Copied to
clipboard

G = C24.63D14  order 448 = 26·7

3rd non-split extension by C24 of D14 acting via D14/C14=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.63D14, (C23×C4).5D7, (C22×C28)⋊10C4, (C23×C28).3C2, (C22×C4)⋊7Dic7, (C22×C14).192D4, (C22×C4).407D14, C23.82(C7⋊D4), C7⋊3(C23.34D4), C23.30(C2×Dic7), C14.C42⋊23C2, C22.62(C4○D28), (C23×C14).98C22, C23.302(C22×D7), C14.48(C42⋊C2), (C22×C14).362C23, (C22×C28).483C22, C22.19(C23.D7), C22.49(C22×Dic7), C14.68(C22.D4), C2.4(C23.23D14), (C22×Dic7).65C22, C2.11(C23.21D14), (C2×C28).281(C2×C4), C2.5(C2×C23.D7), (C2×C14).548(C2×D4), C14.69(C2×C22⋊C4), (C2×C4).66(C2×Dic7), C22.86(C2×C7⋊D4), (C2×C14).90(C4○D4), (C2×C23.D7).17C2, (C2×C14).192(C22×C4), (C22×C14).135(C2×C4), (C2×C14).109(C22⋊C4), SmallGroup(448,745)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C24.63D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×C14 — C22×Dic7 — C2×C23.D7 — C24.63D14
Lower central
C7 — C2×C14 — C24.63D14
Upper central
C1 — C23 — C23×C4

Generators and relations for C24.63D14
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=d, f2=bcd, ab=ba, ac=ca, faf-1=ad=da, ae=ea, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce13 >

Subgroups: 708 in 218 conjugacy classes, 87 normal (13 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, C23, C14, C14, C14, C22⋊C4, C22×C4, C22×C4, C24, Dic7, C28, C2×C14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C23×C4, C2×Dic7, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C23.34D4, C23.D7, C22×Dic7, C22×C28, C22×C28, C23×C14, C14.C42, C2×C23.D7, C23×C28, C24.63D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C4○D4, Dic7, D14, C2×C22⋊C4, C42⋊C2, C22.D4, C2×Dic7, C7⋊D4, C22×D7, C23.34D4, C23.D7, C4○D28, C22×Dic7, C2×C7⋊D4, C23.21D14, C23.23D14, C2×C23.D7, C24.63D14

Smallest permutation representation of C24.63D14
►On 224 points
Generators in S224
(1 67)(2 68)(3 69)(4 70)(5 71)(6 72)(7 73)(8 74)(9 75)(10 76)(11 77)(12 78)(13 79)(14 80)(15 81)(16 82)(17 83)(18 84)(19 57)(20 58)(21 59)(22 60)(23 61)(24 62)(25 63)(26 64)(27 65)(28 66)(29 218)(30 219)(31 220)(32 221)(33 222)(34 223)(35 224)(36 197)(37 198)(38 199)(39 200)(40 201)(41 202)(42 203)(43 204)(44 205)(45 206)(46 207)(47 208)(48 209)(49 210)(50 211)(51 212)(52 213)(53 214)(54 215)(55 216)(56 217)(85 160)(86 161)(87 162)(88 163)(89 164)(90 165)(91 166)(92 167)(93 168)(94 141)(95 142)(96 143)(97 144)(98 145)(99 146)(100 147)(101 148)(102 149)(103 150)(104 151)(105 152)(106 153)(107 154)(108 155)(109 156)(110 157)(111 158)(112 159)(113 171)(114 172)(115 173)(116 174)(117 175)(118 176)(119 177)(120 178)(121 179)(122 180)(123 181)(124 182)(125 183)(126 184)(127 185)(128 186)(129 187)(130 188)(131 189)(132 190)(133 191)(134 192)(135 193)(136 194)(137 195)(138 196)(139 169)(140 170)

