metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.134D14, C14.142- 1+4, (C4×Q8)⋊16D7, (Q8×C28)⋊18C2, C4⋊C4.301D14, (C4×Dic14)⋊40C2, C4.50(C4○D28), Dic7.Q8⋊10C2, (C2×Q8).182D14, C28.3Q8⋊17C2, C28.6Q8⋊27C2, C42⋊2D7.2C2, C42⋊D7.5C2, Dic7⋊Q8⋊10C2, C28.121(C4○D4), (C4×C28).179C22, (C2×C28).624C23, (C2×C14).127C24, D14⋊2Q8.10C2, D14⋊3Q8.10C2, D14⋊C4.126C22, Dic7⋊C4.78C22, C4⋊Dic7.370C22, (Q8×C14).227C22, (C4×Dic7).87C22, (C2×Dic7).58C23, (C22×D7).49C23, C22.148(C23×D7), C7⋊2(C22.35C24), C2.24(D4.10D14), C2.15(Q8.10D14), (C2×Dic14).292C22, C4⋊C4⋊D7.1C2, C2.66(C2×C4○D28), C14.57(C2×C4○D4), (C2×C4×D7).77C22, (C7×C4⋊C4).355C22, (C2×C4).290(C22×D7), SmallGroup(448,1036)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.134D14
G = < a,b,c,d | a4=b4=1, c14=a2b2, d2=a2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=b2c13 >
Subgroups: 740 in 192 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, D7, C14, C42, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×Q8, C4×Q8, C22⋊Q8, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.35C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, Q8×C14, C4×Dic14, C28.6Q8, C42⋊D7, C42⋊2D7, Dic7.Q8, C28.3Q8, D14⋊2Q8, C4⋊C4⋊D7, Dic7⋊Q8, D14⋊3Q8, Q8×C28, C42.134D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.35C24, C4○D28, C23×D7, C2×C4○D28, Q8.10D14, D4.10D14, C42.134D14
►On 224 points
Generators in S224
(1 172 124 97)(2 98 125 173)(3 174 126 99)(4 100 127 175)(5 176 128 101)(6 102 129 177)(7 178 130 103)(8 104 131 179)(9 180 132 105)(10 106 133 181)(11 182 134 107)(12 108 135 183)(13 184 136 109)(14 110 137 185)(15 186 138 111)(16 112 139 187)(17 188 140 85)(18 86 113 189)(19 190 114 87)(20 88 115 191)(21 192 116 89)(22 90 117 193)(23 194 118 91)(24 92 119 195)(25 196 120 93)(26 94 121 169)(27 170 122 95)(28 96 123 171)(29 143 213 67)(30 68 214 144)(31 145 215 69)(32 70 216 146)(33 147 217 71)(34 72 218 148)(35 149 219 73)(36 74 220 150)(37 151 221 75)(38 76 222 152)(39 153 223 77)(40 78 224 154)(41 155 197 79)(42 80 198 156)(43 157 199 81)(44 82 200 158)(45 159 201 83)(46 84 202 160)(47 161 203 57)(48 58 204 162)(49 163 205 59)(50 60 206 164)(51 165 207 61)(52 62 208 166)(53 167 209 63)(54 64 210 168)(55 141 211 65)(56 66 212 142)
(1 80 138 142)(2 81 139 143)(3 82 140 144)(4 83 113 145)(5 84 114 146)(6 57 115 147)(7 58 116 148)(8 59 117 149)(9 60 118 150)(10 61 119 151)(11 62 120 152)(12 63 121 153)(13 64 122 154)(14 65 123 155)(15 66 124 156)(16 67 125 157)(17 68 126 158)(18 69 127 159)(19 70 128 160)(20 71 129 161)(21 72 130 162)(22 73 131 163)(23 74 132 164)(24 75 133 165)(25 76 134 166)(26 77 135 167)(27 78 136 168)(28 79 137 141)(29 173 199 112)(30 174 200 85)(31 175 201 86)(32 176 202 87)(33 177 203 88)(34 178 204 89)(35 179 205 90)(36 180 206 91)(37 181 207 92)(38 182 208 93)(39 183 209 94)(40 184 210 95)(41 185 211 96)(42 186 212 97)(43 187 213 98)(44 188 214 99)(45 189 215 100)(46 190 216 101)(47 191 217 102)(48 192 218 103)(49 193 219 104)(50 194 220 105)(51 195 221 106)(52 196 222 107)(53 169 223 108)(54 170 224 109)(55 171 197 110)(56 172 198 111)
