direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×2- 1+4, C28.91C24, C14.25C25, C2.5(C24×C14), C4.14(C23×C14), (C22×Q8)⋊10C14, (Q8×C14)⋊57C22, D4.8(C22×C14), (C7×D4).41C23, (C7×Q8).42C23, Q8.8(C22×C14), (C2×C14).388C24, (C2×C28).690C23, C22.3(C23×C14), (D4×C14).336C22, C23.47(C22×C14), (C22×C28).468C22, (C22×C14).270C23, (Q8×C2×C14)⋊22C2, C4○D4⋊7(C2×C14), (C14×C4○D4)⋊30C2, (C2×C4○D4)⋊14C14, (C2×Q8)⋊17(C2×C14), (C2×D4).82(C2×C14), (C7×C4○D4)⋊27C22, (C22×C4).79(C2×C14), (C2×C4).51(C22×C14), SmallGroup(448,1390)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×2- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=e2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=b2d >
Subgroups: 834 in 794 conjugacy classes, 754 normal (8 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, D4, Q8, C23, C14, C14, C14, C22×C4, C2×D4, C2×Q8, C4○D4, C28, C2×C14, C2×C14, C2×C14, C22×Q8, C2×C4○D4, 2- 1+4, C2×C28, C7×D4, C7×Q8, C22×C14, C2×2- 1+4, C22×C28, D4×C14, Q8×C14, C7×C4○D4, Q8×C2×C14, C14×C4○D4, C7×2- 1+4, C14×2- 1+4
Quotients: C1, C2, C22, C7, C23, C14, C24, C2×C14, 2- 1+4, C25, C22×C14, C2×2- 1+4, C23×C14, C7×2- 1+4, C24×C14, C14×2- 1+4
►On 224 points
Generators in S224
(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 99 163 188)(2 100 164 189)(3 101 165 190)(4 102 166 191)(5 103 167 192)(6 104 168 193)(7 105 155 194)(8 106 156 195)(9 107 157 196)(10 108 158 183)(11 109 159 184)(12 110 160 185)(13 111 161 186)(14 112 162 187)(15 42 119 198)(16 29 120 199)(17 30 121 200)(18 31 122 201)(19 32 123 202)(20 33 124 203)(21 34 125 204)(22 35 126 205)(23 36 113 206)(24 37 114 207)(25 38 115 208)(26 39 116 209)(27 40 117 210)(28 41 118 197)(43 95 181 147)(44 96 182 148)(45 97 169 149)(46 98 170 150)(47 85 171 151)(48 86 172 152)(49 87 173 153)(50 88 174 154)(51 89 175 141)(52 90 176 142)(53 91 177 143)(54 92 178 144)(55 93 179 145)(56 94 180 146)(57 134 77 221)(58 135 78 222)(59 136 79 223)(60 137 80 224)(61 138 81 211)(62 139 82 212)(63 140 83 213)(64 127 84 214)(65 128 71 215)(66 129 72 216)(67 130 73 217)(68 131 74 218)(69 132 75 219)(70 133 76 220)
(29 199)(30 200)(31 201)(32 202)(33 203)(34 204)(35 205)(36 206)(37 207)(38 208)(39 209)(40 210)(41 197)(42 198)(43 181)(44 182)(45 169)(46 170)(47 171)(48 172)(49 173)(50 174)(51 175)(52 176)(53 177)(54 178)(55 179)(56 180)(99 188)(100 189)(101 190)(102 191)(103 192)(104 193)(105 194)(106 195)(107 196)(108 183)(109 184)(110 185)(111 186)(112 187)(127 214)(128 215)(129 216)(130 217)(131 218)(132 219)(133 220)(134 221)(135 222)(136 223)(137 224)(138 211)(139 212)(140 213)
(1 22 163 126)(2 23 164 113)(3 24 165 114)(4 25 166 115)(5 26 167 116)(6 27 168 117)(7 28 155 118)(8 15 156 119)(9 16 157 120)(10 17 158 121)(11 18 159 122)(12 19 160 123)(13 20 161 124)(14 21 162 125)(29 196 199 107)(30 183 200 108)(31 184 201 109)(32 185 202 110)(33 186 203 111)(34 187 204 112)(35 188 205 99)(36 189 206 100)(37 190 207 101)(38 191 208 102)(39 192 209 103)(40 193 210 104)(41 194 197 105)(42 195 198 106)(43 222 181 135)(44 223 182 136)(45 224 169 137)(46 211 170 138)(47 212 171 139)(48 213 172 140)(49 214 173 127)(50 215 174 128)(51 216 175 129)(52 217 176 130)(53 218 177 131)(54 219 178 132)(55 220 179 133)(56 221 180 134)(57 146 77 94)(58 147 78 95)(59 148 79 96)(60 149 80 97)(61 150 81 98)(62 151 82 85)(63 152 83 86)(64 153 84 87)(65 154 71 88)(66 141 72 89)(67 142 73 90)(68 143 74 91)(69 144 75 92)(70 145 76 93)
