198,30,190,22,182),(15,167,199,31,191,23,183),(16,168,200,32,192,24,184),(33,129,76,121,68,113,64),(34,130,77,122,69,114,57),(35,131,78,123,70,115,58),(36,132,79,124,71,116,59),(37,133,80,125,72,117,60),(38,134,73,126,65,118,61),(39,135,74,127,66,119,62),(40,136,75,128,67,120,63),(81,105,158,97,150,89,142),(82,106,159,98,151,90,143),(83,107,160,99,152,91,144),(84,108,153,100,145,92,137),(85,109,154,101,146,93,138),(86,110,155,102,147,94,139),(87,111,156,103,148,95,140),(88,112,157,104,149,96,141)], [(2,120),(4,114),(6,116),(8,118),(10,141),(12,143),(14,137),(16,139),(18,149),(20,151),(22,145),(24,147),(26,157),(28,159),(30,153),(32,155),(34,218),(36,220),(38,222),(40,224),(42,122),(44,124),(46,126),(48,128),(50,130),(52,132),(54,134),(56,136),(57,170),(59,172),(61,174),(63,176),(65,206),(67,208),(69,202),(71,204),(73,214),(75,216),(77,210),(79,212),(82,164),(84,166),(86,168),(88,162),(90,180),(92,182),(94,184),(96,178),(98,188),(100,190),(102,192),(104,186),(106,196),(108,198),(110,200),(112,194)], [(1,119),(2,120),(3,113),(4,114),(5,115),(6,116),(7,117),(8,118),(9,140),(10,141),(11,142),(12,143),(13,144),(14,137),(15,138),(16,139),(17,148),(18,149),(19,150),(20,151),(21,152),(22,145),(23,146),(24,147),(25,156),(26,157),(27,158),(28,159),(29,160),(30,153),(31,154),(32,155),(33,217),(34,218),(35,219),(36,220),(37,221),(38,222),(39,223),(40,224),(41,121),(42,122),(43,123),(44,124),(45,125),(46,126),(47,127),(48,128),(49,129),(50,130),(51,131),(52,132),(53,133),(54,134),(55,135),(56,136),(57,170),(58,171),(59,172),(60,173),(61,174),(62,175),(63,176),(64,169),(65,206),(66,207),(67,208),(68,201),(69,202),(70,203),(71,204),(72,205),(73,214),(74,215),(75,216),(76,209),(77,210),(78,211),(79,212),(80,213),(81,163),(82,164),(83,165),(84,166),(85,167),(86,168),(87,161),(88,162),(89,179),(90,180),(91,181),(92,182),(93,183),(94,184),(95,177),(96,178),(97,187),(98,188),(99,189),(100,190),(101,191),(102,192),(103,185),(104,186),(105,195),(106,196),(107,197),(108,198),(109,199),(110,200),(111,193),(112,194)], [(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16),(17,21),(18,22),(19,23),(20,24),(25,29),(26,30),(27,31),(28,32),(33,37),(34,38),(35,39),(36,40),(41,45),(42,46),(43,47),(44,48),(49,53),(50,54),(51,55),(52,56),(57,61),(58,62),(59,63),(60,64),(65,69),(66,70),(67,71),(68,72),(73,77),(74,78),(75,79),(76,80),(81,85),(82,86),(83,87),(84,88),(89,93),(90,94),(91,95),(92,96),(97,101),(98,102),(99,103),(100,104),(105,109),(106,110),(107,111),(108,112),(113,117),(114,118),(115,119),(116,120),(121,125),(122,126),(123,127),(124,128),(129,133),(130,134),(131,135),(132,136),(137,141),(138,142),(139,143),(140,144),(145,149),(146,150),(147,151),(148,152),(153,157),(154,158),(155,159),(156,160),(161,165),(162,166),(163,167),(164,168),(169,173),(170,174),(171,175),(172,176),(177,181),(178,182),(179,183),(180,184),(185,189),(186,190),(187,191),(188,192),(193,197),(194,198),(195,199),(196,200),(201,205),(202,206),(203,207),(204,208),(209,213),(210,214),(211,215),(212,216),(217,221),(218,222),(219,223),(220,224)], [(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)], [(1,162),(2,