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## G = C2×D14⋊2Q8order 448 = 26·7

### Direct product of C2 and D14⋊2Q8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — C2×D14⋊2Q8
 Chief series C1 — C7 — C14 — C2×C14 — C22×D7 — C23×D7 — D7×C22×C4 — C2×D14⋊2Q8
 Lower central C7 — C2×C14 — C2×D14⋊2Q8
 Upper central C1 — C23 — C2×C4⋊C4

Generators and relations for C2×D142Q8
G = < a,b,c,d,e | a2=b14=c2=d4=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc=dbd-1=b-1, be=eb, dcd-1=b5c, ce=ec, ede-1=d-1 >

Subgroups: 1476 in 322 conjugacy classes, 135 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×Q8, C24, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C22⋊C4, C2×C4⋊C4, C2×C4⋊C4, C22⋊Q8, C23×C4, C22×Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C2×C22⋊Q8, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, D142Q8, C2×C4⋊Dic7, C2×D14⋊C4, C14×C4⋊C4, C22×Dic14, D7×C22×C4, C2×D142Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, C24, D14, C22⋊Q8, C22×D4, C22×Q8, C2×C4○D4, D28, C22×D7, C2×C22⋊Q8, C2×D28, D42D7, Q8×D7, C23×D7, D142Q8, C22×D28, C2×D42D7, C2×Q8×D7, C2×D142Q8

Smallest permutation representation of C2×D142Q8
On 224 points
Generators in S224
(1 55)(2 56)(3 43)(4 44)(5 45)(6 46)(7 47)(8 48)(9 49)(10 50)(11 51)(12 52)(13 53)(14 54)(15 206)(16 207)(17 208)(18 209)(19 210)(20 197)(21 198)(22 199)(23 200)(24 201)(25 202)(26 203)(27 204)(28 205)(29 71)(30 72)(31 73)(32 74)(33 75)(34 76)(35 77)(36 78)(37 79)(38 80)(39 81)(40 82)(41 83)(42 84)(57 95)(58 96)(59 97)(60 98)(61 85)(62 86)(63 87)(64 88)(65 89)(66 90)(67 91)(68 92)(69 93)(70 94)(99 176)(100 177)(101 178)(102 179)(103 180)(104 181)(105 182)(106 169)(107 170)(108 171)(109 172)(110 173)(111 174)(112 175)(113 149)(114 150)(115 151)(116 152)(117 153)(118 154)(119 141)(120 142)(121 143)(122 144)(123 145)(124 146)(125 147)(126 148)(127 195)(128 196)(129 183)(130 184)(131 185)(132 186)(133 187)(134 188)(135 189)(136 190)(137 191)(138 192)(139 193)(140 194)(155 212)(156 213)(157 214)(158 215)(159 216)(160 217)(161 218)(162 219)(163 220)(164 221)(165 222)(166 223)(167 224)(168 211)
(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)
(1 167)(2 166)(3 165)(4 164)(5 163)(6 162)(7 161)(8 160)(9 159)(10 158)(11 157)(12 156)(13 155)(14 168)(15 39)(16 38)(17 37)(18 36)(19 35)(20 34)(21 33)(22 32)(23 31)(24 30)(25 29)(26 42)(27 41)(28 40)(43 222)(44 221)(45 220)(46 219)(47 218)(48 217)(49 216)(50 215)(51 214)(52 213)(53 212)(54 211)(55 224)(56 223)(57 184)(58 183)(59 196)(60 195)(61 194)(62 193)(63 192)(64 191)(65 190)(66 189)(67 188)(68 187)(69 186)(70 185)(71 202)(72 201)(73 200)(74 199)(75 198)(76 197)(77 210)(78 209)(79 208)(80 207)(81 206)(82 205)(83 204)(84 203)(85 140)(86 139)(87 138)(88 137)(89 136)(90 135)(91 134)(92 133)(93 132)(94 131)(95 130)(96 129)(97 128)(98 127)(99 145)(100 144)(101 143)(102 142)(103 141)(104 154)(105 153)(106 152)(107 151)(108 150)(109 149)(110 148)(111 147)(112 146)(113 172)(114 171)(115 170)(116 169)(117 182)(118 181)(119 180)(120 179)(121 178)(122 177)(123 176)(124 175)(125 174)(126 173)
(1 208 168 73)(2 207 155 72)(3 206 156 71)(4 205 157 84)(5 204 158 83)(6 203 159 82)(7 202 160 81)(8 201 161 80)(9 200 162 79)(10 199 163 78)(11 198 164 77)(12 197 165 76)(13 210 166 75)(14 209 167 74)(15 213 29 43)(16 212 30 56)(17 211 31 55)(18 224 32 54)(19 223 33 53)(20 222 34 52)(21 221 35 51)(22 220 36 50)(23 219 37 49)(24 218 38 48)(25 217 39 47)(26 216 40 46)(27 215 41 45)(28 214 42 44)(57 114 190 174)(58 113 191 173)(59 126 192 172)(60 125 193 171)(61 124 194 170)(62 123 195 169)(63 122 196 182)(64 121 183 181)(65 120 184 180)(66 119 185 179)(67 118 186 178)(68 117 187 177)(69 116 188 176)(70 115 189 175)(85 146 140 107)(86 145 127 106)(87 144 128 105)(88 143 129 104)(89 142 130 103)(90 141 131 102)(91 154 132 101)(92 153 133 100)(93 152 134 99)(94 151 135 112)(95 150 136 111)(96 149 137 110)(97 148 138 109)(98 147 139 108)
(1 180 168 120)(2 181 155 121)(3 182 156 122)(4 169 157 123)(5 170 158 124)(6 171 159 125)(7 172 160 126)(8 173 161 113)(9 174 162 114)(10 175 163 115)(11 176 164 116)(12 177 165 117)(13 178 166 118)(14 179 167 119)(15 128 29 87)(16 129 30 88)(17 130 31 89)(18 131 32 90)(19 132 33 91)(20 133 34 92)(21 134 35 93)(22 135 36 94)(23 136 37 95)(24 137 38 96)(25 138 39 97)(26 139 40 98)(27 140 41 85)(28 127 42 86)(43 105 213 144)(44 106 214 145)(45 107 215 146)(46 108 216 147)(47 109 217 148)(48 110 218 149)(49 111 219 150)(50 112 220 151)(51 99 221 152)(52 100 222 153)(53 101 223 154)(54 102 224 141)(55 103 211 142)(56 104 212 143)(57 200 190 79)(58 201 191 80)(59 202 192 81)(60 203 193 82)(61 204 194 83)(62 205 195 84)(63 206 196 71)(64 207 183 72)(65 208 184 73)(66 209 185 74)(67 210 186 75)(68 197 187 76)(69 198 188 77)(70 199 189 78)

