metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.47D14, C23.43D28, C23.11Dic14, C14.86(C4×D4), C2.4(D4×Dic7), C22⋊C4⋊4Dic7, C22.98(D4×D7), C14.31C22≀C2, C22⋊1(C4⋊Dic7), C22.42(C2×D28), (C22×C14).63D4, (C22×C4).90D14, C2.3(C22⋊D28), (C22×C14).14Q8, C7⋊3(C23.8Q8), (C2×Dic7).174D4, C14.17(C22⋊Q8), (C23×Dic7).5C2, C23.13(C2×Dic7), C14.C42⋊30C2, (C22×C28).59C22, (C23×C14).33C22, C22.25(C2×Dic14), C23.280(C22×D7), C22.46(D4⋊2D7), (C22×C14).325C23, C2.7(C22⋊Dic14), C2.4(C22.D28), C22.39(C22×Dic7), C14.30(C22.D4), (C22×Dic7).184C22, (C2×C28)⋊6(C2×C4), (C2×C14)⋊3(C4⋊C4), C14.31(C2×C4⋊C4), (C7×C22⋊C4)⋊7C4, (C2×C4)⋊2(C2×Dic7), C2.7(C2×C4⋊Dic7), (C2×C4⋊Dic7)⋊10C2, (C2×C14).35(C2×Q8), (C2×C14).319(C2×D4), (C2×C22⋊C4).13D7, (C14×C22⋊C4).15C2, (C22×C14).50(C2×C4), (C2×C23.D7).12C2, (C2×C14).142(C4○D4), (C2×C14).178(C22×C4), SmallGroup(448,484)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.47D14
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=c, f2=b, ab=ba, ac=ca, eae-1=faf-1=ad=da, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce13 >
Subgroups: 916 in 234 conjugacy classes, 91 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, C23, C14, C14, C14, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, C2×C14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C23×C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C23.8Q8, C4⋊Dic7, C23.D7, C7×C22⋊C4, C22×Dic7, C22×Dic7, C22×Dic7, C22×C28, C23×C14, C14.C42, C2×C4⋊Dic7, C2×C23.D7, C14×C22⋊C4, C23×Dic7, C24.47D14
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, D14, C2×C4⋊C4, C4×D4, C22≀C2, C22⋊Q8, C22.D4, Dic14, D28, C2×Dic7, C22×D7, C23.8Q8, C4⋊Dic7, C2×Dic14, C2×D28, D4×D7, D4⋊2D7, C22×Dic7, C22⋊Dic14, C22⋊D28, C22.D28, C2×C4⋊Dic7, D4×Dic7, C24.47D14
►On 224 points
Generators in S224
(1 175)(2 147)(3 177)(4 149)(5 179)(6 151)(7 181)(8 153)(9 183)(10 155)(11 185)(12 157)(13 187)(14 159)(15 189)(16 161)(17 191)(18 163)(19 193)(20 165)(21 195)(22 167)(23 169)(24 141)(25 171)(26 143)(27 173)(28 145)(29 97)(30 124)(31 99)(32 126)(33 101)(34 128)(35 103)(36 130)(37 105)(38 132)(39 107)(40 134)(41 109)(42 136)(43 111)(44 138)(45 85)(46 140)(47 87)(48 114)(49 89)(50 116)(51 91)(52 118)(53 93)(54 120)(55 95)(56 122)(57 106)(58 133)(59 108)(60 135)(61 110)(62 137)(63 112)(64 139)(65 86)(66 113)(67 88)(68 115)(69 90)(70 117)(71 92)(72 119)(73 94)(74 121)(75 96)(76 123)(77 98)(78 125)(79 100)(80 127)(81 102)(82 129)(83 104)(84 131)(142 212)(144 214)(146 216)(148 218)(150 220)(152 222)(154 224)(156 198)(158 200)(160 202)(162 204)(164 206)(166 208)(168 210)(170 211)(172 213)(174 215)(176 217)(178 219)(180 221)(182 223)(184 197)(186 199)(188 201)(190 203)(192 205)(194 207)(196 209)