83),(3,168),(4,81),(5,166),(6,87),(7,164),(8,85),(9,71),(10,207),(11,69),(12,205),(13,67),(14,203),(15,65),(16,201),(17,79),(18,215),(19,77),(20,213),(21,75),(22,211),(23,73),(24,209),(25,36),(26,223),(27,34),(28,221),(29,40),(30,219),(31,38),(32,217),(33,155),(35,153),(37,159),(39,157),(41,184),(42,89),(43,182),(44,95),(45,180),(46,93),(47,178),(48,91),(49,192),(50,97),(51,190),(52,103),(53,188),(54,101),(55,186),(56,99),(57,195),(58,108),(59,193),(60,106),(61,199),(62,112),(63,197),(64,110),(66,141),(68,139),(70,137),(72,143),(74,149),(76,147),(78,145),(80,151),(82,117),(84,115),(86,113),(88,119),(90,125),(92,123),(94,121),(96,127),(98,133),(100,131),(102,129),(104,135),(105,170),(107,176),(109,174),(111,172),(114,163),(116,161),(118,167),(120,165),(122,179),(124,177),(126,183),(128,181),(130,187),(132,185),(134,191),(136,189),(138,206),(140,204),(142,202),(144,208),(146,214),(148,212),(150,210),(152,216),(154,222),(156,220),(158,218),(160,224),(169,200),(171,198),(173,196),(175,194)]])
133 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 14A | ··· | 14R | 14S | ··· | 14AD | 14AE | ··· | 14AJ | 28A | ··· | 28L | 28M | ··· | 28AP | 28AQ | ··· | 28AV | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 7 | ··· | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 2 | 2 | 4 | ··· | 4 | 8 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 8 | ··· | 8 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
133 irreducible representations
| dim | 1 | 1 | 1 | 1 | 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 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | C4○D4 | SD16 | C7×D4 | C7×D4 | C7×C4○D4 | C7×SD16 | C8⋊C22 | C7×C8⋊C22 |
| kernel | C7×C23.46D4 | C7×C22⋊C8 | C7×D4⋊C4 | C7×C4.Q8 | C14×C4⋊C4 | C7×C4⋊D4 | C23.46D4 | C22⋊C8 | D4⋊C4 | C4.Q8 | C2×C4⋊C4 | C4⋊D4 | C2×C28 | C22×C14 | C28 | C2×C14 | C2×C4 | C23 | C4 | C22 | C14 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 6 | 6 | 12 | 12 | 6 | 6 | 1 | 1 | 4 | 4 | 6 | 6 | 24 | 24 | 1 | 6 |
Matrix representation of C7×C23.46D4 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 106 | 0 |
| 0 | 0 | 0 | 106 |
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 0 | 98 | 0 | 0 |
| 15 | 0 | 0 | 0 |
| 0 | 0 | 87 | 87 |
| 0 | 0 | 13 | 0 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 45 | 21 |
| 0 | 0 | 22 | 68 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,106,0,0,0,0,106],[1,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[112,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,112,0,0,0,0,112],[0,15,0,0,98,0,0,0,0,0,87,13,0,0,87,0],[0,1,0,0,1,0,0,0,0,0,45,22,0,0,21,68] >;
C7×C23.46D4 in GAP, Magma, Sage, TeX
C_7\times C_2^3._{46}D_4 % in TeX
G:=Group("C7xC2^3.46D4"); // GroupNames label
G:=SmallGroup(448,889);
// by ID
G=gap.SmallGroup(448,889);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,813,2438,1486,14117,3547,124]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^7=b^2=c^2=d^2=f^2=1,e^4=d,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,e*b*e^-1=f*b*f=b*c=c*b,b*d=d*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f=c*e^3>;
// generators/relations