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G = C24.62D14  order 448 = 26·7

2nd non-split extension by C24 of D14 acting via D14/C14=C2

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

Derived series
C1 — C2×C14 — C24.62D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×C14 — C22×Dic7 — C2×C23.D7 — C24.62D14
Lower central
C7 — C2×C14 — C24.62D14
Upper central
C1 — C23 — C23×C4

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

Smallest permutation representation of C24.62D14
►On 224 points
Generators in S224
(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···2G2H2I2J2K4A···4H4I···4P7A7B7C14A···14AS28A···28AV
order12···222224···44···477714···1428···28
size11···122222···228···282222···22···2

124 irreducible representations

dim111111222222222222
type+++++++-+++-
imageC1C2C2C2C2C4D4D4Q8D7C4○D4D14D14C7⋊D4Dic14C4×D7C7⋊D4C4○D28
kernelC24.62D14C14.C42C2×Dic7⋊C4C2×C23.D7C23×C28C23.D7C2×C28C22×C14C22×C14C23×C4C2×C14C22×C4C24C2×C4C23C23C23C22
# reps12221842234632412121224

Matrix representation of C24.62D14 ►in GL5(𝔽29)

10000
01000
00100
000280
000151
,
280000
028000
002800
00010
00001
,
10000
01000
00100
000280
000028
,
10000
028000
002800
000280
000028
,
170000
020900
0202500
00050
0001923
,
120000
04400
032500
0001814
000811

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
 

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