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 169)(10 170)(11 171)(12 172)(13 173)(14 174)(15 175)(16 176)(17 177)(18 178)(19 179)(20 180)(21 181)(22 182)(23 183)(24 184)(25 185)(26 186)(27 187)(28 188)(29 111)(30 112)(31 85)(32 86)(33 87)(34 88)(35 89)(36 90)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 97)(44 98)(45 99)(46 100)(47 101)(48 102)(49 103)(50 104)(51 105)(52 106)(53 107)(54 108)(55 109)(56 110)(57 118)(58 119)(59 120)(60 121)(61 122)(62 123)(63 124)(64 125)(65 126)(66 127)(67 128)(68 129)(69 130)(70 131)(71 132)(72 133)(73 134)(74 135)(75 136)(76 137)(77 138)(78 139)(79 140)(80 113)(81 114)(82 115)(83 116)(84 117)(141 197)(142 198)(143 199)(144 200)(145 201)(146 202)(147 203)(148 204)(149 205)(150 206)(151 207)(152 208)(153 209)(154 210)(155 211)(156 212)(157 213)(158 214)(159 215)(160 216)(161 217)(162 218)(163 219)(164 220)(165 221)(166 222)(167 223)(168 224)
(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)
(1 216)(2 217)(3 218)(4 219)(5 220)(6 221)(7 222)(8 223)(9 224)(10 197)(11 198)(12 199)(13 200)(14 201)(15 202)(16 203)(17 204)(18 205)(19 206)(20 207)(21 208)(22 209)(23 210)(24 211)(25 212)(26 213)(27 214)(28 215)(29 76)(30 77)(31 78)(32 79)(33 80)(34 81)(35 82)(36 83)(37 84)(38 57)(39 58)(40 59)(41 60)(42 61)(43 62)(44 63)(45 64)(46 65)(47 66)(48 67)(49 68)(50 69)(51 70)(52 71)(53 72)(54 73)(55 74)(56 75)(85 139)(86 140)(87 113)(88 114)(89 115)(90 116)(91 117)(92 118)(93 119)(94 120)(95 121)(96 122)(97 123)(98 124)(99 125)(100 126)(101 127)(102 128)(103 129)(104 130)(105 131)(106 132)(107 133)(108 134)(109 135)(110 136)(111 137)(112 138)(141 170)(142 171)(143 172)(144 173)(145 174)(146 175)(147 176)(148 177)(149 178)(150 179)(151 180)(152 181)(153 182)(154 183)(155 184)(156 185)(157 186)(158 187)(159 188)(160 189)(161 190)(162 191)(163 192)(164 193)(165 194)(166 195)(167 196)(168 169)
(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 77 189 138)(2 76 190 137)(3 75 191 136)(4 74 192 135)(5 73 193 134)(6 72 194 133)(7 71 195 132)(8 70 196 131)(9 69 169 130)(10 68 170 129)(11 67 171 128)(12 66 172 127)(13 65 173 126)(14 64 174 125)(15 63 175 124)(16 62 176 123)(17 61 177 122)(18 60 178 121)(19 59 179 120)(20 58 180 119)(21 57 181 118)(22 84 182 117)(23 83 183 116)(24 82 184 115)(25 81 185 114)(26 80 186 113)(27 79 187 140)(28 78 188 139)(29 161 111 217)(30 160 112 216)(31 159 85 215)(32 158 86 214)(33 157 87 213)(34 156 88 212)(35 155 89 211)(36 154 90 210)(37 153 91 209)(38 152 92 208)(39 151 93 207)(40 150 94 206)(41 149 95 205)(42 148 96 204)(43 147 97 203)(44 146 98 202)(45 145 99 201)(46 144 100 200)(47 143 101 199)(48 142 102 198)(49 141 103 197)(50 168 104 224)(51 167 105 223)(52 166 106 222)(53 165 107 221)(54 164 108 220)(55 163 109 219)(56 162 110 218)
