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, (C7×D4).41C23, D4.8(C22×C14), Q8.8(C22×C14), (C7×Q8).42C23, (C2×C14).388C24, (C2×C28).690C23, C22.3(C23×C14), (D4×C14).336C22, C23.47(C22×C14), (C22×C14).270C23, (C22×C28).468C22, (Q8×C2×C14)⋊22C2, C4○D4⋊7(C2×C14), (C2×C4○D4)⋊14C14, (C14×C4○D4)⋊30C2, (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
Subgroups: 834 in 794 conjugacy classes, 754 normal (8 characteristic)
C1, C2, C2 [×2], C2 [×10], C4 [×20], C22, C22 [×10], C22 [×10], C7, C2×C4 [×70], D4 [×40], Q8 [×40], C23 [×5], C14, C14 [×2], C14 [×10], C22×C4 [×15], C2×D4 [×10], C2×Q8 [×50], C4○D4 [×80], C28 [×20], C2×C14, C2×C14 [×10], C2×C14 [×10], C22×Q8 [×5], C2×C4○D4 [×10], 2- (1+4) [×16], C2×C28 [×70], C7×D4 [×40], C7×Q8 [×40], C22×C14 [×5], C2×2- (1+4), C22×C28 [×15], D4×C14 [×10], Q8×C14 [×50], C7×C4○D4 [×80], Q8×C2×C14 [×5], C14×C4○D4 [×10], C7×2- (1+4) [×16], C14×2- (1+4)
Quotients:
C1, C2 [×31], C22 [×155], C7, C23 [×155], C14 [×31], C24 [×31], C2×C14 [×155], 2- (1+4) [×2], C25, C22×C14 [×155], C2×2- (1+4), C23×C14 [×31], C7×2- (1+4) [×2], C24×C14, C14×2- (1+4)
Generators and relations
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 >
►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 67 74 152)(2 68 75 153)(3 69 76 154)(4 70 77 141)(5 57 78 142)(6 58 79 143)(7 59 80 144)(8 60 81 145)(9 61 82 146)(10 62 83 147)(11 63 84 148)(12 64 71 149)(13 65 72 150)(14 66 73 151)(15 175 32 98)(16 176 33 85)(17 177 34 86)(18 178 35 87)(19 179 36 88)(20 180 37 89)(21 181 38 90)(22 182 39 91)(23 169 40 92)(24 170 41 93)(25 171 42 94)(26 172 29 95)(27 173 30 96)(28 174 31 97)(43 163 204 189)(44 164 205 190)(45 165 206 191)(46 166 207 192)(47 167 208 193)(48 168 209 194)(49 155 210 195)(50 156 197 196)(51 157 198 183)(52 158 199 184)(53 159 200 185)(54 160 201 186)(55 161 202 187)(56 162 203 188)(99 119 129 219)(100 120 130 220)(101 121 131 221)(102 122 132 222)(103 123 133 223)(104 124 134 224)(105 125 135 211)(106 126 136 212)(107 113 137 213)(108 114 138 214)(109 115 139 215)(110 116 140 216)(111 117 127 217)(112 118 128 218)
(15 32)(16 33)(17 34)(18 35)(19 36)(20 37)(21 38)(22 39)(23 40)(24 41)(25 42)(26 29)(27 30)(28 31)(43 204)(44 205)(45 206)(46 207)(47 208)(48 209)(49 210)(50 197)(51 198)(52 199)(53 200)(54 201)(55 202)(56 203)(57 142)(58 143)(59 144)(60 145)(61 146)(62 147)(63 148)(64 149)(65 150)(66 151)(67 152)(68 153)(69 154)(70 141)(113 213)(114 214)(115 215)(116 216)(117 217)(118 218)(119 219)(120 220)(121 221)(122 222)(123 223)(124 224)(125 211)(126 212)
