metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.62D14, C23.15Dic14, C14.84(C4×D4), (C23×C4).4D7, (C2×C28).451D4, (C23×C28).2C2, C23.D7⋊11C4, C23.37(C4×D7), C14.69C22≀C2, (C22×C14).25Q8, C7⋊5(C23.8Q8), C22⋊3(Dic7⋊C4), (C22×C4).406D14, (C22×C14).191D4, C2.1(C24⋊D7), C23.81(C7⋊D4), C14.67(C22⋊Q8), C14.C42⋊22C2, C2.4(C28.48D4), C22.61(C4○D28), (C23×C14).97C22, C22.31(C2×Dic14), C23.301(C22×D7), (C22×C28).482C22, (C22×C14).361C23, C14.67(C22.D4), C2.3(C23.23D14), (C22×Dic7).64C22, (C2×C14)⋊6(C4⋊C4), C14.55(C2×C4⋊C4), C2.28(C4×C7⋊D4), (C2×Dic7)⋊8(C2×C4), (C2×C14).43(C2×Q8), C22.149(C2×C4×D7), (C2×Dic7⋊C4)⋊15C2, (C2×C14).547(C2×D4), C2.20(C2×Dic7⋊C4), C22.85(C2×C7⋊D4), (C2×C14).89(C4○D4), (C2×C4).224(C7⋊D4), (C22×C14).99(C2×C4), (C2×C23.D7).16C2, (C2×C14).142(C22×C4), SmallGroup(448,744)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.62D14
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=f2=b, ab=ba, faf-1=ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=de13 >
Subgroups: 772 in 234 conjugacy classes, 87 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, C23, C14, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, C2×C14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C23×C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C23.8Q8, Dic7⋊C4, C23.D7, C23.D7, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×C14, C14.C42, C2×Dic7⋊C4, C2×C23.D7, C23×C28, C24.62D14
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D14, C2×C4⋊C4, C4×D4, C22≀C2, C22⋊Q8, C22.D4, Dic14, C4×D7, C7⋊D4, C22×D7, C23.8Q8, Dic7⋊C4, C2×Dic14, C2×C4×D7, C4○D28, C2×C7⋊D4, C2×Dic7⋊C4, C28.48D4, C4×C7⋊D4, C23.23D14, C24⋊D7, C24.62D14
(1 213)(2 214)(3 215)(4 216)(5 217)(6 218)(7 219)(8 220)(9 221)(10 222)(11 223)(12 224)(13 197)(14 198)(15 199)(16 200)(17 201)(18 202)(19 203)(20 204)(21 205)(22 206)(23 207)(24 208)(25 209)(26 210)(27 211)(28 212)(29 90)(30 91)(31 92)(32 93)(33 94)(34 95)(35 96)(36 97)(37 98)(38 99)(39 100)(40 101)(41 102)(42 103)(43 104)(44 105)(45 106)(46 107)(47 108)(48 109)(49 110)(50 111)(51 112)(52 85)(53 86)(54 87)(55 88)(56 89)(57 138)(58 139)(59 140)(60 113)(61 114)(62 115)(63 116)(64 117)(65 118)(66 119)(67 120)(68 121)(69 122)(70 123)(71 124)(72 125)(73 126)(74 127)(75 128)(76 129)(77 130)(78 131)(79 132)(80 133)(81 134)(82 135)(83 136)(84 137)(141 186)(142 187)(143 188)(144 189)(145 190)(146 191)(147 192)(148 193)(149 194)(150 195)(151 196)(152 169)(153 170)(154 171)(155 172)(156 173)(157 174)(158 175)(159 176)(160 177)(161 178)(162 179)(163 180)(164 181)(165 182)(166 183)(167 184)(168 185)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(113 127)(114 128)(115 129)(116 130)(117 131)(118 132)(119 133)(120 134)(121 135)(122 136)(123 137)(124 138)(125 139)(126 140)(141 155)(142 156)(143 157)(144 158)(145 159)(146 160)(147 161)(148 162)(149 163)(150 164)(151 165)(152 166)(153 167)(154 168)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)(175 189)(176 190)(177 191)(178 192)(179 193)(180 194)(181 195)(182 196)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)