(1 62 163 82)(2 63 164 83)(3 64 165 84)(4 65 166 71)(5 66 167 72)(6 67 168 73)(7 68 155 74)(8 69 156 75)(9 70 157 76)(10 57 158 77)(11 58 159 78)(12 59 160 79)(13 60 161 80)(14 61 162 81)(15 92 119 144)(16 93 120 145)(17 94 121 146)(18 95 122 147)(19 96 123 148)(20 97 124 149)(21 98 125 150)(22 85 126 151)(23 86 113 152)(24 87 114 153)(25 88 115 154)(26 89 116 141)(27 90 117 142)(28 91 118 143)(29 179 199 55)(30 180 200 56)(31 181 201 43)(32 182 202 44)(33 169 203 45)(34 170 204 46)(35 171 205 47)(36 172 206 48)(37 173 207 49)(38 174 208 50)(39 175 209 51)(40 176 210 52)(41 177 197 53)(42 178 198 54)(99 139 188 212)(100 140 189 213)(101 127 190 214)(102 128 191 215)(103 129 192 216)(104 130 193 217)(105 131 194 218)(106 132 195 219)(107 133 196 220)(108 134 183 221)(109 135 184 222)(110 136 185 223)(111 137 186 224)(112 138 187 211)
G:=sub<Sym(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), (1,99,163,188)(2,100,164,189)(3,101,165,190)(4,102,166,191)(5,103,167,192)(6,104,168,193)(7,105,155,194)(8,106,156,195)(9,107,157,196)(10,108,158,183)(11,109,159,184)(12,110,160,185)(13,111,161,186)(14,112,162,187)(15,42,119,198)(16,29,120,199)(17,30,121,200)(18,31,122,201)(19,32,123,202)(20,33,124,203)(21,34,125,204)(22,35,126,205)(23,36,113,206)(24,37,114,207)(25,38,115,208)(26,39,116,209)(27,40,117,210)(28,41,118,197)(43,95,181,147)(44,96,182,148)(45,97,169,149)(46,98,170,150)(47,85,171,151)(48,86,172,152)(49,87,173,153)(50,88,174,154)(51,89,175,141)(52,90,176,142)(53,91,177,143)(54,92,178,144)(55,93,179,145)(56,94,180,146)(57,134,77,221)(58,135,78,222)(59,136,79,223)(60,137,80,224)(61,138,81,211)(62,139,82,212)(63,140,83,213)(64,127,84,214)(65,128,71,215)(66,129,72,216)(67,130,73,217)(68,131,74,218)(69,132,75,219)(70,133,76,220), (29,199)(30,200)(31,201)(32,202)(33,203)(34,204)(35,205)(36,206)(37,207)(38,208)(39,209)(40,210)(41,197)(42,198)(43,181)(44,182)(45,169)(46,170)(47,171)(48,172)(49,173)(50,174)(51,175)(52,176)(53,177)(54,178)(55,179)(56,180)(99,188)(100,189)(101,190)(102,191)(103,192)(104,193)(105,194)(106,195)(107,196)(108,183)(109,184)(110,185)(111,186)(112,187)(127,214)(128,215)(129,216)(130,217)(131,218)(132,219)(133,220)(134,221)(135,222)(136,223)(137,224)(138,211)(139,212)(140,213), (1,22,163,126)(2,23,164,113)(3,24,165,114)(4,25,166,115)(5,26,167,116)(6,27,168,117)(7,28,155,118)(8,15,156,119)(9,16,157,120)(10,17,158,121)(11,18,159,122)(12,19,160,123)(13,20,161,124)(14,21,162,125)(29,196,199,107)(30,183,200,108)(31,184,201,109)(32,185,202,110)(33,186,203,111)(34,187,204,112)(35,188,205,99)(36,189,206,100)(37,190,207,101)(38,191,208,102)(39,192,209,103)(40,193,210,104)(41,194,197,105)(42,195,198,106)(43,222,181,135)(44,223,182,136)(45,224,169,137)(46,211,170,138)(47,212,171,139)(48,213,172,140)(49,214,173,127