metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.126D14, C14.102- (1+4), C14.1092+ (1+4), Q8⋊9(C4×D7), (C4×Q8)⋊7D7, (Q8×C28)⋊9C2, D28⋊15(C2×C4), (C4×D28)⋊37C2, Q8⋊2D7⋊5C4, (Q8×Dic7)⋊9C2, C4⋊C4.325D14, D28⋊C4⋊17C2, C42⋊D7⋊16C2, C28.37(C22×C4), C14.27(C23×C4), (C2×Q8).202D14, C2.4(D4⋊8D14), (C2×C28).497C23, (C2×C14).118C24, (C4×C28).170C22, D14.11(C22×C4), C22.37(C23×D7), D14⋊C4.163C22, (C2×D28).262C22, C4⋊Dic7.368C22, (Q8×C14).218C22, Dic7.20(C22×C4), (C4×Dic7).85C22, Dic7⋊C4.138C22, C2.3(Q8.10D14), C7⋊4(C23.33C23), (C2×Dic7).214C23, (C22×D7).177C23, C4.37(C2×C4×D7), (D7×C4⋊C4)⋊17C2, (C4×D7)⋊5(C2×C4), (C7×Q8)⋊12(C2×C4), C2.29(D7×C22×C4), (C2×C4×D7).70C22, (C2×Q8⋊2D7).6C2, (C7×C4⋊C4).346C22, (C2×C4).654(C22×D7), SmallGroup(448,1027)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1252 in 294 conjugacy classes, 151 normal (22 characteristic)
C1, C2 [×3], C2 [×6], C4 [×6], C4 [×10], C22, C22 [×12], C7, C2×C4, C2×C4 [×6], C2×C4 [×23], D4 [×12], Q8 [×4], C23 [×3], D7 [×6], C14 [×3], C42 [×3], C42 [×3], C22⋊C4 [×6], C4⋊C4 [×3], C4⋊C4 [×7], C22×C4 [×9], C2×D4 [×3], C2×Q8, C4○D4 [×8], Dic7 [×2], Dic7 [×4], C28 [×6], C28 [×4], D14 [×6], D14 [×6], C2×C14, C2×C4⋊C4 [×3], C42⋊C2 [×3], C4×D4 [×6], C4×Q8, C4×Q8, C2×C4○D4, C4×D7 [×12], C4×D7 [×6], D28 [×12], C2×Dic7 [×2], C2×Dic7 [×3], C2×C28, C2×C28 [×6], C7×Q8 [×4], C22×D7 [×3], C23.33C23, C4×Dic7 [×3], Dic7⋊C4, Dic7⋊C4 [×3], C4⋊Dic7 [×3], D14⋊C4 [×6], C4×C28 [×3], C7×C4⋊C4 [×3], C2×C4×D7 [×9], C2×D28 [×3], Q8⋊2D7 [×8], Q8×C14, C42⋊D7 [×3], C4×D28 [×3], D7×C4⋊C4 [×3], D28⋊C4 [×3], Q8×Dic7, Q8×C28, C2×Q8⋊2D7, C42.126D14
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], D7, C22×C4 [×14], C24, D14 [×7], C23×C4, 2+ (1+4), 2- (1+4), C4×D7 [×4], C22×D7 [×7], C23.33C23, C2×C4×D7 [×6], C23×D7, D7×C22×C4, Q8.10D14, D4⋊8D14, C42.126D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 157 171 219)(2 220 172 158)(3 159 173 221)(4 222 174 160)(5 161 175 223)(6 224 176 162)(7 163 177 197)(8 198 178 164)(9 165 179 199)(10 200 180 166)(11 167 181 201)(12 202 182 168)(13 141 183 203)(14 204 184 142)(15 143 185 205)(16 206 186 144)(17 145 187 207)(18 208 188 146)(19 147 189 209)(20 210 190 148)(21 149 191 211)(22 212 192 150)(23 151 193 213)(24 214 194 152)(25 153 195 215)(26 216 196 154)(27 155 169 217)(28 218 170 156)(29 93 134 65)(30 66 135 94)(31 95 136 67)(32 68 137 96)(33 97 138 69)(34 70 139 98)(35 99 140 71)(36 72 113 100)(37 101 114 73)(38 74 115 102)(39 103 116 75)(40 76 117 104)(41 105 118 77)(42 78 119 106)(43 107 120 79)(44 80 121 108)(45 109 122 81)(46 82 123 110)(47 111 124 83)(48 84 125 112)(49 85 126 57)(50 58 127 86)(51 87 128 59)(52 60 129 88)(53 89 130 61)(54 62 131 90)(55 91 132 63)(56 64 133 92)