(1 70)(2 71)(3 72)(4 73)(5 74)(6 75)(7 76)(8 77)(9 78)(10 79)(11 80)(12 81)(13 82)(14 83)(15 84)(16 57)(17 58)(18 59)(19 60)(20 61)(21 62)(22 63)(23 64)(24 65)(25 66)(26 67)(27 68)(28 69)(29 161)(30 162)(31 163)(32 164)(33 165)(34 166)(35 167)(36 168)(37 141)(38 142)(39 143)(40 144)(41 145)(42 146)(43 147)(44 148)(45 149)(46 150)(47 151)(48 152)(49 153)(50 154)(51 155)(52 156)(53 157)(54 158)(55 159)(56 160)(85 173)(86 174)(87 175)(88 176)(89 177)(90 178)(91 179)(92 180)(93 181)(94 182)(95 183)(96 184)(97 185)(98 186)(99 187)(100 188)(101 189)(102 190)(103 191)(104 192)(105 193)(106 194)(107 195)(108 196)(109 169)(110 170)(111 171)(112 172)(113 203)(114 204)(115 205)(116 206)(117 207)(118 208)(119 209)(120 210)(121 211)(122 212)(123 213)(124 214)(125 215)(126 216)(127 217)(128 218)(129 219)(130 220)(131 221)(132 222)(133 223)(134 224)(135 197)(136 198)(137 199)(138 200)(139 201)(140 202)
(1 199)(2 200)(3 201)(4 202)(5 203)(6 204)(7 205)(8 206)(9 207)(10 208)(11 209)(12 210)(13 211)(14 212)(15 213)(16 214)(17 215)(18 216)(19 217)(20 218)(21 219)(22 220)(23 221)(24 222)(25 223)(26 224)(27 197)(28 198)(29 192)(30 193)(31 194)(32 195)(33 196)(34 169)(35 170)(36 171)(37 172)(38 173)(39 174)(40 175)(41 176)(42 177)(43 178)(44 179)(45 180)(46 181)(47 182)(48 183)(49 184)(50 185)(51 186)(52 187)(53 188)(54 189)(55 190)(56 191)(57 124)(58 125)(59 126)(60 127)(61 128)(62 129)(63 130)(64 131)(65 132)(66 133)(67 134)(68 135)(69 136)(70 137)(71 138)(72 139)(73 140)(74 113)(75 114)(76 115)(77 116)(78 117)(79 118)(80 119)(81 120)(82 121)(83 122)(84 123)(85 142)(86 143)(87 144)(88 145)(89 146)(90 147)(91 148)(92 149)(93 150)(94 151)(95 152)(96 153)(97 154)(98 155)(99 156)(100 157)(101 158)(102 159)(103 160)(104 161)(105 162)(106 163)(107 164)(108 165)(109 166)(110 167)(111 168)(112 141)
(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)
(1 176 15 190)(2 54 16 40)(3 174 17 188)(4 52 18 38)(5 172 19 186)(6 50 20 36)(7 170 21 184)(8 48 22 34)(9 196 23 182)(10 46 24 32)(11 194 25 180)(12 44 26 30)(13 192 27 178)(14 42 28 56)(29 197 43 211)(31 223 45 209)(33 221 47 207)(35 219 49 205)(37 217 51 203)(39 215 53 201)(41 213 55 199)(57 144 71 158)(58 100 72 86)(59 142 73 156)(60 98 74 112)(61 168 75 154)(62 96 76 110)(63 166 77 152)(64 94 78 108)(65 164 79 150)(66 92 80 106)(67 162 81 148)(68 90 82 104)(69 160 83 146)(70 88 84 102)(85 140 99 126)(87 138 101 124)(89 136 103 122)(91 134 105 120)(93 132 107 118)(95 130 109 116)(97 128 111 114)(113 141 127 155)(115 167 129 153)(117 165 131 151)(119 163 133 149)(121 161 135 147)(123 159 137 145)(125 157 139 143)(169 206 183 220)(171 204 185 218)(173 202 187 216)(175 200 189 214)(177 198 191 212)(179 224 193 210)(181 222 195 208)
G:=sub<Sym(224)| (1,213)(2,214)(3,215)(4,216)(5,217)(6,218)(7,219)(8,220)(9,221)(10,222)(11,223)(12,224)(13,197)(14,198)(15,199)(16,200)(17,201)(18,202)(19,203)(20,204)(21,205)(22,206)(23,207)(24,208)(25,209)(26,210)(27,211)(28,212)(29,90)(30,91)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,101)(41,102)(42,103)(43,104)(44,105)(45,106)(46,107)(47,108)(48,109)(49,110)(50,111)(51,112)(52,85)(53,86)(54,87)(55,88)(56,89)(57,138)(58,139)(59,140)(60,113)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,121)(69,122)(70,123)(71,124)(72,125)(73,126)(74,127)(