(1 88)(2 89)(3 90)(4 91)(5 92)(6 93)(7 94)(8 95)(9 96)(10 97)(11 98)(12 99)(13 100)(14 101)(15 102)(16 103)(17 104)(18 105)(19 106)(20 107)(21 108)(22 109)(23 110)(24 111)(25 112)(26 85)(27 86)(28 87)(29 121)(30 122)(31 123)(32 124)(33 125)(34 126)(35 127)(36 128)(37 129)(38 130)(39 131)(40 132)(41 133)(42 134)(43 135)(44 136)(45 137)(46 138)(47 139)(48 140)(49 113)(50 114)(51 115)(52 116)(53 117)(54 118)(55 119)(56 120)(57 153)(58 154)(59 155)(60 156)(61 157)(62 158)(63 159)(64 160)(65 161)(66 162)(67 163)(68 164)(69 165)(70 166)(71 167)(72 168)(73 141)(74 142)(75 143)(76 144)(77 145)(78 146)(79 147)(80 148)(81 149)(82 150)(83 151)(84 152)(169 208)(170 209)(171 210)(172 211)(173 212)(174 213)(175 214)(176 215)(177 216)(178 217)(179 218)(180 219)(181 220)(182 221)(183 222)(184 223)(185 224)(186 197)(187 198)(188 199)(189 200)(190 201)(191 202)(192 203)(193 204)(194 205)(195 206)(196 207)

(1 163)(2 164)(3 165)(4 166)(5 167)(6 168)(7 141)(8 142)(9 143)(10 144)(11 145)(12 146)(13 147)(14 148)(15 149)(16 150)(17 151)(18 152)(19 153)(20 154)(21 155)(22 156)(23 157)(24 158)(25 159)(26 160)(27 161)(28 162)(29 193)(30 194)(31 195)(32 196)(33 169)(34 170)(35 171)(36 172)(37 173)(38 174)(39 175)(40 176)(41 177)(42 178)(43 179)(44 180)(45 181)(46 182)(47 183)(48 184)(49 185)(50 186)(51 187)(52 188)(53 189)(54 190)(55 191)(56 192)(57 106)(58 107)(59 108)(60 109)(61 110)(62 111)(63 112)(64 85)(65 86)(66 87)(67 88)(68 89)(69 90)(70 91)(71 92)(72 93)(73 94)(74 95)(75 96)(76 97)(77 98)(78 99)(79 100)(80 101)(81 102)(82 103)(83 104)(84 105)(113 224)(114 197)(115 198)(116 199)(117 200)(118 201)(119 202)(120 203)(121 204)(122 205)(123 206)(124 207)(125 208)(126 209)(127 210)(128 211)(129 212)(130 213)(131 214)(132 215)(133 216)(134 217)(135 218)(136 219)(137 220)(138 221)(139 222)(140 223)

(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 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 56 81 217)(2 177 82 119)(3 54 83 215)(4 175 84 117)(5 52 57 213)(6 173 58 115)(7 50 59 211)(8 171 60 113)(9 48 61 209)(10 169 62 139)(11 46 63 207)(12 195 64 137)(13 44 65 205)(14 193 66 135)(15 42 67 203)(16 191 68 133)(17 40 69 201)(18 189 70 131)(19 38 71 199)(20 187 72 129)(21 36 73 197)(22 185 74 127)(23 34 75 223)(24 183 76 125)(25 32 77 221)(26 181 78 123)(27 30 79 219)(28 179 80 121)(29 87 218 148)(31 85 220 146)(33 111 222 144)(35 109 224 142)(37 107 198 168)(39 105 200 166)(41 103 202 164)(43 101 204 162)(45 99 206 160)(47 97 208 158)(49 95 210 156)(51 93 212 154)(53 91 214 152)(55 89 216 150)(86 122 147 180)(88 120 149 178)(90 118 151 176)(92 116 153 174)(94 114 155 172)(96 140 157 170)(98 138 159 196)(100 136 161 194)(102 134 163 192)(104 132 165 190)(106 130 167 188)(108 128 141 186)(110 126 143 184)(112 124 145 182)
 