(1 72 185 86)(2 73 186 87)(3 74 187 88)(4 75 188 89)(5 76 189 90)(6 77 190 91)(7 78 191 92)(8 79 192 93)(9 80 193 94)(10 81 194 95)(11 82 195 96)(12 83 196 97)(13 84 169 98)(14 57 170 99)(15 58 171 100)(16 59 172 101)(17 60 173 102)(18 61 174 103)(19 62 175 104)(20 63 176 105)(21 64 177 106)(22 65 178 107)(23 66 179 108)(24 67 180 109)(25 68 181 110)(26 69 182 111)(27 70 183 112)(28 71 184 85)(29 164 120 212)(30 165 121 213)(31 166 122 214)(32 167 123 215)(33 168 124 216)(34 141 125 217)(35 142 126 218)(36 143 127 219)(37 144 128 220)(38 145 129 221)(39 146 130 222)(40 147 131 223)(41 148 132 224)(42 149 133 197)(43 150 134 198)(44 151 135 199)(45 152 136 200)(46 153 137 201)(47 154 138 202)(48 155 139 203)(49 156 140 204)(50 157 113 205)(51 158 114 206)(52 159 115 207)(53 160 116 208)(54 161 117 209)(55 162 118 210)(56 163 119 211)
(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)
(1 133 15 119)(2 118 16 132)(3 131 17 117)(4 116 18 130)(5 129 19 115)(6 114 20 128)(7 127 21 113)(8 140 22 126)(9 125 23 139)(10 138 24 124)(11 123 25 137)(12 136 26 122)(13 121 27 135)(14 134 28 120)(29 170 43 184)(30 183 44 169)(31 196 45 182)(32 181 46 195)(33 194 47 180)(34 179 48 193)(35 192 49 178)(36 177 50 191)(37 190 51 176)(38 175 52 189)(39 188 53 174)(40 173 54 187)(41 186 55 172)(42 171 56 185)(57 164 71 150)(58 149 72 163)(59 162 73 148)(60 147 74 161)(61 160 75 146)(62 145 76 159)(63 158 77 144)(64 143 78 157)(65 156 79 142)(66 141 80 155)(67 154 81 168)(68 167 82 153)(69 152 83 166)(70 165 84 151)(85 198 99 212)(86 211 100 197)(87 224 101 210)(88 209 102 223)(89 222 103 208)(90 207 104 221)(91 220 105 206)(92 205 106 219)(93 218 107 204)(94 203 108 217)(95 216 109 202)(96 201 110 215)(97 214 111 200)(98 199 112 213)
G:=sub<Sym(224)| (1,157,171,219)(2,220,172,158)(3,159,173,221)(4,222,174,160)(5,161,175,223)(6,224,176,162)(7,163,177,197)(8,198,178,164)(9,165,179,199)(10,200,180,166)(11,167,181,201)(12,202,182,168)(13,141,183,203)(14,204,184,142)(15,143,185,205)(16,206,186,144)(17,145,187,207)(18,208,188,146)(19,147,189,209)(20,210,190,148)(21,149,191,211)(22,212,192,150)(23,151,193,213)(24,214,194,152)(25,153,195,215)(26,216,196,154)(27,155,169,217)(28,218,170,156)(29,93,134,65)(30,66,135,94)(31,95,136,67)(32,68,137,96)(33,97,138,69)(34,70,139,98)(35,99,140,71)(36,72,113,100)(37,101,114,73)(38,74,115,102)(39,103,116,75)(40,76,117,104)(41,105,118,77)(42,78,119,106)(43,107,120,79)(44,80,121,108)(45,109,122,81)(46,82,123,110)(47,111,124,83)(48,84,125,112)(49,85,126,57)(50,58,127,86)(51,87,128,59)(52,60,129,88)(53,89,130,61)(54,62,131,90)(55,91,132,63)(56,64,133,92), (1,72,185,86)(2,73,186,87)(3,74,187,88)(4,75,188,89)(5,76,189,90)(6,77,190,91)(7,78,191,92)(8,79,192,93)(9,80,193,94)(10,81,194,95)(11,82,195,96)(12,83,196,97)(13,84,169,98)(14,57,170,99)(15,58,171,100)(16,59,172,101)(17,60,173,102)(18,61,174,103)(19,62,175,104)(20,63,176,105)(21,64,177,106)(22,65,178,107)(23,66,179,108)(24,67,180,109)(25,68,181,110)(26,69,182,111)(27,70,183,112)(28,71