75,128)(76,129)(77,130)(78,131)(79,132)(80,133)(81,134)(82,135)(83,136)(84,137)(141,186)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,196)(152,169)(153,170)(154,171)(155,172)(156,173)(157,174)(158,175)(159,176)(160,177)(161,178)(162,179)(163,180)(164,181)(165,182)(166,183)(167,184)(168,185), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,76)(8,77)(9,78)(10,79)(11,80)(12,81)(13,82)(14,83)(15,84)(16,57)(17,58)(18,59)(19,60)(20,61)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,161)(30,162)(31,163)(32,164)(33,165)(34,166)(35,167)(36,168)(37,141)(38,142)(39,143)(40,144)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(85,173)(86,174)(87,175)(88,176)(89,177)(90,178)(91,179)(92,180)(93,181)(94,182)(95,183)(96,184)(97,185)(98,186)(99,187)(100,188)(101,189)(102,190)(103,191)(104,192)(105,193)(106,194)(107,195)(108,196)(109,169)(110,170)(111,171)(112,172)(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,209)(120,210)(121,211)(122,212)(123,213)(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202), (1,199)(2,200)(3,201)(4,202)(5,203)(6,204)(7,205)(8,206)(9,207)(10,208)(11,209)(12,210)(13,211)(14,212)(15,213)(16,214)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,197)(28,198)(29,192)(30,193)(31,194)(32,195)(33,196)(34,169)(35,170)(36,171)(37,172)(38,173)(39,174)(40,175)(41,176)(42,177)(43,178)(44,179)(45,180)(46,181)(47,182)(48,183)(49,184)(50,185)(51,186)(52,187)(53,188)(54,189)(55,190)(56,191)(57,124)(58,125)(59,126)(60,127)(61,128)(62,129)(63,130)(64,131)(65,132)(66,133)(67,134)(68,135)(69,136)(70,137)(71,138)(72,139)(73,140)(74,113)(75,114)(76,115)(77,116)(78,117)(79,118)(80,119)(81,120)(82,121)(83,122)(84,123)(85,142)(86,143)(87,144)(88,145)(89,146)(90,147)(91,148)(92,149)(93,150)(94,151)(95,152)(96,153)(97,154)(98,155)(99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,141), (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), (1,176,15,190)(2,54,16,40)(3,174,17,188)(4,52,18,38)(5,172,19,186)(6,50,20,36)(7,170,21,184)(8,48,22,34)(9,196,23,182)(10,46,24,32)(11,194,25,180)(12,44,26,30)(13,192,27,178)(14,42,28,56)(29,197,43,211)(31,223,45,209)(33,221,47,207)(35,219,49,205)(37,217,51,203)(39,215,53,201)(41,213,55,199)(57,144,71,158)(58,100,72,86)(59,142,73,156)(60,98,74,112)(61,168,75,154)(62,96,76,110)(63,166,77,152)(64,94,78,108)(65,164,79,150)(66,92,80,106)(67,162,81,148)(68,90,82,104)(69,160,83,146)(70,88,84,102)(85,140,99,126)(87,138,101,124)(89,136,103,122)(91,134,105,120)(93,132,107,118)(95,130,109,116)(97,128,111,114)(113,141,127,155)(115,167,129,153)(117,165,131,151)(119,163,133,149)(121,161,135,147)(123,159,137,145)(125,157,139,143)(169,206,183,220)(171,204,185,218)(173,202,187,216)(175,200,189,214)(177,198,191,212)(179,224,193,210)(181,222,195,208)>;
