metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.114D14, C14.202+ (1+4), (C4×D4)⋊21D7, (D4×C28)⋊23C2, C4⋊C4.319D14, C28⋊D4.7C2, D28⋊C4⋊16C2, (C4×Dic14)⋊34C2, D14.D4⋊8C2, (C2×D4).220D14, C4.16(C4○D28), C28.17D4⋊9C2, C4.D28⋊19C2, (C22×C4).48D14, Dic7⋊3Q8⋊16C2, C28.111(C4○D4), (C2×C28).701C23, (C4×C28).158C22, (C2×C14).103C24, D14⋊C4.87C22, C22⋊C4.116D14, Dic7.D4⋊8C2, C2.21(D4⋊6D14), Dic7.35(C4○D4), (D4×C14).263C22, (C2×D28).139C22, Dic7⋊C4.66C22, C4⋊Dic7.301C22, (C2×Dic7).44C23, (C4×Dic7).76C22, (C22×D7).37C23, C23.100(C22×D7), C22.128(C23×D7), C23.23D14⋊18C2, (C22×C14).173C23, (C22×C28).365C22, C7⋊1(C22.53C24), C23.D7.107C22, (C2×Dic14).145C22, (C4×C7⋊D4)⋊45C2, C2.26(D7×C4○D4), C14.45(C2×C4○D4), C2.52(C2×C4○D28), (C2×C4×D7).202C22, (C7×C4⋊C4).332C22, (C2×C4).286(C22×D7), (C2×C7⋊D4).116C22, (C7×C22⋊C4).127C22, SmallGroup(448,1012)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1076 in 236 conjugacy classes, 97 normal (43 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×11], C22, C22 [×12], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×10], D4 [×10], Q8 [×4], C23 [×2], C23 [×2], D7 [×2], C14 [×3], C14 [×2], C42, C42 [×4], C22⋊C4 [×2], C22⋊C4 [×10], C4⋊C4, C4⋊C4 [×5], C22×C4 [×2], C22×C4 [×2], C2×D4, C2×D4 [×5], C2×Q8 [×2], Dic7 [×2], Dic7 [×5], C28 [×2], C28 [×4], D14 [×6], C2×C14, C2×C14 [×6], C4×D4, C4×D4 [×3], C4×Q8 [×2], C22.D4 [×4], C4.4D4 [×4], C4⋊1D4, Dic14 [×4], C4×D7 [×2], D28 [×2], C2×Dic7 [×4], C2×Dic7 [×2], C7⋊D4 [×6], C2×C28 [×3], C2×C28 [×2], C2×C28 [×2], C7×D4 [×2], C22×D7 [×2], C22×C14 [×2], C22.53C24, C4×Dic7 [×2], C4×Dic7 [×2], Dic7⋊C4 [×2], Dic7⋊C4 [×2], C4⋊Dic7, D14⋊C4 [×6], C23.D7 [×4], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14 [×2], C2×C4×D7 [×2], C2×D28, C2×C7⋊D4 [×4], C22×C28 [×2], D4×C14, C4×Dic14, C4.D28, D14.D4 [×2], Dic7.D4 [×2], Dic7⋊3Q8, D28⋊C4, C4×C7⋊D4 [×2], C23.23D14 [×2], C28.17D4, C28⋊D4, D4×C28, C42.114D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2+ (1+4), C22×D7 [×7], C22.53C24, C4○D28 [×2], C23×D7, C2×C4○D28, D4⋊6D14, D7×C4○D4, C42.114D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=a-1b2, dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 78 125 95)(2 110 126 65)(3 80 127 97)(4 112 128 67)(5 82 129 99)(6 86 130 69)(7 84 131 101)(8 88 132 71)(9 58 133 103)(10 90 134 73)(11 60 135 105)(12 92 136 75)(13 62 137 107)(14 94 138 77)(15 64 139 109)(16 96 140 79)(17 66 113 111)(18 98 114 81)(19 68 115 85)(20 100 116 83)(21 70 117 87)(22 102 118 57)(23 72 119 89)(24 104 120 59)(25 74 121 91)(26 106 122 61)(27 76 123 93)(28 108 124 63)(29 159 201 181)(30 196 202 146)(31 161 203 183)(32 170 204 148)(33 163 205 185)(34 172 206 150)(35 165 207 187)(36 174 208 152)(37 167 209 189)(38 176 210 154)(39 141 211 191)(40 178 212 156)(41 143 213 193)(42 180 214 158)(43 145 215 195)(44 182 216 160)(45 147 217 169)(46 184 218 162)(47 149 219 171)(48 186 220 164)(49 151 221 173)(50 188 222 166)(51 153 223 175)(52 190 224 168)(53 155 197 177)(54 192 198 142)(55 157 199 179)(56 194 200 144)