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

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

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

88 conjugacy classes

 class 1 2A ··· 2G 2H 2I 2J 2K 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L 4M 4N 4O 4P 7A 7B 7C 14A ··· 14U 28A ··· 28AJ order 1 2 ··· 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 ··· 1 14 14 14 14 2 2 2 2 4 4 4 4 14 14 14 14 28 28 28 28 2 2 2 2 ··· 2 4 ··· 4

88 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 type + + + + + + + + - + + + + - - image C1 C2 C2 C2 C2 C2 C2 D4 Q8 D7 C4○D4 D14 D14 D28 D4⋊2D7 Q8×D7 kernel C2×D14⋊2Q8 D14⋊2Q8 C2×C4⋊Dic7 C2×D14⋊C4 C14×C4⋊C4 C22×Dic14 D7×C22×C4 C2×C28 C22×D7 C2×C4⋊C4 C2×C14 C4⋊C4 C22×C4 C2×C4 C22 C22 # reps 1 8 2 2 1 1 1 4 4 3 4 12 9 24 6 6

Matrix representation of C2×D142Q8 in GL6(𝔽29)

 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
,
 28 0 0 0 0 0 0 28 0 0 0 0 0 0 20 10 0 0 0 0 9 6 0 0 0 0 0 0 28 0 0 0 0 0 0 28
,
 28 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 16 28 0 0 0 0 0 0 1 0 0 0 0 0 0 28
,
 0 28 0 0 0 0 28 0 0 0 0 0 0 0 6 20 0 0 0 0 20 23 0 0 0 0 0 0 0 28 0 0 0 0 1 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 12 0 0 0 0 0 0 17

G:=sub<GL(6,GF(29))| [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],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,20,9,0,0,0,0,10,6,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,16,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28],[0,28,0,0,0,0,28,0,0,0,0,0,0,0,6,20,0,0,0,0,20,23,0,0,0,0,0,0,0,1,0,0,0,0,28,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,0,17] >;

C2×D142Q8 in GAP, Magma, Sage, TeX

C_2\times D_{14}\rtimes_2Q_8
% in TeX

G:=Group("C2xD14:2Q8");
// GroupNames label

G:=SmallGroup(448,962);
// by ID

G=gap.SmallGroup(448,962);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,184,675,297,192,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^14=c^2=d^4=1,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=b^5*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