)(50,215,174,128)(51,216,175,129)(52,217,176,130)(53,218,177,131)(54,219,178,132)(55,220,179,133)(56,221,180,134)(57,146,77,94)(58,147,78,95)(59,148,79,96)(60,149,80,97)(61,150,81,98)(62,151,82,85)(63,152,83,86)(64,153,84,87)(65,154,71,88)(66,141,72,89)(67,142,73,90)(68,143,74,91)(69,144,75,92)(70,145,76,93), (1,62,163,82)(2,63,164,83)(3,64,165,84)(4,65,166,71)(5,66,167,72)(6,67,168,73)(7,68,155,74)(8,69,156,75)(9,70,157,76)(10,57,158,77)(11,58,159,78)(12,59,160,79)(13,60,161,80)(14,61,162,81)(15,92,119,144)(16,93,120,145)(17,94,121,146)(18,95,122,147)(19,96,123,148)(20,97,124,149)(21,98,125,150)(22,85,126,151)(23,86,113,152)(24,87,114,153)(25,88,115,154)(26,89,116,141)(27,90,117,142)(28,91,118,143)(29,179,199,55)(30,180,200,56)(31,181,201,43)(32,182,202,44)(33,169,203,45)(34,170,204,46)(35,171,205,47)(36,172,206,48)(37,173,207,49)(38,174,208,50)(39,175,209,51)(40,176,210,52)(41,177,197,53)(42,178,198,54)(99,139,188,212)(100,140,189,213)(101,127,190,214)(102,128,191,215)(103,129,192,216)(104,130,193,217)(105,131,194,218)(106,132,195,219)(107,133,196,220)(108,134,183,221)(109,135,184,222)(110,136,185,223)(111,137,186,224)(112,138,187,211)>;
G:=Group( (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), (1,99,163,188)(2,100,164,189)(3,101,165,190)(4,102,166,191)(5,103,167,192)(6,104,168,193)(7,105,155,194)(8,106,156,195)(9,107,157,196)(10,108,158,183)(11,109,159,184)(12,110,160,185)(13,111,161,186)(14,112,162,187)(15,42,119,198)(16,29,120,199)(17,30,121,200)(18,31,122,201)(19,32,123,202)(20,33,124,203)(21,34,125,204)(22,35,126,205)(23,36,113,206)(24,37,114,207)(25,38,115,208)(26,39,116,209)(27,40,117,210)(28,41,118,197)(43,95,181,147)(44,96,182,148)(45,97,169,149)(46,98,170,150)(47,85,171,151)(48,86,172,152)(49,87,173,153)(50,88,174,154)(51,89,175,141)(52,90,176,142)(53,91,177,143)(54,92,178,144)(55,93,179,145)(56,94,180,146)(57,134,77,221)(58,135,78,222)(59,136,79,223)(60,137,80,224)(61,138,81,211)(62,139,82,212)(63,140,83,213)(64,127,84,214)(65,128,71,215)(66,129,72,216)(67,130,73,217)(68,131,74,218)(69,132,75,219)(70,133,76,220), (29,199)(30,200)(31,201)(32,202)(33,203)(34,204)(35,205)(36,206)(37,207)(38,208)(39,209)(40,210)(41,197)(42,198)(43,181)(44,182)(45,169)(46,170)(47,171)(48,172)(49,173)(50,174)(51,175)(52,176)(53,177)(54,178)(55,179)(56,180)(99,188)(100,189)(101,190)(102,191)(103,192)(104,193)(105,194)(106,195)(107,196)(108,183)(109,184)(110,185)(111,186)(112,187)(127,214)(128,215)(129,216)(130,217)(131,218)(132,219)(133,220)(134,221)(135,222)(136,223)(137,224)(138,211)(139,212)(140,213), (1,22,163,126)(2,23,164,113)(3,24,165,114)(4,25,166,115)(5,26,167,116)(6,27,168,117)(7,28,155,118)(8,15,156,119)(9,16,157,120)(10,17,158,121)(11,18,159,122)(12,19,160,123)(13,20,161,124)(14,21,162,125)(29,196,199,107)(30,183,200,108)(31,184,201,109)(32,185,202,110)(33,186,203,111)(34,187,204,112)(35,188,205,99)(36,189,206,100)(37,190,207,101)(38,191,208,102)(39,192,209,103)(40,193,210,104)(41,194,197,105)(42,195,198,106)(43,222,181,135)(44,223,182,136)(45,224,169,137)(46,211,170,138)(47,212,171,139)(48,213,172,140)(49,214,173,127)(50,215