(1 159 15 145)(2 160 16 146)(3 161 17 147)(4 162 18 148)(5 163 19 149)(6 164 20 150)(7 165 21 151)(8 166 22 152)(9 167 23 153)(10 168 24 154)(11 141 25 155)(12 142 26 156)(13 143 27 157)(14 144 28 158)(29 109 43 95)(30 110 44 96)(31 111 45 97)(32 112 46 98)(33 85 47 99)(34 86 48 100)(35 87 49 101)(36 88 50 102)(37 89 51 103)(38 90 52 104)(39 91 53 105)(40 92 54 106)(41 93 55 107)(42 94 56 108)(57 208 71 222)(58 209 72 223)(59 210 73 224)(60 211 74 197)(61 212 75 198)(62 213 76 199)(63 214 77 200)(64 215 78 201)(65 216 79 202)(66 217 80 203)(67 218 81 204)(68 219 82 205)(69 220 83 206)(70 221 84 207)(113 169 127 183)(114 170 128 184)(115 171 129 185)(116 172 130 186)(117 173 131 187)(118 174 132 188)(119 175 133 189)(120 176 134 190)(121 177 135 191)(122 178 136 192)(123 179 137 193)(124 180 138 194)(125 181 139 195)(126 182 140 196)
(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 56 15 42)(2 41 16 55)(3 54 17 40)(4 39 18 53)(5 52 19 38)(6 37 20 51)(7 50 21 36)(8 35 22 49)(9 48 23 34)(10 33 24 47)(11 46 25 32)(12 31 26 45)(13 44 27 30)(14 29 28 43)(57 151 71 165)(58 164 72 150)(59 149 73 163)(60 162 74 148)(61 147 75 161)(62 160 76 146)(63 145 77 159)(64 158 78 144)(65 143 79 157)(66 156 80 142)(67 141 81 155)(68 154 82 168)(69 167 83 153)(70 152 84 166)(85 176 99 190)(86 189 100 175)(87 174 101 188)(88 187 102 173)(89 172 103 186)(90 185 104 171)(91 170 105 184)(92 183 106 169)(93 196 107 182)(94 181 108 195)(95 194 109 180)(96 179 110 193)(97 192 111 178)(98 177 112 191)(113 212 127 198)(114 197 128 211)(115 210 129 224)(116 223 130 209)(117 208 131 222)(118 221 132 207)(119 206 133 220)(120 219 134 205)(121 204 135 218)(122 217 136 203)(123 202 137 216)(124 215 138 201)(125 200 139 214)(126 213 140 199)
G:=sub<Sym(224)| (1,78,125,95)(2,110,126,65)(3,80,127,97)(4,112,128,67)(5,82,129,99)(6,86,130,69)(7,84,131,101)(8,88,132,71)(9,58,133,103)(10,90,134,73)(11,60,135,105)(12,92,136,75)(13,62,137,107)(14,94,138,77)(15,64,139,109)(16,96,140,79)(17,66,113,111)(18,98,114,81)(19,68,115,85)(20,100,116,83)(21,70,117,87)(22,102,118,57)(23,72,119,89)(24,104,120,59)(25,74,121,91)(26,106,122,61)(27,76,123,93)(28,108,124,63)(29,159,201,181)(30,196,202,146)(31,161,203,183)(32,170,204,148)(33,163,205,185)(34,172,206,150)(35,165,207,187)(36,174,208,152)(37,167,209,189)(38,176,210,154)(39,141,211,191)(40,178,212,156)(41,143,213,193)(42,180,214,158)(43,145,215,195)(44,182,216,160)(45,147,217,169)(46,184,218,162)(47,149,219,171)(48,186,220,164)(49,151,221,173)(50,188,222,166)(51,153,223,175)(52,190,224,168)(53,155,197,177)(54,192,198,142)(55,157,199,179)(56,194,200,144), (1,159,15,145)(2,160,16,146)(3,161,17,147)(4,162,18,148)(5,163,19,149)(6,164,20,150)(7,165,21,151)(8,166,22,152)(9,167,23,153)(10,168,24,154)(11,141,25,155)(12,142,26,156)(13,143,27,157)(14,144,28,158)(29,109,43,95)(30,110,44,96)(31,111,45,97)(32,112,46,98)(33,85,47,99)(34,86,48,100)(35,87,49,101)(36,88,50,102)(37,89,51,103)(38,90,52,104)(39,91,53,105)(40,92,54,106)(41,93,55,107)(42,94,56,108)(57,208,71,222)(58,209,72,223)(59,210,73,224)(60,211,74,197)(61,212,75,198)(62,213,76,199)(63,214,77,200)(64,215,78,201)(65,216,79,202)(66,217,80,203)(67,218,81,204)(68,219,82,205)(69,220,83,206)(70,221,84,207)(113,169,127,183)(114,170,128,184)(115,171,129,185)(116,172,130,186)(117,173,131,187)(118,174,132,188)(119,175,133,189)(120,176,134,190)(121,177,135,191)(122,178,136,192)(123,179,137,193)(124,180,138,194)(125,181,139,195)(126,182,140,196), (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), (1,56,15,42)(2,41,16,55)(3,54,17,40)(4,39,18,53)(5,52,19,38)(6,37,20,51)(7,50,21,36)(8,35,22,49)(9,48,23,34)(10,33,24,47)(11,46,25,32)(12,31,26,45)(13,44,27,30)(14,29,28,43)(57,151,71,165)(58,164,72,150)(59,149,73,163)(60,162,74,148)(61,147,75,161)(62,160,76,146)(63,145,77,159)(64,158,78,144)(65,143,79,157)(66,156,80,142)(67,141,81,155)(68,154,82,168)(69,167,83,153)(70,152,84,166)(85,176,99,190)(86,189,100,175)(87,174,101,188)(88,187,102,173)(89,172,103,186)(90,185,104,171)(91,170,105,184)(92,183,106,169)(93,196,107,182)(94,181,108,195)(95,194,109,180)(96,179,110,193)(97,192,111,178)(98,177,112,191)(113,212,127,198)(114,197,128,211)(115,210,129,224)(116,223,130,209)(117,208,131,222)(118,221,132,207)(119,206,133,220)(120,219,134,205)(121,204,135,218)(122,217,136,203)(123,202,137,216)(124,215,138,201)(125,200,139,214)(126,213,140,199)>;
G:=Group( (1,78,125,95)(2,110,126,65)(3,80,127,97)(4,112,128,67)(5,82,129,99)(6,86,130,69)(7,84,131,101)(8,88,132,71)(9,58,133,103)(10,90,134,73)(11,60,135,105)(12,92,136,75)(13,62,137,107)(14,94,138,77)(15,64,139,109)(16,96,140,79)(17,66,113,111)(18,98,114,81)(19,68,115,85)(20,100,116,83)(21,70,117,87)(22,102,118,57)(23,72,119,89)(24,104,120,59)(25,74,121,91)(26,106,122,61)(27,76,123,93)(28,108,124,63)(29,159,201,181)(30,196,202,146)(31,161,203,183)(32,170,204,148)(33,163,205,185)(34,172,206,150)(35,165,207,187)(36,174,208,152)(37,167,209,189)(38,176,210,154)(39,141,211,191)(40,178,212,156)(41,143,213,193)(42,180,214,158)(43,145,215,195)(44,182,216,160)(45,147,217,169)(46,184,218,162)(47,149,219,171)(48,186,220,164)(49,151,221,173)(50,188,222,166)(51,153,223,175)(52,190,224,168)(53,155,197,177)(54,192,198,142)(55,157,199,179)(56,194,200,144), (1,159,15,145)(2,160,16,146)(3,161,17,147)(4,162,18,148)(5,163,19,149)(6,164,20,150)(7,165,21,151)(8,166,22,152)(9,167,23,153)(10,168,24,154)(11,141,25,155)(12,142,26,156)(13,143,27,157)(14,144,28,158)(29,109,43,95)(30,110,44,96)(31,111,45,97)(32,112,46,98)(33,85,47,99)(34,86,48,100)(35,87,49,101)(36,88,50,102)(37,89,51,103)(38,90,52,104)(39,91,53,105)(40,92,54,106)(41,93,55,107)(42,94,56,108)(57,208,71,222)(58,209,72,223)(59,210,73,224)(60,211,74,197)(61,212,75,198)(62,213,76,199)(63,214,77,200)(64,215,78,201)(65,216,79,202)(66,217,80,203)(67,218,81,204)(68,219,82,205)(69,220,83,206)(70,221,84,207)(113,169,127,183)(114,170,128,184)(115,171,129,185)(116,172,130,186)(117,173,131,187)(118,174,132,188)(119,175,133,189)(120,176,134,190)(121,177,135,191)(122,178,136,192)(123,179,137,193)(124,180,138,194)(125,181,139,195)(126,182,140,196), (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), (1,56,15,42)(2,41,16,55)(3,54,17,40)(4,39,18,53)(5,52,19,38)(6,37,20,51)(7,50,21,36)(8,35,22,49)(9,48,23,34)(10,33,24,47)(11,46,25,32)(12,31,26,45)(13,44,27,30)(14,29,28,43)(57,151,71,165)(58,164,72,150)(59,149,73,163)(60,162,74,148)(61,147,75,161)(62,160,76,146)(63,145,77,159)(64,158,78,144)(65,143,79,157)(66,156,80,142)(67,141,81,155)(68,154,82,168)(69,167,83,153)(70,152,84,166)(85,176,99,190)(86,189,100,175)(87,174,101,188)(88,187,102,173)(89,172,103,186)(90,185,104,171)(91,170,105,184)(92,183,106,169)(93,196,107,182)(94,181,108,195)(95,194,109,180)(96,179,110,193)(97,192,111,178)(98,177,112,191)(113,212,127,198)(114,197,128,211)(115,210,129,224)(116,223,130,209)(117,208,131,222)(118,221,132,207)(119,206,133,220)(120,219,134,205)(121,204,135,218)(122,217,136,203)(123,202,137,216)(124,215,138,201)(125,200,139,214)(126,213,140,199) );
G=PermutationGroup([(1,78,125,95),(2,110,126,65),(3,80,127,97),(4,112,128,67),(5,82,129,99),(6,86,130,69),(7,84,131,101),(8,88,132,71),(9,58,133,103),(10,90,134,73),(11,60,135,105),(12,92,136,75),(13,62,137,107),(14,94,138,77),(15,64,139,109),(16,96,140,79),(17,66,113,111),(18,98,114,81),(19,68,115,85),(20,100,116,83),(21,70,117,87),(22,102,118,57),(23,72,119,89),(24,104,120,59),(25,74,121,91),(26,106,122,61),(27,76,123,93),(28,108,124,63),(29,159,201,181),(30,196,202,146),(31,161,203,183),(32,170,204,148),(33,163,205,185),(34,172,206,150),(35,165,207,187),(36,174,208,152),(37,167,209,189),(38,176,210,154),(39,141,211,191),(40,178,212,156),(41,143,213,193),(42,180,214,158),(43,145,215,195),(44,182,216,160),(45,147,217,169),(46,184,218,162),(47,149,219,171),(48,186,220,164),(49,151,221,173),(50,188,222,166),(51,153,223,175),(52,190,224,168),(53,155,197,177),(54,192,198,142),(55,157,199,179),(56,194,200,144)], [(1,159,15,145),(2,160,16,146),(3,161,17,147),(4,162,18,148),(5,163,19,149),(6,164,20,150),(7,165,21,151),(8,166,22,152),(9,167,23,153),(10,168,24,154),(11,141,25,155),