,184,85)(29,164,120,212)(30,165,121,213)(31,166,122,214)(32,167,123,215)(33,168,124,216)(34,141,125,217)(35,142,126,218)(36,143,127,219)(37,144,128,220)(38,145,129,221)(39,146,130,222)(40,147,131,223)(41,148,132,224)(42,149,133,197)(43,150,134,198)(44,151,135,199)(45,152,136,200)(46,153,137,201)(47,154,138,202)(48,155,139,203)(49,156,140,204)(50,157,113,205)(51,158,114,206)(52,159,115,207)(53,160,116,208)(54,161,117,209)(55,162,118,210)(56,163,119,211), (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), (1,133,15,119)(2,118,16,132)(3,131,17,117)(4,116,18,130)(5,129,19,115)(6,114,20,128)(7,127,21,113)(8,140,22,126)(9,125,23,139)(10,138,24,124)(11,123,25,137)(12,136,26,122)(13,121,27,135)(14,134,28,120)(29,170,43,184)(30,183,44,169)(31,196,45,182)(32,181,46,195)(33,194,47,180)(34,179,48,193)(35,192,49,178)(36,177,50,191)(37,190,51,176)(38,175,52,189)(39,188,53,174)(40,173,54,187)(41,186,55,172)(42,171,56,185)(57,164,71,150)(58,149,72,163)(59,162,73,148)(60,147,74,161)(61,160,75,146)(62,145,76,159)(63,158,77,144)(64,143,78,157)(65,156,79,142)(66,141,80,155)(67,154,81,168)(68,167,82,153)(69,152,83,166)(70,165,84,151)(85,198,99,212)(86,211,100,197)(87,224,101,210)(88,209,102,223)(89,222,103,208)(90,207,104,221)(91,220,105,206)(92,205,106,219)(93,218,107,204)(94,203,108,217)(95,216,109,202)(96,201,110,215)(97,214,111,200)(98,199,112,213)>;
G:=Group( (1,157,171,219)(2,220,172,158)(3,159,173,221)(4,222,174,160)(5,161,175,223)(6,224,176,162)(7,163,177,197)(8,198,178,164)(9,165,179,199)(10,200,180,166)(11,167,181,201)(12,202,182,168)(13,141,183,203)(14,204,184,142)(15,143,185,205)(16,206,186,144)(17,145,187,207)(18,208,188,146)(19,147,189,209)(20,210,190,148)(21,149,191,211)(22,212,192,150)(23,151,193,213)(24,214,194,152)(25,153,195,215)(26,216,196,154)(27,155,169,217)(28,218,170,156)(29,93,134,65)(30,66,135,94)(31,95,136,67)(32,68,137,96)(33,97,138,69)(34,70,139,98)(35,99,140,71)(36,72,113,100)(37,101,114,73)(38,74,115,102)(39,103,116,75)(40,76,117,104)(41,105,118,77)(42,78,119,106)(43,107,120,79)(44,80,121,108)(45,109,122,81)(46,82,123,110)(47,111,124,83)(48,84,125,112)(49,85,126,57)(50,58,127,86)(51,87,128,59)(52,60,129,88)(53,89,130,61)(54,62,131,90)(55,91,132,63)(56,64,133,92), (1,72,185,86)(2,73,186,87)(3,74,187,88)(4,75,188,89)(5,76,189,90)(6,77,190,91)(7,78,191,92)(8,79,192,93)(9,80,193,94)(10,81,194,95)(11,82,195,96)(12,83,196,97)(13,84,169,98)(14,57,170,99)(15,58,171,100)(16,59,172,101)(17,60,173,102)(18,61,174,103)(19,62,175,104)(20,63,176,105)(21,64,177,106)(22,65,178,107)(23,66,179,108)(24,67,180,109)(25,68,181,110)(26,69,182,111)(27,70,183,112)(28,71,184,85)(29,164,120,212)(30,165,121,213)(31,166,122,214)(32,167,123,215)(33,168,124,216)(34,141,125,217)(35,142,126,218)(36,143,127,219)(37,144,128,220)(38,145,129,221)(39,146,130,222)(40,147,131,223)(41,148,132,224)(42,149,133,197)(43,150,134