G:=sub<Sym(224)| (1,67)(2,68)(3,69)(4,70)(5,71)(6,72)(7,73)(8,74)(9,75)(10,76)(11,77)(12,78)(13,79)(14,80)(15,81)(16,82)(17,83)(18,84)(19,57)(20,58)(21,59)(22,60)(23,61)(24,62)(25,63)(26,64)(27,65)(28,66)(29,218)(30,219)(31,220)(32,221)(33,222)(34,223)(35,224)(36,197)(37,198)(38,199)(39,200)(40,201)(41,202)(42,203)(43,204)(44,205)(45,206)(46,207)(47,208)(48,209)(49,210)(50,211)(51,212)(52,213)(53,214)(54,215)(55,216)(56,217)(85,160)(86,161)(87,162)(88,163)(89,164)(90,165)(91,166)(92,167)(93,168)(94,141)(95,142)(96,143)(97,144)(98,145)(99,146)(100,147)(101,148)(102,149)(103,150)(104,151)(105,152)(106,153)(107,154)(108,155)(109,156)(110,157)(111,158)(112,159)(113,171)(114,172)(115,173)(116,174)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,169)(140,170), (1,88)(2,89)(3,90)(4,91)(5,92)(6,93)(7,94)(8,95)(9,96)(10,97)(11,98)(12,99)(13,100)(14,101)(15,102)(16,103)(17,104)(18,105)(19,106)(20,107)(21,108)(22,109)(23,110)(24,111)(25,112)(26,85)(27,86)(28,87)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,131)(40,132)(41,133)(42,134)(43,135)(44,136)(45,137)(46,138)(47,139)(48,140)(49,113)(50,114)(51,115)(52,116)(53,117)(54,118)(55,119)(56,120)(57,153)(58,154)(59,155)(60,156)(61,157)(62,158)(63,159)(64,160)(65,161)(66,162)(67,163)(68,164)(69,165)(70,166)(71,167)(72,168)(73,141)(74,142)(75,143)(76,144)(77,145)(78,146)(79,147)(80,148)(81,149)(82,150)(83,151)(84,152)(169,208)(170,209)(171,210)(172,211)(173,212)(174,213)(175,214)(176,215)(177,216)(178,217)(179,218)(180,219)(181,220)(182,221)(183,222)(184,223)(185,224)(186,197)(187,198)(188,199)(189,200)(190,201)(191,202)(192,203)(193,204)(194,205)(195,206)(196,207), (1,163)(2,164)(3,165)(4,166)(5,167)(6,168)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,193)(30,194)(31,195)(32,196)(33,169)(34,170)(35,171)(36,172)(37,173)(38,174)(39,175)(40,176)(41,177)(42,178)(43,179)(44,180)(45,181)(46,182)(47,183)(48,184)(49,185)(50,186)(51,187)(52,188)(53,189)(54,190)(55,191)(56,192)(57,106)(58,107)(59,108)(60,109)(61,110)(62,111)(63,112)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,92)(72,93)(73,94)(74,95)(75,96)(76,97)(77,98)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(113,224)(114,197)(115,198)(116,199)(117,200)(118,201)(119,202)(120,203)(121,204)(122,205)(123,206)(124,207)(125,208)(126,209)(127,210)(128,211)(129,212)(130,213)(131,214)(132,215)(133,216)(134,217)(135,218)(136,219)(137,220)(138,221)(139,222)(140,223), (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), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(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), (1,56,81,217)(2,177,82,119)(3,54,83,215)(4,175,84,117)(5,52,57,213)(6,173,58,115)(7,50,59,211)(8,171,60,113)(9,48,61,209)(10,169,62,139)(11,46,63,207)(12,195,64,137)(13,44,65,205)(14,193,66,135)(15,42,67,203)(16,191,68,133)(17,40,69,201)(18,189,70,131)(19,38,71,199)(20,187,72,129)(21,36,73,197)(22,185,74,127)(23,34,75,223)(24,183,76,125)(25,32,77,221)(26,181,78,123)(27,30,79,219)(28,179,80,121)(29,87,218,148)(31,85,220,146)(33,111,222,144)(35,109,224,142)(37,107,198,168)(39,105,200,166)(41,103,202,164)(43,101,204,162)(45,99,206,160)(47,97,208,158)(49,95,210,156)(51,93,212,154)(53,91,214,152)(55,89,216,150)(86,122,147,180)(88,120,149,178)(90,118,151,176)(92,116,153,174)(94,114,155,172)(96,140,157,170)(98,138,159,196)(100,136,161,194)(102,134,163,192)(104,132,165,190)(106,130,167,188)(108,128,141,186)(110,126,143,184)(112,124,145,182)>;
 
G:=Group( (1,67)(2,68)(3,69)(4,70)(5,71)(6,72)(7,73)(8,74)(9,75)(10,76)(11,77)(12,78)(13,79)(14,80)(15,81)(16,82)(17,83)(18,84)(19,57)(20,58)(21,59)(22,60)(23,61)(24,62)(25,63)(26,64)(27,65)(28,66)(29,218)(30,219)(31,220)(32,221)(33,222)(34,223)(35,224)(36,197)(37,198)(38,199)(39,200)(40,201)(41,202)(42,203)(43,204)(44,205)(45,206)(46,207)(47,208)(48,209)(49,210)(50,211)(51,212)(52,213)(53,214)(54,215)(55,216)(56,217)(85,160)(86,161)(87,162)(88,163)(89,164)(90,165)(91,166)(92,167)(93,168)(94,141)(95,142)(96,143)(97,144)(98,145)(99,146)(100,147)(101,148)(102,149)(103,150)(104,151)(105,152)(106,153)(107,154)(108,155)(109,156)(110,157)(111,158)(112,159)(113,171)(114,172)(115,173)(116,174)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,169)(140,170), (1,88)(2,89)(3,90)(4,91)(5,92)(6,93)(7,94)(8,95)(9,96)(10,97)(11,98)(12,99)(13,100)(14,101)(15,102)(16,103)(17,104)(18,105)(19,106)(20,107)(21,108)(22,109)(23,110)(24,111)(25,112)(26,85)(27,86)(28,87)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,127)(36,128)(37,129)(38,130)(39,131)(40,132)(41,133)(42,134)(43,135)(44,136)(45,137)(46,138)(47,139)(48,140)(49,113)(50,114)(51,115)(52,116)(53,117)(54,118)(55,119)(56,120)(57,153)(58,154)(59,155)(60,156)(61,157)(62,158)(63,159)(64,160)(65,161)(66,162)(67,163)(68,164)(69,165)(70,166)(71,167)(72,168)(73,141)(74,142)(75,143)(76,144)(77,145)(78,146)(79,147)(80,148)(81,149)(82,150)(83,151)(84,152)(169,208)(170,209)(171,210)(172,211)(173,212)(174,213)(175,214)(176,215)(177,216)(178,217)(179,218)(180,219)(181,220)(182,221)(183,222)(184,223)(185,224)(186,197)(187,198)(188,199)(189,200)(190,201)(191,202)(192,203)(193,204)(194,205)(195,206)(196,207), (1,163)(2,164)(3,165)(4,166)(5,167)(6,168)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,193)(30,194)(31,195)(32,196)(33,169)(34,170)(35,171)(36,172)(37,173)(38,174)(39,175)(40,176)(41,177)(42,178)(43,179)(44,180)(45,181)(46,182)(47,183)(48,184)(49,185)(50,186)(51,187)(52,188)(53,189)(54,190)(55,191)(56,192)(57,106)(58,107)(59,108)(60,109)(61,110)(62,111)(63,112)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,92)(72,93)(73,94)(74,95)(75,96)(76,97)(77,98)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(113,224)(114,197)(115,198)(116,199)(117,200)(118,201)(119,202)(120,203)(121,204)(122,205)(123,206)(124,207)(125,208)(126,209)(127,210)(128,211)(129,212)(130,213)(131,214)(132,215)(133,216)(134,217)(135,218)(136,219)(137,220)(138,221)(139,222)(140,223), (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), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(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), (1,56,81,217)(2,177,82,119)(3,54,83,215)(4,175,84,117)(5,52,57,213)(6,173,58,115)(7,50,59,211)(8,171,60,113)(9,48,61,209)(10,169,62,139)(11,46,63,207)(12,195,64,137)(13,44,65,205)(14,193,66,135)(15,42,67,203)(16,191,68,133)(17,40,69,201)(18,189,70,131)(19,38,71,199)(20,187,72,129)(21,36,73,197)(22,185,74,127)(23,34,75,223)(24,183,76,125)(25,32,77,221)(26,181,78,123)(27,30,79,219)(28,179,80,121)(29,87,218,148)(31,85,220,146)(33,111,222,144)(35,109,224,142)(37,107,198,168)(39,105,200,166)(41,103,202,164)(43,101,204,162)(45,99,206,160)(47,97,208,158)(49,95,210,156)(51,93,212,154)(53,91,214,152)(55,89,216,150)(86,122,147,180)(88,120,149,178)(90,118,151,176)(92,116,153,174)(94,114,155,172)(96,140,157,170)(98,138,159,196)(100,136,161,194)(102,134,163,192)(104,132,165,190)(106,130,167,188)(108,128,141,186)(110,126,143,184)(112,124,145,182) );
 