(1 189 74 163)(2 190 75 164)(3 191 76 165)(4 192 77 166)(5 193 78 167)(6 194 79 168)(7 195 80 155)(8 196 81 156)(9 183 82 157)(10 184 83 158)(11 185 84 159)(12 186 71 160)(13 187 72 161)(14 188 73 162)(15 223 32 123)(16 224 33 124)(17 211 34 125)(18 212 35 126)(19 213 36 113)(20 214 37 114)(21 215 38 115)(22 216 39 116)(23 217 40 117)(24 218 41 118)(25 219 42 119)(26 220 29 120)(27 221 30 121)(28 222 31 122)(43 152 204 67)(44 153 205 68)(45 154 206 69)(46 141 207 70)(47 142 208 57)(48 143 209 58)(49 144 210 59)(50 145 197 60)(51 146 198 61)(52 147 199 62)(53 148 200 63)(54 149 201 64)(55 150 202 65)(56 151 203 66)(85 134 176 104)(86 135 177 105)(87 136 178 106)(88 137 179 107)(89 138 180 108)(90 139 181 109)(91 140 182 110)(92 127 169 111)(93 128 170 112)(94 129 171 99)(95 130 172 100)(96 131 173 101)(97 132 174 102)(98 133 175 103)
(1 137 74 107)(2 138 75 108)(3 139 76 109)(4 140 77 110)(5 127 78 111)(6 128 79 112)(7 129 80 99)(8 130 81 100)(9 131 82 101)(10 132 83 102)(11 133 84 103)(12 134 71 104)(13 135 72 105)(14 136 73 106)(15 200 32 53)(16 201 33 54)(17 202 34 55)(18 203 35 56)(19 204 36 43)(20 205 37 44)(21 206 38 45)(22 207 39 46)(23 208 40 47)(24 209 41 48)(25 210 42 49)(26 197 29 50)(27 198 30 51)(28 199 31 52)(57 217 142 117)(58 218 143 118)(59 219 144 119)(60 220 145 120)(61 221 146 121)(62 222 147 122)(63 223 148 123)(64 224 149 124)(65 211 150 125)(66 212 151 126)(67 213 152 113)(68 214 153 114)(69 215 154 115)(70 216 141 116)(85 160 176 186)(86 161 177 187)(87 162 178 188)(88 163 179 189)(89 164 180 190)(90 165 181 191)(91 166 182 192)(92 167 169 193)(93 168 170 194)(94 155 171 195)(95 156 172 196)(96 157 173 183)(97 158 174 184)(98 159 175 185)
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), (1,67,74,152)(2,68,75,153)(3,69,76,154)(4,70,77,141)(5,57,78,142)(6,58,79,143)(7,59,80,144)(8,60,81,145)(9,61,82,146)(10,62,83,147)(11,63,84,148)(12,64,71,149)(13,65,72,150)(14,66,73,151)(15,175,32,98)(16,176,33,85)(17,177,34,86)(18,178,35,87)(19,179,36,88)(20,180,37,89)(21,181,38,90)(22,182,39,91)(23,169,40,92)(24,170,41,93)(25,171,42,94)(26,172,29,95)(27,173,30,96)(28,174,31,97)(43,163,204,189)(44,164,205,190)(45,165,206,191)(46,166,207,192)(47,167,208,193)(48,168,209,194)(49,155,210,195)(50,156,197,196)(51,157,198,183)(52,158,199,184)(53,159,200,185)(54,160,201,186)(55,161,202,187)(56,162,203,188)(99,119,129,219)(100,120,130,220)(101,121,131,221)(102,122,132,222)(103,123,133,223)(104,124,134,224)(105,125,135,211)(106,126,136,212)(107,113,137,213)(108,114,138,214)(109,115,139,215)(110,116,140,216)(111,117,127,217)(112,118,128,218), (15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,29)(27,30)(28,31)(43,204)(44,205)(45,206)(46,207)(47,208)(48,209)(49,210)(50,197)(51,198)(52,199)(53,200)(54,201)(55,202)(56,203)(57,142)(58,143)(59,144)(60,145)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,141)(113,213)(114,214)(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)(122