,198)(44,151,135,199)(45,152,136,200)(46,153,137,201)(47,154,138,202)(48,155,139,203)(49,156,140,204)(50,157,113,205)(51,158,114,206)(52,159,115,207)(53,160,116,208)(54,161,117,209)(55,162,118,210)(56,163,119,211), (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), (1,133,15,119)(2,118,16,132)(3,131,17,117)(4,116,18,130)(5,129,19,115)(6,114,20,128)(7,127,21,113)(8,140,22,126)(9,125,23,139)(10,138,24,124)(11,123,25,137)(12,136,26,122)(13,121,27,135)(14,134,28,120)(29,170,43,184)(30,183,44,169)(31,196,45,182)(32,181,46,195)(33,194,47,180)(34,179,48,193)(35,192,49,178)(36,177,50,191)(37,190,51,176)(38,175,52,189)(39,188,53,174)(40,173,54,187)(41,186,55,172)(42,171,56,185)(57,164,71,150)(58,149,72,163)(59,162,73,148)(60,147,74,161)(61,160,75,146)(62,145,76,159)(63,158,77,144)(64,143,78,157)(65,156,79,142)(66,141,80,155)(67,154,81,168)(68,167,82,153)(69,152,83,166)(70,165,84,151)(85,198,99,212)(86,211,100,197)(87,224,101,210)(88,209,102,223)(89,222,103,208)(90,207,104,221)(91,220,105,206)(92,205,106,219)(93,218,107,204)(94,203,108,217)(95,216,109,202)(96,201,110,215)(97,214,111,200)(98,199,112,213) );
G=PermutationGroup([(1,157,171,219),(2,220,172,158),(3,159,173,221),(4,222,174,160),(5,161,175,223),(6,224,176,162),(7,163,177,197),(8,198,178,164),(9,165,179,199),(10,200,180,166),(11,167,181,201),(12,202,182,168),(13,141,183,203),(14,204,184,142),(15,143,185,205),(16,206,186,144),(17,145,187,207),(18,208,188,146),(19,147,189,209),(20,210,190,148),(21,149,191,211),(22,212,192,150),(23,151,193,213),(24,214,194,152),(25,153,195,215),(26,216,196,154),(27,155,169,217),(28,218,170,156),(29,93,134,65),(30,66,135,94),(31,95,136,67),(32,68,137,96),(33,97,138,69),(34,70,139,98),(35,99,140,71),(36,72,113,100),(37,101,114,73),(38,74,115,102),(39,103,116,75),(40,76,117,104),(41,105,118,77),(42,78,119,106),(43,107,120,79),(44,80,121,108),(45,109,122,81),(46,82,123,110),(47,111,124,83),(48,84,125,112),(49,85,126,57),(50,58,127,86),(51,87,128,59),(52,60,129,88),(53,89,130,61),(54,62,131,90),(55,91,132,63),(56,64,133,92)], [(1,72,185,86),(2,73,186,87),(3,74,187,88),(4,75,188,89),(5,76,189,90),(6,77,190,91),(7,78,191,92),(8,79,192,93),(9,80,193,94),(10,81,194,95),(11,82,195,96),(12,83,196,97),(13,84,169,98),(14,57,170,99),(15,58,171,100),(16,59,172,101),(17,60,173,102),(18,61,174,103),(19,62,175,104),(20,63,176,105),(21,64,177,106),(22,65,178,107),(23,66,179,108),(24,67,180,109),(25,68,181,110),(26,69,182,111),(27,70,183,112),(28,71,184,85),(29,164,120,212),(30,165,121,213),(31,166,122,214),(32,167,123,215),(33,168,124,216),(34,141,125,217),(35,142,126,218),(36,143,127,219),(37,144,128,220),(38,145,129,221),(39,146,130,222),(40,147,131,223),(41,148,132,224),(42,149,133,197),(43,150,134,198),(44,151,135,199),(45,152,136,200),(46,153,137,201),(47,154,138,202),(48,155,139,203),(49,156,140,204),(50,157,113,205),(51,158,114,206),(52,159,115,207),(53,160,116,208),(54,161,117,209),(55,162,118,210),(56,163,119,211)], [(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)], [(1,133,15,119),(2,118,16,132),(3,131,17,117),(4,116,18,130),(5,129,19,115),(6,114,20,128),(7,127,21,113),(8,140,22,126),(9,125,23,139),(10,138,24,124),(11,123,25,137),(12,136,26,122),(13,121,27,135),(14,134,28,120),(29,170,43,184),(30,183,44,169),(31,196,45,182),(32,181,46,195),(33,194,47,180),(34,179,48,193),(35,192,49,178),(36,177,50,191),(37,190,51,176),(38,175,52,189),(39,188,53,174),(40,173,54,187),(41,186,55,172),(42,171,56,185),(57,164,71,150),(58,149,72,163),(59,162,73,148),(60,147,74,161),(61,160,75,146),(62,145,76,159),(63,158,77,144),(64,143,78,157),(65,156,79,142),(66,141,80,155),(67,154,81,168),(68,167,82,153),(69,152,83,166),(70,165,84,151),(85,198,99,212),(86,211,100,197),(87,224,101,210),(88,209,102,223),(89,222,103,208),(90,207,104,221),(91,220,105,206),(92,205,106,219),(93,218,107,204),(94,203,108,217),(95,216,109,202),(96,201,110,215),(97,214,111,200),(98,199,112,213)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 24 | 0 |
| 0 | 0 | 0 | 17 | 0 | 24 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 16 | 0 | 0 |
| 0 | 0 | 13 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 16 |
| 0 | 0 | 0 | 0 | 13 | 24 |
| 16 | 10 | 0 | 0 | 0 | 0 |
| 19 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 21 | 16 | 16 |
| 0 | 0 | 8 | 26 | 13 | 6 |
| 0 | 0 | 21 | 21 | 8 | 8 |
| 0 | 0 | 8 | 26 | 21 | 3 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 12 | 24 | 5 |
| 0 | 0 | 5 | 12 | 19 | 5 |
| 0 | 0 | 17 | 12 | 12 | 17 |
| 0 | 0 | 5 | 12 | 24 | 17 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,24,0,12,0,0,0,0,24,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,5,13,0,0,0,0,16,24,0,0,0,0,0,0,5,13,0,0,0,0,16,24],[16,19,0,0,0,0,10,10,0,0,0,0,0,0,21,8,21,8,0,0,21,26,21,26,0,0,16,13,8,21,0,0,16,6,8,3],[0,17,0,0,0,0,17,0,0,0,0,0,0,0,17,5,17,5,0,0,12,12,12,12,0,0,24,19,12,24,0,0,5,5,17,17] >;
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 4A | ··· | 4N | 4O | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | ··· | 14 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | D14 | C4×D7 | 2+ (1+4) | 2- (1+4) | Q8.10D14 | D4⋊8D14 |
| kernel | C42.126D14 | C42⋊D7 | C4×D28 | D7×C4⋊C4 | D28⋊C4 | Q8×Dic7 | Q8×C28 | C2×Q8⋊2D7 | Q8⋊2D7 | C4×Q8 | C42 | C4⋊C4 | C2×Q8 | Q8 | C14 | C14 | C2 | C2 |
| # reps | 1 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 16 | 3 | 9 | 9 | 3 | 24 | 1 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{126}D_{14} % in TeX
G:=Group("C4^2.126D14"); // GroupNames label
G:=SmallGroup(448,1027);
// by ID
G=gap.SmallGroup(448,1027);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=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
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