,174,128)(51,216,175,129)(52,217,176,130)(53,218,177,131)(54,219,178,132)(55,220,179,133)(56,221,180,134)(57,146,77,94)(58,147,78,95)(59,148,79,96)(60,149,80,97)(61,150,81,98)(62,151,82,85)(63,152,83,86)(64,153,84,87)(65,154,71,88)(66,141,72,89)(67,142,73,90)(68,143,74,91)(69,144,75,92)(70,145,76,93), (1,62,163,82)(2,63,164,83)(3,64,165,84)(4,65,166,71)(5,66,167,72)(6,67,168,73)(7,68,155,74)(8,69,156,75)(9,70,157,76)(10,57,158,77)(11,58,159,78)(12,59,160,79)(13,60,161,80)(14,61,162,81)(15,92,119,144)(16,93,120,145)(17,94,121,146)(18,95,122,147)(19,96,123,148)(20,97,124,149)(21,98,125,150)(22,85,126,151)(23,86,113,152)(24,87,114,153)(25,88,115,154)(26,89,116,141)(27,90,117,142)(28,91,118,143)(29,179,199,55)(30,180,200,56)(31,181,201,43)(32,182,202,44)(33,169,203,45)(34,170,204,46)(35,171,205,47)(36,172,206,48)(37,173,207,49)(38,174,208,50)(39,175,209,51)(40,176,210,52)(41,177,197,53)(42,178,198,54)(99,139,188,212)(100,140,189,213)(101,127,190,214)(102,128,191,215)(103,129,192,216)(104,130,193,217)(105,131,194,218)(106,132,195,219)(107,133,196,220)(108,134,183,221)(109,135,184,222)(110,136,185,223)(111,137,186,224)(112,138,187,211) );
G=PermutationGroup([[(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)], [(1,99,163,188),(2,100,164,189),(3,101,165,190),(4,102,166,191),(5,103,167,192),(6,104,168,193),(7,105,155,194),(8,106,156,195),(9,107,157,196),(10,108,158,183),(11,109,159,184),(12,110,160,185),(13,111,161,186),(14,112,162,187),(15,42,119,198),(16,29,120,199),(17,30,121,200),(18,31,122,201),(19,32,123,202),(20,33,124,203),(21,34,125,204),(22,35,126,205),(23,36,113,206),(24,37,114,207),(25,38,115,208),(26,39,116,209),(27,40,117,210),(28,41,118,197),(43,95,181,147),(44,96,182,148),(45,97,169,149),(46,98,170,150),(47,85,171,151),(48,86,172,152),(49,87,173,153),(50,88,174,154),(51,89,175,141),(52,90,176,142),(53,91,177,143),(54,92,178,144),(55,93,179,145),(56,94,180,146),(57,134,77,221),(58,135,78,222),(59,136,79,223),(60,137,80,224),(61,138,81,211),(62,139,82,212),(63,140,83,213),(64,127,84,214),(65,128,71,215),(66,129,72,216),(67,130,73,217),(68,131,74,218),(69,132,75,219),(70,133,76,220)], [(29,199),(30,200),(31,201),(32,202),(33,203),(34,204),(35,205),(36,206),(37,207),(38,208),(39,209),(40,210),(41,197),(42,198),(43,181),(44,182),(45,169),(46,170),(47,171),(48,172),(49,173),(50,174),(51,175),(52,176),(53,177),(54,178),(55,179),(56,180),(99,188),(100,189),(101,190),(102,191),(103,192),(104,193),(105,194),(106,195),(107,196),(108,183),(109,184),(110,185),(111,186),(112,187),(127,214),(128,215),(129,216),(130,217),(131,218),(132,219),(133,220),(134,221),(135,222),(136,223),(137,224),(138,211),(139,212),(140,213)], [(1,22,163,126),(2,23,164,113),(3,24,165,114),(4,25,166,115),(5,26,167,116),(6,27,168,117),(7,28,155,118),(8,15,156,119),(9,16,157,120),(10,17,158,121),(11,18,159,122),(12,19,160,123),(13,20,161,124),(14,21,162,125),(29,196,199,107),(30,183,200,108),(31,184,201,109),(32,185,202,110),(33,186,203,111),(34,187,204,112),(35,188,205,99),(36,189,206,100),(37,190,207,101),(38,191,208,102),(39,192,209,103),(40,193,210,104),(41