G:=Group( (1,213)(2,214)(3,215)(4,216)(5,217)(6,218)(7,219)(8,220)(9,221)(10,222)(11,223)(12,224)(13,197)(14,198)(15,199)(16,200)(17,201)(18,202)(19,203)(20,204)(21,205)(22,206)(23,207)(24,208)(25,209)(26,210)(27,211)(28,212)(29,90)(30,91)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,101)(41,102)(42,103)(43,104)(44,105)(45,106)(46,107)(47,108)(48,109)(49,110)(50,111)(51,112)(52,85)(53,86)(54,87)(55,88)(56,89)(57,138)(58,139)(59,140)(60,113)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,121)(69,122)(70,123)(71,124)(72,125)(73,126)(74,127)(75,128)(76,129)(77,130)(78,131)(79,132)(80,133)(81,134)(82,135)(83,136)(84,137)(141,186)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,196)(152,169)(153,170)(154,171)(155,172)(156,173)(157,174)(158,175)(159,176)(160,177)(161,178)(162,179)(163,180)(164,181)(165,182)(166,183)(167,184)(168,185), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,76)(8,77)(9,78)(10,79)(11,80)(12,81)(13,82)(14,83)(15,84)(16,57)(17,58)(18,59)(19,60)(20,61)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,161)(30,162)(31,163)(32,164)(33,165)(34,166)(35,167)(36,168)(37,141)(38,142)(39,143)(40,144)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(85,173)(86,174)(87,175)(88,176)(89,177)(90,178)(91,179)(92,180)(93,181)(94,182)(95,183)(96,184)(97,185)(98,186)(99,187)(100,188)(101,189)(102,190)(103,191)(104,192)(105,193)(106,194)(107,195)(108,196)(109,169)(110,170)(111,171)(112,172)(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,209)(120,210)(121,211)(122,212)(123,213)(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202), (1,199)(2,200)(3,201)(4,202)(5,203)(6,204)(7,205)(8,206)(9,207)(10,208)(11,209)(12,210)(13,211)(14,212)(15,213)(16,214)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,197)(28,198)(29,192)(30,193)(31,194)(32,195)(33,196)(34,169)(35,170)(36,171)(37,172)(38,173)(39,174)(40,175)(41,176)(42,177)(43,178)(44,179)(45,180)(46,181)(47,182)(48,183)(49,184)(50,185)(51,186)(52,187)(53,188)(54,189)(55,190)(56,191)(57,124)(58,125)(59,126)(60,127)(61,128)(62,129)(63,130)(64,131)(65,132)(66,133)(67,134)(68,135)(69,136)(70,137)(71,138)(72,139)(73,140)(74,113)(75,114)(76,115)(77,116)(78,117)(79,118)(80,119)(81,120)(82,121)(83,122)(84,123)(85,142)(86,143)(87,144)(88,145)(89,146)(90,147)(91,148)(92,149)(93,150)(94,151)(95,152)(96,153)(97,154)(98,155)(99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,141), (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), (1,176,15,190)(2,54,16,40)(3,174,17,188)(4,52,18,38)(5,172,19,186)(6,50,20,36)(7,170,21,184)(8,48,22,34)(9,196,23,182)(10,46,24,32)(11,194,25,180)(12,44,26,30)(13,192,27,178)(14,42,28,56)(29,197,43,211)(31,223,45,209)(33,221,47,207)(35,219,49,205)(37,217,51,203)(39,215,53,201)(41,213,55,199)(57,144,71,158)(58,100,72,86)(59,142,73,156)(60,98,74,112)(61,168,75,154)(62,96,76,110)(63,166,77,152)(64,94,78,108)(65,164,79,150)(66,92,80,106)(67,162,81,148)(68,90,82,104)(69,160,83,146)(70,88,84,102)(85,140,99,126)(87,138,101,124)(89,136,103,122)(91,134,105,120)(93,132,107,118)(95,130,109,116)(97,128,111,114)(113,141,127,155)(115,167,129,153)(117,165,131,151)(119,163,133,149)(121,161,135,147)(123,159,137,145)(125,157,139,143)(169,206,183,220)(171,204,185,218)(173,202,187,216)(175,200,189,214)(177,198,191,212)(179,224,193,210)(181,222,195,208) );
