Copied to
clipboard

G = C24.46D14  order 448 = 26·7

4th non-split extension by C24 of D14 acting via D14/D7=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.46D14, C23.10Dic14, C14.43(C4×D4), C23.D7⋊10C4, C22.97(D4×D7), C23.25(C4×D7), C14.35C22≀C2, (C22×C14).62D4, (C22×C4).26D14, C2.1(C23⋊D14), (C22×C14).11Q8, C7⋊2(C23.8Q8), C22⋊2(Dic7⋊C4), (C2×Dic7).173D4, C23.51(C7⋊D4), C14.16(C22⋊Q8), (C23×Dic7).4C2, C14.C42⋊12C2, (C22×C28).23C22, (C23×C14).29C22, C22.24(C2×Dic14), C23.279(C22×D7), C2.26(Dic7⋊4D4), C22.45(D4⋊2D7), (C22×C14).321C23, C2.6(C22⋊Dic14), C14.72(C22.D4), C2.3(C23.18D14), (C22×Dic7).37C22, (C2×C14)⋊2(C4⋊C4), C14.30(C2×C4⋊C4), (C2×Dic7⋊C4)⋊8C2, (C2×Dic7)⋊4(C2×C4), C2.6(C2×Dic7⋊C4), (C2×C22⋊C4).8D7, (C2×C14).31(C2×Q8), C22.125(C2×C4×D7), (C2×C14).315(C2×D4), (C14×C22⋊C4).7C2, C22.49(C2×C7⋊D4), (C2×C23.D7).8C2, (C22×C14).49(C2×C4), (C2×C14).141(C4○D4), (C2×C14).107(C22×C4), SmallGroup(448,480)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C24.46D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×C14 — C22×Dic7 — C23×Dic7 — C24.46D14
Lower central
C7 — C2×C14 — C24.46D14
Upper central
C1 — C23 — C2×C22⋊C4

Generators and relations for C24.46D14
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=d, f2=b, ab=ba, eae-1=faf-1=ac=ca, ad=da, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=be13 >

Subgroups: 916 in 234 conjugacy classes, 83 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, 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×C22⋊C4, C2×C4⋊C4, C23×C4, C2×Dic7, C2×Dic7, C2×C28, C22×C14, C22×C14, C22×C14, C23.8Q8, Dic7⋊C4, C23.D7, C7×C22⋊C4, C22×Dic7, C22×Dic7, C22×C28, C23×C14, C14.C42, C2×Dic7⋊C4, C2×C23.D7, C14×C22⋊C4, C23×Dic7, C24.46D14
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, D4×D7, D4⋊2D7, C2×C7⋊D4, C22⋊Dic14, Dic7⋊4D4, C2×Dic7⋊C4, C23.18D14, C23⋊D14, C24.46D14

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

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

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

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

88 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C4D4E···4L4M4N4O4P7A7B7C14A···14U14V···14AG28A···28X
order12···2222244444···4444477714···1414···1428···28
size11···12222444414···14282828282222···24···44···4

88 irreducible representations

dim1111111222222222244
type++++++++-+++-+-
imageC1C2C2C2C2C2C4D4D4Q8D7C4○D4D14D14Dic14C4×D7C7⋊D4D4×D7D4⋊2D7
kernelC24.46D14C14.C42C2×Dic7⋊C4C2×C23.D7C14×C22⋊C4C23×Dic7C23.D7C2×Dic7C22×C14C22×C14C2×C22⋊C4C2×C14C22×C4C24C23C23C23C22C22
# reps1221118422346312121266

Matrix representation of C24.46D14 ►in GL6(𝔽29)

2800000
0280000
0028000
0002800
0000280
000001
,
2800000
0280000
001000
000100
0000280
0000028
,
100000
010000
001000
000100
0000280
0000028
,
100000
010000
0028000
0002800
000010
000001
,
16130000
25130000
0011800
0002100
000001
000010
,
670000
3230000
0027700
0012200
000001
0000280

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[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],[16,25,0,0,0,0,13,13,0,0,0,0,0,0,11,0,0,0,0,0,8,21,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[6,3,0,0,0,0,7,23,0,0,0,0,0,0,27,12,0,0,0,0,7,2,0,0,0,0,0,0,0,28,0,0,0,0,1,0] >;
 

C24.46D14 in GAP, Magma, Sage, TeX 

C_2^4._{46}D_{14}
 
% in TeX
 
G:=Group("C2^4.46D14");
 
// GroupNames label
 
G:=SmallGroup(448,480);
 
// by ID
 
G=gap.SmallGroup(448,480);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,254,219,184,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^14=d,f^2=b,a*b=b*a,e*a*e^-1=f*a*f^-1=a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=b*e^13>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