G=PermutationGroup([[(1,67),(2,68),(3,69),(4,70),(5,71),(6,72),(7,73),(8,74),(9,75),(10,76),(11,77),(12,78),(13,79),(14,80),(15,81),(16,82),(17,83),(18,84),(19,57),(20,58),(21,59),(22,60),(23,61),(24,62),(25,63),(26,64),(27,65),(28,66),(29,218),(30,219),(31,220),(32,221),(33,222),(34,223),(35,224),(36,197),(37,198),(38,199),(39,200),(40,201),(41,202),(42,203),(43,204),(44,205),(45,206),(46,207),(47,208),(48,209),(49,210),(50,211),(51,212),(52,213),(53,214),(54,215),(55,216),(56,217),(85,160),(86,161),(87,162),(88,163),(89,164),(90,165),(91,166),(92,167),(93,168),(94,141),(95,142),(96,143),(97,144),(98,145),(99,146),(100,147),(101,148),(102,149),(103,150),(104,151),(105,152),(106,153),(107,154),(108,155),(109,156),(110,157),(111,158),(112,159),(113,171),(114,172),(115,173),(116,174),(117,175),(118,176),(119,177),(120,178),(121,179),(122,180),(123,181),(124,182),(125,183),(126,184),(127,185),(128,186),(129,187),(130,188),(131,189),(132,190),(133,191),(134,192),(135,193),(136,194),(137,195),(138,196),(139,169),(140,170)], [(1,88),(2,89),(3,90),(4,91),(5,92),(6,93),(7,94),(8,95),(9,96),(10,97),(11,98),(12,99),(13,100),(14,101),(15,102),(16,103),(17,104),(18,105),(19,106),(20,107),(21,108),(22,109),(23,110),(24,111),(25,112),(26,85),(27,86),(28,87),(29,121),(30,122),(31,123),(32,124),(33,125),(34,126),(35,127),(36,128),(37,129),(38,130),(39,131),(40,132),(41,133),(42,134),(43,135),(44,136),(45,137),(46,138),(47,139),(48,140),(49,113),(50,114),(51,115),(52,116),(53,117),(54,118),(55,119),(56,120),(57,153),(58,154),(59,155),(60,156),(61,157),(62,158),(63,159),(64,160),(65,161),(66,162),(67,163),(68,164),(69,165),(70,166),(71,167),(72,168),(73,141),(74,142),(75,143),(76,144),(77,145),(78,146),(79,147),(80,148),(81,149),(82,150),(83,151),(84,152),(169,208),(170,209),(171,210),(172,211),(173,212),(174,213),(175,214),(176,215),(177,216),(178,217),(179,218),(180,219),(181,220),(182,221),(183,222),(184,223),(185,224),(186,197),(187,198),(188,199),(189,200),(190,201),(191,202),(192,203),(193,204),(194,205),(195,206),(196,207)], [(1,163),(2,164),(3,165),(4,166),(5,167),(6,168),(7,141),(8,142),(9,143),(10,144),(11,145),(12,146),(13,147),(14,148),(15,149),(16,150),(17,151),(18,152),(19,153),(20,154),(21,155),(22,156),(23,157),(24,158),(25,159),(26,160),(27,161),(28,162),(29,193),(30,194),(31,195),(32,196),(33,169),(34,170),(35,171),(36,172),(37,173),(38,174),(39,175),(40,176),(41,177),(42,178),(43,179),(44,180),(45,181),(46,182),(47,183),(48,184),(49,185),(50,186),(51,187),(52,188),(53,189),(54,190),(55,191),(56,192),(57,106),(58,107),(59,108),(60,109),(61,110),(62,111),(63,112),(64,85),(65,86),(66,87),(67,88),(68,89),(69,90),(70,91),(71,92),(72,93),(73,94),(74,95),(75,96),(76,97),(77,98),(78,99),(79,100),(80,101),(81,102),(82,103),(83,104),(84,105),(113,224),(114,197),(115,198),(116,199),(117,200),(118,201),(119,202),(120,203),(121,204),(122,205),(123,206),(124,207),(125,208),(126,209),(127,210),(128,211),(129,212),(130,213),(131,214),(132,215),(133,216),(134,217),(135,218),(136,219),(137,220),(138,221),(139,222),(140,223)], [(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)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28),(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)], [(1,56,81,217),(2,177,82,119),(3,54,83,215),(4,175,84,117),(5,52,57,213),(6,173,58,115),(7,50,59,211),(8,171,60,113),(9,48,61,209),(10,169,62,139),(11,46,63,207),(12,195,64,137),(13,44,65,205),(14,193,66,135),(15,42,67,203),(16,191,68,133),(17,40,69,201),(18,189,70,131),(19,38,71,199),(20,187,72,129),(21,36,73,197),(22,185,74,127),(23,34,75,223),(24,183,76,125),(25,32,77,221),(26,181,78,123),(27,30,79,219),(28,179,80,121),(29,87,218,148),(31,85,220,146),(33,111,222,144),(35,109,224,142),(37,107,198,168),(39,105,200,166),(41,103,202,164),(43,101,204,162),(45,99,206,160),(47,97,208,158),(49,95,210,156),(51,93,212,154),(53,91,214,152),(55,89,216,150),(86,122,147,180),(88,120,149,178),(90,118,151,176),(92,116,153,174),(94,114,155,172),(96,140,157,170),(98,138,159,196),(100,136,161,194),(102,134,163,192),(104,132,165,190),(106,130,167,188),(108,128,141,186),(110,126,143,184),(112,124,145,182)]])
 