G=PermutationGroup([[(1,213),(2,214),(3,215),(4,216),(5,217),(6,218),(7,219),(8,220),(9,221),(10,222),(11,223),(12,224),(13,197),(14,198),(15,199),(16,200),(17,201),(18,202),(19,203),(20,204),(21,205),(22,206),(23,207),(24,208),(25,209),(26,210),(27,211),(28,212),(29,90),(30,91),(31,92),(32,93),(33,94),(34,95),(35,96),(36,97),(37,98),(38,99),(39,100),(40,101),(41,102),(42,103),(43,104),(44,105),(45,106),(46,107),(47,108),(48,109),(49,110),(50,111),(51,112),(52,85),(53,86),(54,87),(55,88),(56,89),(57,138),(58,139),(59,140),(60,113),(61,114),(62,115),(63,116),(64,117),(65,118),(66,119),(67,120),(68,121),(69,122),(70,123),(71,124),(72,125),(73,126),(74,127),(75,128),(76,129),(77,130),(78,131),(79,132),(80,133),(81,134),(82,135),(83,136),(84,137),(141,186),(142,187),(143,188),(144,189),(145,190),(146,191),(147,192),(148,193),(149,194),(150,195),(151,196),(152,169),(153,170),(154,171),(155,172),(156,173),(157,174),(158,175),(159,176),(160,177),(161,178),(162,179),(163,180),(164,181),(165,182),(166,183),(167,184),(168,185)], [(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(113,127),(114,128),(115,129),(116,130),(117,131),(118,132),(119,133),(120,134),(121,135),(122,136),(123,137),(124,138),(125,139),(126,140),(141,155),(142,156),(143,157),(144,158),(145,159),(146,160),(147,161),(148,162),(149,163),(150,164),(151,165),(152,166),(153,167),(154,168),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188),(175,189),(176,190),(177,191),(178,192),(179,193),(180,194),(181,195),(182,196),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224)], [(1,70),(2,71),(3,72),(4,73),(5,74),(6,75),(7,76),(8,77),(9,78),(10,79),(11,80),(12,81),(13,82),(14,83),(15,84),(16,57),(17,58),(18,59),(19,60),(20,61),(21,62),(22,63),(23,64),(24,65),(25,66),(26,67),(27,68),(28,69),(29,161),(30,162),(31,163),(32,164),(33,165),(34,166),(35,167),(36,168),(37,141),(38,142),(39,143),(40,144),(41,145),(42,146),(43,147),(44,148),(45,149),(46,150),(47,151),(48,152),(49,153),(50,154),(51,155),(52,156),(53,157),(54,158),(55,159),(56,160),(85,173),(86,174),(87,175),(88,176),(89,177),(90,178),(91,179),(92,180),(93,181),(94,182),(95,183),(96,184),(97,185),(98,186),(99,187),(100,188),(101,189),(102,190),(103,191),(104,192),(105,193),(106,194),(107,195),(108,196),(109,169),(110,170),(111,171),(112,172),(113,203),(114,204),(115,205),(116,206),(117,207),(118,208),(119,209),(120,210),(121,211),(122,212),(123,213),(124,214),(125,215),(126,216),(127,217),(128,218),(129,219),(130,220),(131,221),(132,222),(133,223),(134,224),(135,197),(136,198),(137,199),(138,200),(139,201),(140,202)], [(1,199),(2,200),(3,201),(4,202),(5,203),(6,204),(7,205),(8,206),(9,207),(10,208),(11,209),(12,210),(13,211),(14,212),(15,213),(16,214),(17,215),(18,216),(19,217),(20,218),(21,219),(22,220),(23,221),(24,222),(25,223),(26,224),(27,197),(28,198),(29,192),(30,193),(31,194),(32,195),(33,196),(34,169),(35,170),(36,171),(37,172),(38,173),(39,174),(40,175),(41,176),(42,177),(43,178),(44,179),(45,180),(46,181),(47,182),(48,183),(49,184),(50,185),(51,186),(52,187),(53,188),(54,189),(55,190),(56,191),(57,124),(58,125),(59,126),(60,127),(61,128),(62,129),(63,130),(64,131),(65,132),(66,133),(67,134),(68,135),(69,136),(70,137),(71,138),(72,139),(73,140),(74,113),(75,114),(76,115),(77,116),(78,117),(79,118),(80,119),(81,120),(82,121),(83,122),(84,123),(85,142),(86,143),(87,144),(88,145),(89,146),(90,147),(91,148),(92,149),(93,150),(94,151