,194,197,105),(42,195,198,106),(43,222,181,135),(44,223,182,136),(45,224,169,137),(46,211,170,138),(47,212,171,139),(48,213,172,140),(49,214,173,127),(50,215,174,128),(51,216,175,129),(52,217,176,130),(53,218,177,131),(54,219,178,132),(55,220,179,133),(56,221,180,134),(57,146,77,94),(58,147,78,95),(59,148,79,96),(60,149,80,97),(61,150,81,98),(62,151,82,85),(63,152,83,86),(64,153,84,87),(65,154,71,88),(66,141,72,89),(67,142,73,90),(68,143,74,91),(69,144,75,92),(70,145,76,93)], [(1,62,163,82),(2,63,164,83),(3,64,165,84),(4,65,166,71),(5,66,167,72),(6,67,168,73),(7,68,155,74),(8,69,156,75),(9,70,157,76),(10,57,158,77),(11,58,159,78),(12,59,160,79),(13,60,161,80),(14,61,162,81),(15,92,119,144),(16,93,120,145),(17,94,121,146),(18,95,122,147),(19,96,123,148),(20,97,124,149),(21,98,125,150),(22,85,126,151),(23,86,113,152),(24,87,114,153),(25,88,115,154),(26,89,116,141),(27,90,117,142),(28,91,118,143),(29,179,199,55),(30,180,200,56),(31,181,201,43),(32,182,202,44),(33,169,203,45),(34,170,204,46),(35,171,205,47),(36,172,206,48),(37,173,207,49),(38,174,208,50),(39,175,209,51),(40,176,210,52),(41,177,197,53),(42,178,198,54),(99,139,188,212),(100,140,189,213),(101,127,190,214),(102,128,191,215),(103,129,192,216),(104,130,193,217),(105,131,194,218),(106,132,195,219),(107,133,196,220),(108,134,183,221),(109,135,184,222),(110,136,185,223),(111,137,186,224),(112,138,187,211)]])
238 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2M | 4A | ··· | 4T | 7A | ··· | 7F | 14A | ··· | 14R | 14S | ··· | 14BZ | 28A | ··· | 28DP |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 |
238 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 |
| type | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | 2- 1+4 | C7×2- 1+4 |
| kernel | C14×2- 1+4 | Q8×C2×C14 | C14×C4○D4 | C7×2- 1+4 | C2×2- 1+4 | C22×Q8 | C2×C4○D4 | 2- 1+4 | C14 | C2 |
| # reps | 1 | 5 | 10 | 16 | 6 | 30 | 60 | 96 | 2 | 12 |
Matrix representation of C14×2- 1+4 ►in GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 4 | 4 | 13 | 1 |
| 0 | 16 | 5 | 1 | 16 |
| 0 | 2 | 9 | 25 | 13 |
| 0 | 9 | 21 | 25 | 24 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 5 | 14 | 28 | 0 |
| 0 | 14 | 13 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 28 |
| 0 | 20 | 0 | 1 | 0 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 15 | 8 | 0 | 0 |
| 0 | 8 | 14 | 0 | 0 |
| 0 | 13 | 14 | 14 | 21 |
| 0 | 14 | 4 | 21 | 15 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,4],[28,0,0,0,0,0,4,16,2,9,0,4,5,9,21,0,13,1,25,25,0,1,16,13,24],[28,0,0,0,0,0,1,0,5,14,0,0,1,14,13,0,0,0,28,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,20,0,1,0,9,0,0,0,0,0,1,0,0,0,28,0],[28,0,0,0,0,0,15,8,13,14,0,8,14,14,4,0,0,0,14,21,0,0,0,21,15] >;
C14×2- 1+4 in GAP, Magma, Sage, TeX
C_{14}\times 2_-^{1+4} % in TeX
G:=Group("C14xES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1390);
// by ID
G=gap.SmallGroup(448,1390);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-7,-2,3165,1576,2403,1192,6499]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=e^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations