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G = C22×D14⋊C4  order 448 = 26·7

Direct product of C22 and D14⋊C4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C22×D14⋊C4, C23.64D28, C24.78D14, (C23×C4)⋊2D7, (C23×C28)⋊3C2, (C23×D7)⋊7C4, (C2×C28)⋊12C23, D14⋊7(C22×C4), (C22×C4)⋊41D14, (D7×C24).3C2, C2.3(C22×D28), C23.69(C4×D7), C14.38(C23×C4), (C23×Dic7)⋊6C2, (C2×Dic7)⋊8C23, C22.76(C2×D28), (C2×C14).285C24, (C22×C28)⋊55C22, C14.131(C22×D4), (C22×C14).204D4, C22.42(C23×D7), C23.103(C7⋊D4), C23.335(C22×D7), (C23×C14).107C22, (C22×C14).414C23, (C22×Dic7)⋊46C22, (C22×D7).236C23, (C23×D7).111C22, C14⋊2(C2×C22⋊C4), C7⋊2(C22×C22⋊C4), C22.79(C2×C4×D7), C2.38(D7×C22×C4), (C2×C4)⋊10(C22×D7), (C2×C14)⋊6(C22⋊C4), C2.2(C22×C7⋊D4), (C2×C14).572(C2×D4), (C22×D7)⋊15(C2×C4), C22.101(C2×C7⋊D4), (C2×C14).158(C22×C4), (C22×C14).105(C2×C4), SmallGroup(448,1240)

Series: Derived ►Chief ►Lower central ►Upper central

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

Generators and relations for C22×D14⋊C4
 G = < a,b,c,d,e | a2=b2=c14=d2=e4=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd=c-1, ce=ec, ede-1=c7d >

Subgroups: 3332 in 674 conjugacy classes, 247 normal (17 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C14, C22⋊C4, C22×C4, C22×C4, C24, C24, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C22⋊C4, C23×C4, C23×C4, C25, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C22×C22⋊C4, D14⋊C4, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, C23×D7, C23×C14, C2×D14⋊C4, C23×Dic7, C23×C28, D7×C24, C22×D14⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C24, D14, C2×C22⋊C4, C23×C4, C22×D4, C4×D7, D28, C7⋊D4, C22×D7, C22×C22⋊C4, D14⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, C23×D7, C2×D14⋊C4, D7×C22×C4, C22×D28, C22×C7⋊D4, C22×D14⋊C4

Smallest permutation representation of C22×D14⋊C4
►On 224 points
Generators in S224
(1 131)(2 132)(3 133)(4 134)(5 135)(6 136)(7 137)(8 138)(9 139)(10 140)(11 127)(12 128)(13 129)(14 130)(15 121)(16 122)(17 123)(18 124)(19 125)(20 126)(21 113)(22 114)(23 115)(24 116)(25 117)(26 118)(27 119)(28 120)(29 163)(30 164)(31 165)(32 166)(33 167)(34 168)(35 155)(36 156)(37 157)(38 158)(39 159)(40 160)(41 161)(42 162)(43 142)(44 143)(45 144)(46 145)(47 146)(48 147)(49 148)(50 149)(51 150)(52 151)(53 152)(54 153)(55 154)(56 141)(57 187)(58 188)(59 189)(60 190)(61 191)(62 192)(63 193)(64 194)(65 195)(66 196)(67 183)(68 184)(69 185)(70 186)(71 178)(72 179)(73 180)(74 181)(75 182)(76 169)(77 170)(78 171)(79 172)(80 173)(81 174)(82 175)(83 176)(84 177)(85 216)(86 217)(87 218)(88 219)(89 220)(90 221)(91 222)(92 223)(93 224)(94 211)(95 212)(96 213)(97 214)(98 215)(99 203)(100 204)(101 205)(102 206)(103 207)(104 208)(105 209)(106 210)(107 197)(108 198)(109 199)(110 200)(111 201)(112 202)

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

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

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

136 conjugacy classes

class 1 2A···2O2P···2W4A···4H4I···4P7A7B7C14A···14AS28A···28AV
order12···22···24···44···477714···1428···28
size11···114···142···214···142222···22···2

136 irreducible representations

dim1111112222222
type++++++++++
imageC1C2C2C2C2C4D4D7D14D14C4×D7D28C7⋊D4
kernelC22×D14⋊C4C2×D14⋊C4C23×Dic7C23×C28D7×C24C23×D7C22×C14C23×C4C22×C4C24C23C23C23
# reps1121111683183242424

Matrix representation of C22×D14⋊C4 ►in GL5(𝔽29)

280000
01000
00100
000280
000028
,
280000
028000
002800
00010
00001
,
10000
01000
00100
0001825
00044
,
10000
028000
00100
0001825
000111
,
10000
017000
00100
000112
0002718

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,18,4,0,0,0,25,4],[1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,18,1,0,0,0,25,11],[1,0,0,0,0,0,17,0,0,0,0,0,1,0,0,0,0,0,11,27,0,0,0,2,18] >;
 

C22×D14⋊C4 in GAP, Magma, Sage, TeX 

C_2^2\times D_{14}\rtimes C_4
 
% in TeX
 
G:=Group("C2^2xD14:C4");
 
// GroupNames label
 
G:=SmallGroup(448,1240);
 
// by ID
 
G=gap.SmallGroup(448,1240);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,1123,80,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^14=d^2=e^4=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d=c^-1,c*e=e*c,e*d*e^-1=c^7*d>;
 
// generators/relations
 

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×
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