,222)(123,223)(124,224)(125,211)(126,212), (1,189,74,163)(2,190,75,164)(3,191,76,165)(4,192,77,166)(5,193,78,167)(6,194,79,168)(7,195,80,155)(8,196,81,156)(9,183,82,157)(10,184,83,158)(11,185,84,159)(12,186,71,160)(13,187,72,161)(14,188,73,162)(15,223,32,123)(16,224,33,124)(17,211,34,125)(18,212,35,126)(19,213,36,113)(20,214,37,114)(21,215,38,115)(22,216,39,116)(23,217,40,117)(24,218,41,118)(25,219,42,119)(26,220,29,120)(27,221,30,121)(28,222,31,122)(43,152,204,67)(44,153,205,68)(45,154,206,69)(46,141,207,70)(47,142,208,57)(48,143,209,58)(49,144,210,59)(50,145,197,60)(51,146,198,61)(52,147,199,62)(53,148,200,63)(54,149,201,64)(55,150,202,65)(56,151,203,66)(85,134,176,104)(86,135,177,105)(87,136,178,106)(88,137,179,107)(89,138,180,108)(90,139,181,109)(91,140,182,110)(92,127,169,111)(93,128,170,112)(94,129,171,99)(95,130,172,100)(96,131,173,101)(97,132,174,102)(98,133,175,103), (1,137,74,107)(2,138,75,108)(3,139,76,109)(4,140,77,110)(5,127,78,111)(6,128,79,112)(7,129,80,99)(8,130,81,100)(9,131,82,101)(10,132,83,102)(11,133,84,103)(12,134,71,104)(13,135,72,105)(14,136,73,106)(15,200,32,53)(16,201,33,54)(17,202,34,55)(18,203,35,56)(19,204,36,43)(20,205,37,44)(21,206,38,45)(22,207,39,46)(23,208,40,47)(24,209,41,48)(25,210,42,49)(26,197,29,50)(27,198,30,51)(28,199,31,52)(57,217,142,117)(58,218,143,118)(59,219,144,119)(60,220,145,120)(61,221,146,121)(62,222,147,122)(63,223,148,123)(64,224,149,124)(65,211,150,125)(66,212,151,126)(67,213,152,113)(68,214,153,114)(69,215,154,115)(70,216,141,116)(85,160,176,186)(86,161,177,187)(87,162,178,188)(88,163,179,189)(89,164,180,190)(90,165,181,191)(91,166,182,192)(92,167,169,193)(93,168,170,194)(94,155,171,195)(95,156,172,196)(96,157,173,183)(97,158,174,184)(98,159,175,185)>;
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), (1,67,74,152)(2,68,75,153)(3,69,76,154)(4,70,77,141)(5,57,78,142)(6,58,79,143)(7,59,80,144)(8,60,81,145)(9,61,82,146)(10,62,83,147)(11,63,84,148)(12,64,71,149)(13,65,72,150)(14,66,73,151)(15,175,32,98)(16,176,33,85)(17,177,34,86)(18,178,35,87)(19,179,36,88)(20,180,37,89)(21,181,38,90)(22,182,39,91)(23,169,40,92)(24,170,41,93)(25,171,42,94)(26,172,29,95)(27,173,30,96)(28,174,31,97)(43,163,204,189)(44,164,205,190)(45,165,206,191)(46,166,207,192)(47,167,208,193)(48,168,209,194)(49,155,210,195)(50,156,197,196)(51,157,198,183)(52,158,199,184)(53,159,200,185)(54,160,201,186)(55,161,202,187)(56,162,203,188)(99,119,129,219)(100,120,130,220)(101,121,131,221)(102,122,132,222)(103,123,133,223)(104,124,134,224)(105,125,135,211)(106,126,136,212)(107,113,137,213)(108,114,138,214)(109,115,139,215)(110,116,140,216)(111,117,127,217)(112,118,128,218), (15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,29)(27,30)(28,31)(43,204)(44,205)(45,206)