G:=sub<Sym(224)| (1,175)(2,147)(3,177)(4,149)(5,179)(6,151)(7,181)(8,153)(9,183)(10,155)(11,185)(12,157)(13,187)(14,159)(15,189)(16,161)(17,191)(18,163)(19,193)(20,165)(21,195)(22,167)(23,169)(24,141)(25,171)(26,143)(27,173)(28,145)(29,97)(30,124)(31,99)(32,126)(33,101)(34,128)(35,103)(36,130)(37,105)(38,132)(39,107)(40,134)(41,109)(42,136)(43,111)(44,138)(45,85)(46,140)(47,87)(48,114)(49,89)(50,116)(51,91)(52,118)(53,93)(54,120)(55,95)(56,122)(57,106)(58,133)(59,108)(60,135)(61,110)(62,137)(63,112)(64,139)(65,86)(66,113)(67,88)(68,115)(69,90)(70,117)(71,92)(72,119)(73,94)(74,121)(75,96)(76,123)(77,98)(78,125)(79,100)(80,127)(81,102)(82,129)(83,104)(84,131)(142,212)(144,214)(146,216)(148,218)(150,220)(152,222)(154,224)(156,198)(158,200)(160,202)(162,204)(164,206)(166,208)(168,210)(170,211)(172,213)(174,215)(176,217)(178,219)(180,221)(182,223)(184,197)(186,199)(188,201)(190,203)(192,205)(194,207)(196,209), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,169)(10,170)(11,171)(12,172)(13,173)(14,174)(15,175)(16,176)(17,177)(18,178)(19,179)(20,180)(21,181)(22,182)(23,183)(24,184)(25,185)(26,186)(27,187)(28,188)(29,111)(30,112)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,118)(58,119)(59,120)(60,121)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,113)(81,114)(82,115)(83,116)(84,117)(141,197)(142,198)(143,199)(144,200)(145,201)(146,202)(147,203)(148,204)(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)(168,224), (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), (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,76)(30,77)(31,78)(32,79)(33,80)(34,81)(35,82)(36,83)(37,84)(38,57)(39,58)(40,59)(41,60)(42,61)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,71)(53,72)(54,73)(55,74)(56,75)(85,139)(86,140)(87,113)(88,114)(89,115)(90,116)(91,117)(92,118)(93,119)(94,120)(95,121)(96,122)(97,123)(98,124)(99,125)(100,126)(101,127)(102,128)(103,129)(104,130)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(141,170)(142,171)(143,172)(144,173)(145,174)(146,175)(147,176)(148,177)(149,178)(150,179)(151,180)(152,181)(153,182)(154,183)(155,184)(156,185)(157,186)(158,187)(159,188)(160,189)(161,190)(162,191)(163,192)(164,193)(165,194)(166,195)(167,196)(168,169), (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), (1,77,189,138)(2,76,190,137)(3,75,191,136)(4,74,192,135)(5,73,193,134)(6,72,194,133)(7,71,195,132)(8,70,196,131)(9,69,169,130)(10,68,170,129)(11,67,171,128)(12,66,172,127)(13,65,173,126)(14,64,174,125)(15,63,175,124)(16,62,176,123)(17,61,177,122)(18,60,178,121)(19,59,179,120)(20,58,180,119)(21,57,181,118)(22,84,182,117)(23,83,183,116)(24,82,184,115)(25,81,185,114)(26,80,186,113)(27,79,187,140)(28,78,188,139)(29,161,111,217)(30,160,112,216)(31,159,85,215)(32,158,86,214)(33,157,87,213)(34,156,88,212)(35,155,89,211)(36,154,90,210)(37,153,91,209)(38,152,92,208)(39,151,93,207)(40,150,94,206)(41,149,95,205)(42,148,96,204)(43,147,97,203)(44,146,98,202)(45,145,99,201)(46,144,100,200)(47,143,101,199)(48,142,102,198)(49,141,103,197)(50,168,104,224)(51,167,105,223)(52,166,106,222)(53,165,107,221)(54,164,108,220)(55,163,109,219)(56,162,110,218)>;