(12,142,26,156),(13,143,27,157),(14,144,28,158),(29,109,43,95),(30,110,44,96),(31,111,45,97),(32,112,46,98),(33,85,47,99),(34,86,48,100),(35,87,49,101),(36,88,50,102),(37,89,51,103),(38,90,52,104),(39,91,53,105),(40,92,54,106),(41,93,55,107),(42,94,56,108),(57,208,71,222),(58,209,72,223),(59,210,73,224),(60,211,74,197),(61,212,75,198),(62,213,76,199),(63,214,77,200),(64,215,78,201),(65,216,79,202),(66,217,80,203),(67,218,81,204),(68,219,82,205),(69,220,83,206),(70,221,84,207),(113,169,127,183),(114,170,128,184),(115,171,129,185),(116,172,130,186),(117,173,131,187),(118,174,132,188),(119,175,133,189),(120,176,134,190),(121,177,135,191),(122,178,136,192),(123,179,137,193),(124,180,138,194),(125,181,139,195),(126,182,140,196)], [(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)], [(1,56,15,42),(2,41,16,55),(3,54,17,40),(4,39,18,53),(5,52,19,38),(6,37,20,51),(7,50,21,36),(8,35,22,49),(9,48,23,34),(10,33,24,47),(11,46,25,32),(12,31,26,45),(13,44,27,30),(14,29,28,43),(57,151,71,165),(58,164,72,150),(59,149,73,163),(60,162,74,148),(61,147,75,161),(62,160,76,146),(63,145,77,159),(64,158,78,144),(65,143,79,157),(66,156,80,142),(67,141,81,155),(68,154,82,168),(69,167,83,153),(70,152,84,166),(85,176,99,190),(86,189,100,175),(87,174,101,188),(88,187,102,173),(89,172,103,186),(90,185,104,171),(91,170,105,184),(92,183,106,169),(93,196,107,182),(94,181,108,195),(95,194,109,180),(96,179,110,193),(97,192,111,178),(98,177,112,191),(113,212,127,198),(114,197,128,211),(115,210,129,224),(116,223,130,209),(117,208,131,222),(118,221,132,207),(119,206,133,220),(120,219,134,205),(121,204,135,218),(122,217,136,203),(123,202,137,216),(124,215,138,201),(125,200,139,214),(126,213,140,199)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 5 |
| 0 | 0 | 0 | 0 | 10 | 26 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 10 | 0 | 0 |
| 0 | 0 | 9 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 5 |
| 0 | 0 | 0 | 0 | 27 | 26 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 28 | 0 | 0 |
| 0 | 0 | 12 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [0,28,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,3,10,0,0,0,0,5,26],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,23,9,0,0,0,0,10,9,0,0,0,0,0,0,3,27,0,0,0,0,5,26],[12,0,0,0,0,0,0,17,0,0,0,0,0,0,19,12,0,0,0,0,28,10,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | D4⋊6D14 | D7×C4○D4 |
| kernel | C42.114D14 | C4×Dic14 | C4.D28 | D14.D4 | Dic7.D4 | Dic7⋊3Q8 | D28⋊C4 | C4×C7⋊D4 | C23.23D14 | C28.17D4 | C28⋊D4 | D4×C28 | C4×D4 | Dic7 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{114}D_{14} % in TeX
G:=Group("C4^2.114D14"); // GroupNames label
G:=SmallGroup(448,1012);
// by ID
G=gap.SmallGroup(448,1012);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