(46,207)(47,208)(48,209)(49,210)(50,197)(51,198)(52,199)(53,200)(54,201)(55,202)(56,203)(57,142)(58,143)(59,144)(60,145)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,141)(113,213)(114,214)(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)(122,222)(123,223)(124,224)(125,211)(126,212), (1,189,74,163)(2,190,75,164)(3,191,76,165)(4,192,77,166)(5,193,78,167)(6,194,79,168)(7,195,80,155)(8,196,81,156)(9,183,82,157)(10,184,83,158)(11,185,84,159)(12,186,71,160)(13,187,72,161)(14,188,73,162)(15,223,32,123)(16,224,33,124)(17,211,34,125)(18,212,35,126)(19,213,36,113)(20,214,37,114)(21,215,38,115)(22,216,39,116)(23,217,40,117)(24,218,41,118)(25,219,42,119)(26,220,29,120)(27,221,30,121)(28,222,31,122)(43,152,204,67)(44,153,205,68)(45,154,206,69)(46,141,207,70)(47,142,208,57)(48,143,209,58)(49,144,210,59)(50,145,197,60)(51,146,198,61)(52,147,199,62)(53,148,200,63)(54,149,201,64)(55,150,202,65)(56,151,203,66)(85,134,176,104)(86,135,177,105)(87,136,178,106)(88,137,179,107)(89,138,180,108)(90,139,181,109)(91,140,182,110)(92,127,169,111)(93,128,170,112)(94,129,171,99)(95,130,172,100)(96,131,173,101)(97,132,174,102)(98,133,175,103), (1,137,74,107)(2,138,75,108)(3,139,76,109)(4,140,77,110)(5,127,78,111)(6,128,79,112)(7,129,80,99)(8,130,81,100)(9,131,82,101)(10,132,83,102)(11,133,84,103)(12,134,71,104)(13,135,72,105)(14,136,73,106)(15,200,32,53)(16,201,33,54)(17,202,34,55)(18,203,35,56)(19,204,36,43)(20,205,37,44)(21,206,38,45)(22,207,39,46)(23,208,40,47)(24,209,41,48)(25,210,42,49)(26,197,29,50)(27,198,30,51)(28,199,31,52)(57,217,142,117)(58,218,143,118)(59,219,144,119)(60,220,145,120)(61,221,146,121)(62,222,147,122)(63,223,148,123)(64,224,149,124)(65,211,150,125)(66,212,151,126)(67,213,152,113)(68,214,153,114)(69,215,154,115)(70,216,141,116)(85,160,176,186)(86,161,177,187)(87,162,178,188)(88,163,179,189)(89,164,180,190)(90,165,181,191)(91,166,182,192)(92,167,169,193)(93,168,170,194)(94,155,171,195)(95,156,172,196)(96,157,173,183)(97,158,174,184)(98,159,175,185) );
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)], [(1,67,74,152),(2,68,75,153),(3,69,76,154),(4,70,77,141),(5,57,78,142),(6,58,79,143),(7,59,80,144),(8,60,81,145),(9,61,82,146),(10,62,83,147),(11,63,84,148),(12,64,71,149),(13,65,72,150),(14,66,73,151),(15,175,32,98),(16,176,33,85),(17,177,34,86),(18,178,35,87),(19,179,36,88),(20,180,37,89),(21,181,38,90),(22,182,39,91),(23,169,40,92),(24,170,41,93),(25,171,42,94),(26,172,29,95),(27,173,30,96),(28,174,31,97),(43,163,204,189),(44,164,205,190),(45,165,206,191),(46,166,207,192),(47,167,208,193),(48,168,209,194),(49,155,210,195),(50,156,197,196),(51,157,198,183),(52,158,199,184),(53,159,200,185),(54,160,201,186),(55,161,202,187),(56,162,203,188),(99,119,129,219),(100,120,130,220),(101,121,131,221),(102,122,132,222),(103,123,133,223),(104,124,134,224),(105,125,135,211),(106,126,136,212),(107,113,137,213),(108,114,138,214),(109,115,139,215),(110,116,140,216),(111,117,127,217),(112,118,128,218)], [(15,32),(16,33),(17,34),(18,35),(19,36),(20,37),(21,38),(22,39),(23,40),(24,41),(25,42),(26,29),(27,30),(28,31),(43,204),(44,205),(45,206),(46,207),(47,208),(48,209),(49,210),(50,197),(51,198),(52,199),(53,200),(54,201),(55,202),(56,203),(57,142),(58,143),(59,144),(60,145),(61,146),(62,147),(63,148),(64,149),(65,150),(66,151),(67,152),(68,153),(69,154),(70,141),(113,213),(114,214),(115,215),(116,216),(117,217),(118,218),(119,219),(120,220),(121,221),(122,222),(123,223),(124,224),(125,211),(126,212)], [(1,189,74,163),(2,190,75,164),(3,191,76,165),(4,192,77,166),(5,193,78,167),(6,194,79,168),(7,195,80,155),(8,196,81,156),(9,183,82,157),(10,184,83,158),(11,185,84,159),(12,186,71,160),(13,187,72,161),(14,188,73,162),(15,223,32,123),(16,224,33,124),(17,211,34,125),(18,212,35,126),(19,213,36,113),(20,214,37,114),(21,215,38,115),(22,216,39,116),(23,217,40,117),(24,218,41,118),(25,219,42,119),(26,220,29,120),(27,221,30,121),(28,222,31,122),(43,152,204,67),(44,153,205,68),(45,154,206,69),(46,141,207,70),(47,142,208,57),(48,143,209,58),(49,144,210,59),(50,145,197,60),(51,146,198,61),(52,147,199,62),(53,148,200,63),(54,149,201,64),(55,150,202,65),(56,151,203,66),(85,134,176,104),(86,135,177,105),(87,136,178,106),(88,137,179,107),(89,138,180,108),(90,139,181,109),(91,140,182,110),(92,127,169,111),(93,128,170,112),(94,129,171,99),(95,130,172,100),(96,131,173,101),(97,132,174,102),(98,133,175,103)], [(1,137,74,107),(2,138,75,108),(3,139,76,109),(4,140,77,110),(5,127,78,111),(6,128,79,112),(7,129,80,99),(8,130,81,100),(9,131,82,101),(10,132,83,102),(11,133,84,103),(12,134,71,104),(13,135,72,105),(14,136,73,106),(15,200,32,53),(16,201,33,54),(17,202,34,55),(18,203,35,56),(19,204,36,43),(20,205,37,44),(21,206,38,45),(22,207,39,46),(23,208,40,47),(24,209,41,48),(25,210,42,49),(26,197,29,50),(27,198,30,51),(28,199,31,52),(57,217,142,117),(58,218,143,118),(59,219,144,119),(60,220,145,120),(61,221,146,121),(62,222,147,122),(63,223,148,123),(64,224,149,124),(65,211,150,125),(66,212,151,126),(67,213,152,113),(68,214,153,114),(69,215,154,115),(70,216,141,116),(85,160,176,186),(86,161,177,187),(87,162,178,188),(88,163,179,189),(89,164,180,190),(90,165,181,191),(91,166,182,192),(92,167,169,193),(93,168,170,194),(94,155,171,195),(95,156,172,196),(96,157,173,183),(97,158,174,184),(98,159,175,185)])
Matrix representation ►G ⊆ 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] >;
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 |
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
×
⋊
ℤ
𝔽
○
≀