G:=Group( (1,175)(2,147)(3,177)(4,149)(5,179)(6,151)(7,181)(8,153)(9,183)(10,155)(11,185)(12,157)(13,187)(14,159)(15,189)(16,161)(17,191)(18,163)(19,193)(20,165)(21,195)(22,167)(23,169)(24,141)(25,171)(26,143)(27,173)(28,145)(29,97)(30,124)(31,99)(32,126)(33,101)(34,128)(35,103)(36,130)(37,105)(38,132)(39,107)(40,134)(41,109)(42,136)(43,111)(44,138)(45,85)(46,140)(47,87)(48,114)(49,89)(50,116)(51,91)(52,118)(53,93)(54,120)(55,95)(56,122)(57,106)(58,133)(59,108)(60,135)(61,110)(62,137)(63,112)(64,139)(65,86)(66,113)(67,88)(68,115)(69,90)(70,117)(71,92)(72,119)(73,94)(74,121)(75,96)(76,123)(77,98)(78,125)(79,100)(80,127)(81,102)(82,129)(83,104)(84,131)(142,212)(144,214)(146,216)(148,218)(150,220)(152,222)(154,224)(156,198)(158,200)(160,202)(162,204)(164,206)(166,208)(168,210)(170,211)(172,213)(174,215)(176,217)(178,219)(180,221)(182,223)(184,197)(186,199)(188,201)(190,203)(192,205)(194,207)(196,209), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,169)(10,170)(11,171)(12,172)(13,173)(14,174)(15,175)(16,176)(17,177)(18,178)(19,179)(20,180)(21,181)(22,182)(23,183)(24,184)(25,185)(26,186)(27,187)(28,188)(29,111)(30,112)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,118)(58,119)(59,120)(60,121)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,113)(81,114)(82,115)(83,116)(84,117)(141,197)(142,198)(143,199)(144,200)(145,201)(146,202)(147,203)(148,204)(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)(168,224), (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), (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,76)(30,77)(31,78)(32,79)(33,80)(34,81)(35,82)(36,83)(37,84)(38,57)(39,58)(40,59)(41,60)(42,61)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,71)(53,72)(54,73)(55,74)(56,75)(85,139)(86,140)(87,113)(88,114)(89,115)(90,116)(91,117)(92,118)(93,119)(94,120)(95,121)(96,122)(97,123)(98,124)(99,125)(100,126)(101,127)(102,128)(103,129)(104,130)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(141,170)(142,171)(143,172)(144,173)(145,174)(146,175)(147,176)(148,177)(149,178)(150,179)(151,180)(152,181)(153,182)(154,183)(155,184)(156,185)(157,186)(158,187)(159,188)(160,189)(161,190)(162,191)(163,192)(164,193)(165,194)(166,195)(167,196)(168,169), (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), (1,77,189,138)(2,76,190,137)(3,75,191,136)(4,74,192,135)(5,73,193,134)(6,72,194,133)(7,71,195,132)(8,70,196,131)(9,69,169,130)(10,68,170,129)(11,67,171,128)(12,66,172,127)(13,65,173,126)(14,64,174,125)(15,63,175,124)(16,62,176,123)(17,61,177,122)(18,60,178,121)(19,59,179,120)(20,58,180,119)(21,57,181,118)(22,84,182,117)(23,83,183,116)(24,82,184,115)(25,81,185,114)(26,80,186,113)(27,79,187,140)(28,78,188,139)(29,161,111,217)(30,160,112,216)(31,159,85,215)(32,158,86,214)(33,157,87,213)(34,156,88,212)(35,155,89,211)(36,154,90,210)(37,153,91,209)(38,152,92,208)(39,151,93,207)(40,150,94,206)(41,149,95,205)(42,148,96,204)(43,147,97,203)(44,146,98,202)(45,145,99,201)(46,144,100,200)(47,143,101,199)(48,142,102,198)(49,141,103,197)(50,168,104,224)(51,167,105,223)(52,166,106,222)(53,165,107,221)(54,164,108,220)(55,163,109,219)(56,162,110,218) );
G=PermutationGroup([[(1,175),(2,147),(3,177),(4,149),(5,179),(6,151),(7,181),(8,153),(9,183),(10,155),(11,185),(12,157),(13,187),(14,159),(15,189),(16,161),(17,191),(18,163),(19,193),(20,165),(21,195),(22,167),(23,169),(24,141),(25,171),(26,143),(27,173),(28,145),(29,97),(30,124),(31,99),(32,126),(33,101),(34,128),(35,103),(36,130),(37,105),(38,132),(39,107),(40,134),(41,109),(42,136),(43,111),(44,138),(45,85),(46,140),(47,87),(48,114),(49,89),(50,116),(51,91),(52,118),(53,93),(54,120),(55,95),(56,122),(57,106),(58,133),(59,108),(60,135),(61,110),(62,137),(63,112),(64,139),(65,86),(66,113),(67,88),(68,115),(69,90),(70,117),(71,92),(72,119),(73,94),(74,121),(75,96),(76,123),(77,98),(78,125),(79,100),(80,127),(81,102),(82,129),(83,104),(84,131),(142,212),(144,214),(146,216),(148,218),(150,220),(152,222),(154,224),(156,198),(158,200),(160,202),(162,204),(164,206),(166,208),(168,210),(170,211),(172,213),(174,215),(176,217),(178,219),(180,221),(182,223),(184,197),(186,199),(188,201),(190,203),(192,205),(194,207),(196,209)], [(1,189),(2,190),(3,191),(4,192),(5,193),(6,194),(7,195),(8,196),(9,169),(10,170),(11,171),(12,172),(13,173),(14,174),(15,175),(16,176),(17,177),(18,178),(19,179),(20,180),(21,181),(22,182),(23,183),(24,184),(25,185),(26,186),(27,187),(28,188),(29,111),(30,112),(31,85),(32,86),(33,87),(34,88),(35,89),(36,90),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,97),(44,98),(45,99),(46,100),(47,101),(48,102),(49,103),(50,104),(51,105),(52,106),(53,107),(54,108),(55,109),(56,110),(57,118),(58,119),(59,120),(60,121),(61,122),(62,123),(63,124),(64,125),(65,126),(66,127),(67,128),(68,129),(69,130),(70,131),(71,132),(72,133),(73,134),(74,135),(75,136),(76,137),(77,138),(78,139),(79,140),(80,113),(81,114),(82,115),(83,116),(84,117),(141,197),(142,198),(143,199),(144,200),(145,201),(146,202),(147,203),(148,204),(149,205),(150,206),(151,207),(152,208),(153,209),(154,210),(155,211),(156,212),(157,213),(158,214),(159,215),(160,216),(161,217),(162,218),(163,219),(164,220),(165,221),(166,222),(167,223),(168,224)], [(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)], [(1,216),(2,217),(3,218),(4,219),(5,220),(6,221),(7,222),(8,223),(9,224),(10,197),(11,198),(12,199),(13,200),(14,201),(15,202),(16,203),(17,204),(18,205),(19,206),(20,207),(21,208),(22,209),(23,210),(24,211),(25,212),(26,213),(27,214),(28,215),(29,76),(30,77),(31,78),(32,79),(33,80),(34,81),(35,82),(36,83),(37,84),(38,57),(39,58),(40,59),(41,60),(42,61),(43,62),(44,63),(45,64),(46,65),(47,66),(48,67),(49,68),(50,69),(51,70),(52,71),(53,72),(54,73),(55,74),(56,75),(85,139),(86,140),(87,113),(88,114),(89,115),(90,116),(91,117),(92,118),(93,119),(94,120),(95,121),(96,122),(97,123),(98,124),(99,125),(100,126),(101,127),(102,128),(103,129),(104,130),(105,131),(106,132),(107,133),(108,134),(109,135),(110,136),(111,137),(112,138),(141,170),(142,171),(143,172),(144,173),(145,174),(146,175),(147,176),(148,177),(149,178),(150,179),(151,180),(152,181),(153,182),(154,183),(155,184),(156,185),(157,186),(158,187),(159,188),(160,189),(161,190),(162,191),(163,192),(164,193),(165,194),(166,195),(167,196),(168,169)], [(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)], [(1,77,189,138),(2,76,190,137),(3,75,191,136),(4,74,192,135),(5,73,193,134),(6,72,194,133),(7,71,195,132),(8,70,196,131),(9,69,169,130),(10,68,170,129),(11,67,171,128),(12,66,172,127),(13,65,173,126),(14,64,174,125),(15,63,175,124),(16,62,176,123),(17,61,177,122),(18,60,178,121),(19,59,179,120),(20,58,180,119),(21,57,181,118),(22,84,182,117),(23,83,183,116),(24,82,184,115),(25,81,185,114),(26,80,186,113),(27,79,187,140),(28,78,188,139),(29,161,111,217),(30,160,112,216),(31,159,85,215),(32,158,86,214),(33,157,87,213),(34,156,88,212),(35,155,89,211),(36,154,90,210),(37,153,91,209),(38,152,92,208),(39,151,93,207),(40,150,94,206),(41,149,95,205),(42,148,96,204),(43,147,97,203),(44,146,98,202),(45,145,99,201),(46,144,100,200),(47,143,101,199),(48,142,102,198),(49,141,103,197),(50,168,104,224),(51,167,105,223),(52,166,106,222),(53,165,107,221),(54,164,108,220),(55,163,109,219),(56,162,110,218)]])
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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | - | + | + | - | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | Q8 | D7 | C4○D4 | Dic7 | D14 | D14 | Dic14 | D28 | D4×D7 | D4⋊2D7 |
| kernel | C24.47D14 | C14.C42 | C2×C4⋊Dic7 | C2×C23.D7 | C14×C22⋊C4 | C23×Dic7 | C7×C22⋊C4 | C2×Dic7 | C22×C14 | C22×C14 | C2×C22⋊C4 | C2×C14 | C22⋊C4 | C22×C4 | C24 | C23 | C23 | C22 | C22 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 4 | 2 | 2 | 3 | 4 | 12 | 6 | 3 | 12 | 12 | 6 | 6 |
Matrix representation of C24.47D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 5 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 0 | 0 | 2 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 1 | 0 | 0 |
| 0 | 0 | 3 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 27 |
| 0 | 0 | 0 | 0 | 14 | 0 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,6,5,0,0,0,0,0,5,0,0,0,0,0,0,15,0,0,0,0,0,0,2],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,24,3,0,0,0,0,1,5,0,0,0,0,0,0,0,14,0,0,0,0,27,0] >;
C24.47D14 in GAP, Magma, Sage, TeX
C_2^4._{47}D_{14} % in TeX
G:=Group("C2^4.47D14"); // GroupNames label
G:=SmallGroup(448,484);
// by ID
G=gap.SmallGroup(448,484);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,422,387,100,18822]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^14=c,f^2=b,a*b=b*a,a*c=c*a,e*a*e^-1=f*a*f^-1=a*d=d*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=c*e^13>;
// generators/relations