),(95,152),(96,153),(97,154),(98,155),(99,156),(100,157),(101,158),(102,159),(103,160),(104,161),(105,162),(106,163),(107,164),(108,165),(109,166),(110,167),(111,168),(112,141)], [(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)], [(1,176,15,190),(2,54,16,40),(3,174,17,188),(4,52,18,38),(5,172,19,186),(6,50,20,36),(7,170,21,184),(8,48,22,34),(9,196,23,182),(10,46,24,32),(11,194,25,180),(12,44,26,30),(13,192,27,178),(14,42,28,56),(29,197,43,211),(31,223,45,209),(33,221,47,207),(35,219,49,205),(37,217,51,203),(39,215,53,201),(41,213,55,199),(57,144,71,158),(58,100,72,86),(59,142,73,156),(60,98,74,112),(61,168,75,154),(62,96,76,110),(63,166,77,152),(64,94,78,108),(65,164,79,150),(66,92,80,106),(67,162,81,148),(68,90,82,104),(69,160,83,146),(70,88,84,102),(85,140,99,126),(87,138,101,124),(89,136,103,122),(91,134,105,120),(93,132,107,118),(95,130,109,116),(97,128,111,114),(113,141,127,155),(115,167,129,153),(117,165,131,151),(119,163,133,149),(121,161,135,147),(123,159,137,145),(125,157,139,143),(169,206,183,220),(171,204,185,218),(173,202,187,216),(175,200,189,214),(177,198,191,212),(179,224,193,210),(181,222,195,208)]])
124 conjugacy classes
class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 4I | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14AS | 28A | ··· | 28AV |
order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
type | + | + | + | + | + | + | + | - | + | + | + | - | ||||||
image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | Q8 | D7 | C4○D4 | D14 | D14 | C7⋊D4 | Dic14 | C4×D7 | C7⋊D4 | C4○D28 |
kernel | C24.62D14 | C14.C42 | C2×Dic7⋊C4 | C2×C23.D7 | C23×C28 | C23.D7 | C2×C28 | C22×C14 | C22×C14 | C23×C4 | C2×C14 | C22×C4 | C24 | C2×C4 | C23 | C23 | C23 | C22 |
# reps | 1 | 2 | 2 | 2 | 1 | 8 | 4 | 2 | 2 | 3 | 4 | 6 | 3 | 24 | 12 | 12 | 12 | 24 |
Matrix representation of C24.62D14 ►in GL5(𝔽29)
1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 28 | 0 |
0 | 0 | 0 | 15 | 1 |
28 | 0 | 0 | 0 | 0 |
0 | 28 | 0 | 0 | 0 |
0 | 0 | 28 | 0 | 0 |
0 | 0 | 0 | 1 | 0 |
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 |
1 | 0 | 0 | 0 | 0 |
0 | 28 | 0 | 0 | 0 |
0 | 0 | 28 | 0 | 0 |
0 | 0 | 0 | 28 | 0 |
0 | 0 | 0 | 0 | 28 |
17 | 0 | 0 | 0 | 0 |
0 | 20 | 9 | 0 | 0 |
0 | 20 | 25 | 0 | 0 |
0 | 0 | 0 | 5 | 0 |
0 | 0 | 0 | 19 | 23 |
12 | 0 | 0 | 0 | 0 |
0 | 4 | 4 | 0 | 0 |
0 | 3 | 25 | 0 | 0 |
0 | 0 | 0 | 18 | 14 |
0 | 0 | 0 | 8 | 11 |
G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,15,0,0,0,0,1],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1],[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],[1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28],[17,0,0,0,0,0,20,20,0,0,0,9,25,0,0,0,0,0,5,19,0,0,0,0,23],[12,0,0,0,0,0,4,3,0,0,0,4,25,0,0,0,0,0,18,8,0,0,0,14,11] >;
C24.62D14 in GAP, Magma, Sage, TeX
C_2^4._{62}D_{14}
% in TeX
G:=Group("C2^4.62D14");
// GroupNames label
G:=SmallGroup(448,744);
// by ID
G=gap.SmallGroup(448,744);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,758,58,18822]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^14=f^2=b,a*b=b*a,f*a*f^-1=a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=d*e^13>;
// generators/relations