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G = C24.9D14  order 448 = 26·7

9th non-split extension by C24 of D14 acting via D14/C7=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.9D14, (C2×Dic7).56D4, C22.240(D4×D7), (C22×C4).30D14, (C22×C14).64D4, C14.84(C4⋊D4), C23.17(C7⋊D4), C7⋊3(C23.11D4), C14.C42⋊14C2, C2.9(Dic7⋊D4), C14.33(C4.4D4), C22.97(C4○D28), (C22×C28).24C22, (C23×C14).35C22, C23.369(C22×D7), C14.15(C42⋊2C2), C2.21(D14.D4), C22.95(D4⋊2D7), (C22×C14).327C23, C2.21(Dic7.D4), C14.57(C22.D4), C2.7(C23.18D14), C2.6(C23.23D14), C2.13(C23.D14), (C22×Dic7).41C22, (C2×C22⋊C4).9D7, (C2×Dic7⋊C4)⋊10C2, (C2×C14).431(C2×D4), (C14×C22⋊C4).8C2, C22.125(C2×C7⋊D4), (C2×C23.D7).14C2, (C2×C14).143(C4○D4), SmallGroup(448,486)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C22×C14 — C24.9D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×C14 — C22×Dic7 — C2×C23.D7 — C24.9D14
Lower central
C7 — C22×C14 — C24.9D14
Upper central
C1 — C23 — C2×C22⋊C4

Generators and relations for C24.9D14
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=c, f2=bcd, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=be13 >

Subgroups: 692 in 170 conjugacy classes, 57 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C23, C23, C23, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C22×C14, C22×C14, C22×C14, C23.11D4, Dic7⋊C4, C23.D7, C7×C22⋊C4, C22×Dic7, C22×C28, C23×C14, C14.C42, C2×Dic7⋊C4, C2×C23.D7, C14×C22⋊C4, C24.9D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C22.D4, C4.4D4, C42⋊2C2, C7⋊D4, C22×D7, C23.11D4, C4○D28, D4×D7, D4⋊2D7, C2×C7⋊D4, C23.D14, D14.D4, Dic7.D4, C23.23D14, C23.18D14, Dic7⋊D4, C24.9D14

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

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

(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)

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

82 conjugacy classes

class 1 2A···2G2H2I4A4B4C4D4E···4L7A7B7C14A···14U14V···14AG28A···28X
order12···22244444···477714···1414···1428···28
size11···144444428···282222···24···44···4

82 irreducible representations

dim111112222222244
type+++++++++++-
imageC1C2C2C2C2D4D4D7C4○D4D14D14C7⋊D4C4○D28D4×D7D4⋊2D7
kernelC24.9D14C14.C42C2×Dic7⋊C4C2×C23.D7C14×C22⋊C4C2×Dic7C22×C14C2×C22⋊C4C2×C14C22×C4C24C23C22C22C22
# reps131212231063122439

Matrix representation of C24.9D14 ►in GL6(𝔽29)

2800000
0280000
001000
0002800
0000280
000071
,
2800000
0280000
001000
000100
0000280
0000028
,
100000
010000
001000
000100
0000280
0000028
,
100000
010000
0028000
0002800
000010
000001
,
7220000
7260000
000100
001000
0000120
0000317
,
2230000
2270000
0001700
0017000
00001922
00001010

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,7,0,0,0,0,0,1],[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],[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],[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],[7,7,0,0,0,0,22,26,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,12,3,0,0,0,0,0,17],[22,22,0,0,0,0,3,7,0,0,0,0,0,0,0,17,0,0,0,0,17,0,0,0,0,0,0,0,19,10,0,0,0,0,22,10] >;
 

C24.9D14 in GAP, Magma, Sage, TeX 

C_2^4._9D_{14}
 
% in TeX
 
G:=Group("C2^4.9D14");
 
// GroupNames label
 
G:=SmallGroup(448,486);
 
// by ID
 
G=gap.SmallGroup(448,486);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,254,387,100,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^14=c,f^2=b*c*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*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=b*e^13>;
 
// generators/relations
 

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