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

dim1111122222222
type++++++-++
imageC1C2C2C2C4D4D7C4○D4Dic7D14D14C7⋊D4C4○D28
kernelC24.63D14C14.C42C2×C23.D7C23×C28C22×C28C22×C14C23×C4C2×C14C22×C4C22×C4C24C23C22
# reps1421843812632448

Matrix representation of C24.63D14 ►in GL5(𝔽29)

10000
01000
00100
000127
000028
,
280000
028000
002800
00010
00001
,
10000
028000
002800
00010
00001
,
10000
01000
00100
000280
000028
,
280000
082800
0132000
000212
000014
,
120000
081200
022100
00097
000920

G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,27,28],[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],[1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1],[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],[28,0,0,0,0,0,8,13,0,0,0,28,20,0,0,0,0,0,2,0,0,0,0,12,14],[12,0,0,0,0,0,8,2,0,0,0,12,21,0,0,0,0,0,9,9,0,0,0,7,20] >;
 

C24.63D14 in GAP, Magma, Sage, TeX 

C_2^4._{63}D_{14}
 
% in TeX
 
G:=Group("C2^4.63D14");
 
// GroupNames label
 
G:=SmallGroup(448,745);
 
// by ID
 
G=gap.SmallGroup(448,745);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,477,422,184,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^14=d,f^2=b*c*d,a*b=b*a,a*c=c*a,f*a*f^-1=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=c*e^13>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