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G = C24.13D14  order 448 = 26·7

13rd non-split extension by C24 of D14 acting via D14/C7=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.13D14, (C2×C28)⋊21D4, C14.65(C4×D4), (C2×Dic7)⋊10D4, C23.18(C4×D7), C2.1(C28⋊D4), (C22×C4).32D14, C22.102(D4×D7), C2.7(D14⋊D4), C14.85(C4⋊D4), C14.12(C4⋊1D4), Dic7⋊1(C22⋊C4), C2.3(Dic7⋊D4), C14.34(C4.4D4), C22.54(C4○D28), (C23×C14).40C22, (C22×C28).25C22, C7⋊2(C24.3C22), (C23×D7).13C22, C23.284(C22×D7), C2.28(Dic7⋊4D4), C22.49(D4⋊2D7), (C22×C14).331C23, C2.7(Dic7.D4), (C22×Dic7).44C22, (C2×C7⋊D4)⋊5C4, (C2×D14⋊C4)⋊5C2, (C2×C4)⋊9(C7⋊D4), (C2×C22⋊C4)⋊4D7, (C2×C4×Dic7)⋊24C2, C2.10(C4×C7⋊D4), (C2×C23.D7)⋊4C2, C2.30(D7×C22⋊C4), C22.128(C2×C4×D7), (C14×C22⋊C4)⋊23C2, (C2×Dic7⋊C4)⋊11C2, (C2×C14).323(C2×D4), C14.29(C2×C22⋊C4), (C22×C7⋊D4).3C2, C22.52(C2×C7⋊D4), (C22×C14).54(C2×C4), (C2×Dic7).60(C2×C4), (C22×D7).20(C2×C4), (C2×C14).146(C4○D4), (C2×C14).110(C22×C4), SmallGroup(448,491)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C24.13D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×C14 — C23×D7 — C22×C7⋊D4 — C24.13D14
Lower central
C7 — C2×C14 — C24.13D14
Upper central
C1 — C23 — C2×C22⋊C4

Generators and relations for C24.13D14
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=b, f2=db=bd, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bc=cb, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=de13 >

Subgroups: 1300 in 258 conjugacy classes, 77 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, C24, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C22×D4, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C22×C14, C22×C14, C24.3C22, C4×Dic7, Dic7⋊C4, D14⋊C4, C23.D7, C7×C22⋊C4, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, C23×D7, C23×C14, C2×C4×Dic7, C2×Dic7⋊C4, C2×D14⋊C4, C2×C23.D7, C14×C22⋊C4, C22×C7⋊D4, C24.13D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C4○D4, D14, C2×C22⋊C4, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4×D7, C7⋊D4, C22×D7, C24.3C22, C2×C4×D7, C4○D28, D4×D7, D4⋊2D7, C2×C7⋊D4, D7×C22⋊C4, Dic7⋊4D4, D14⋊D4, Dic7.D4, C4×C7⋊D4, Dic7⋊D4, C28⋊D4, C24.13D14

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

(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)

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

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

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

88 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C4D4E4F4G···4N4O4P7A7B7C14A···14U14V···14AG28A···28X
order12···222224444444···44477714···1414···1428···28
size11···144282822224414···1428282222···24···44···4

88 irreducible representations

dim1111111122222222244
type+++++++++++++-
imageC1C2C2C2C2C2C2C4D4D4D7C4○D4D14D14C7⋊D4C4×D7C4○D28D4×D7D4⋊2D7
kernelC24.13D14C2×C4×Dic7C2×Dic7⋊C4C2×D14⋊C4C2×C23.D7C14×C22⋊C4C22×C7⋊D4C2×C7⋊D4C2×Dic7C2×C28C2×C22⋊C4C2×C14C22×C4C24C2×C4C23C22C22C22
# reps1112111862346312121293

Matrix representation of C24.13D14 ►in GL6(𝔽29)

2800000
0280000
00282700
000100
0000280
0000261
,
2800000
0280000
0028000
0002800
0000280
0000028
,
100000
010000
0028000
0002800
000010
000001
,
100000
010000
001000
000100
0000280
0000028
,
440000
2530000
0017000
0001700
0000178
0000012
,
25250000
2640000
0012000
00171700
0000178
00002212

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,27,1,0,0,0,0,0,0,28,26,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[4,25,0,0,0,0,4,3,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,8,12],[25,26,0,0,0,0,25,4,0,0,0,0,0,0,12,17,0,0,0,0,0,17,0,0,0,0,0,0,17,22,0,0,0,0,8,12] >;
 

C24.13D14 in GAP, Magma, Sage, TeX 

C_2^4._{13}D_{14}
 
% in TeX
 
G:=Group("C2^4.13D14");
 
// GroupNames label
 
G:=SmallGroup(448,491);
 
// by ID
 
G=gap.SmallGroup(448,491);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,758,387,58,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^14=b,f^2=d*b=b*d,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*c*d,b*c=c*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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