(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 14 124 137)(2 136 125 13)(3 12 126 135)(4 134 127 11)(5 10 128 133)(6 132 129 9)(7 8 130 131)(15 28 138 123)(16 122 139 27)(17 26 140 121)(18 120 113 25)(19 24 114 119)(20 118 115 23)(21 22 116 117)(29 40 213 224)(30 223 214 39)(31 38 215 222)(32 221 216 37)(33 36 217 220)(34 219 218 35)(41 56 197 212)(42 211 198 55)(43 54 199 210)(44 209 200 53)(45 52 201 208)(46 207 202 51)(47 50 203 206)(48 205 204 49)(57 60 161 164)(58 163 162 59)(61 84 165 160)(62 159 166 83)(63 82 167 158)(64 157 168 81)(65 80 141 156)(66 155 142 79)(67 78 143 154)(68 153 144 77)(69 76 145 152)(70 151 146 75)(71 74 147 150)(72 149 148 73)(85 94 188 169)(86 196 189 93)(87 92 190 195)(88 194 191 91)(89 90 192 193)(95 112 170 187)(96 186 171 111)(97 110 172 185)(98 184 173 109)(99 108 174 183)(100 182 175 107)(101 106 176 181)(102 180 177 105)(103 104 178 179)
G:=sub<Sym(224)| (1,172,124,97)(2,98,125,173)(3,174,126,99)(4,100,127,175)(5,176,128,101)(6,102,129,177)(7,178,130,103)(8,104,131,179)(9,180,132,105)(10,106,133,181)(11,182,134,107)(12,108,135,183)(13,184,136,109)(14,110,137,185)(15,186,138,111)(16,112,139,187)(17,188,140,85)(18,86,113,189)(19,190,114,87)(20,88,115,191)(21,192,116,89)(22,90,117,193)(23,194,118,91)(24,92,119,195)(25,196,120,93)(26,94,121,169)(27,170,122,95)(28,96,123,171)(29,143,213,67)(30,68,214,144)(31,145,215,69)(32,70,216,146)(33,147,217,71)(34,72,218,148)(35,149,219,73)(36,74,220,150)(37,151,221,75)(38,76,222,152)(39,153,223,77)(40,78,224,154)(41,155,197,79)(42,80,198,156)(43,157,199,81)(44,82,200,158)(45,159,201,83)(46,84,202,160)(47,161,203,57)(48,58,204,162)(49,163,205,59)(50,60,206,164)(51,165,207,61)(52,62,208,166)(53,167,209,63)(54,64,210,168)(55,141,211,65)(56,66,212,142), (1,80,138,142)(2,81,139,143)(3,82,140,144)(4,83,113,145)(5,84,114,146)(6,57,115,147)(7,58,116,148)(8,59,117,149)(9,60,118,150)(10,61,119,151)(11,62,120,152)(12,63,121,153)(13,64,122,154)(14,65,123,155)(15,66,124,156)(16,67,125,157)(17,68,126,158)(18,69,127,159)(19,70,128,160)(20,71,129,161)(21,72,130,162)(22,73,131,163)(23,74,132,164)(24,75,133,165)(25,76,134,166)(26,77,135,167)(27,78,136,168)(28,79,137,141)(29,173,199,112)(30,174,200,85)(31,175,201,86)(32,176,202,87)(33,177,203,88)(34,178,204,89)(35,179,205,90)(36,180,206,91)(37,181,207,92)(38,182,208,93)(39,183,209,94)(40,184,210,95)(41,185,211,96)(42,186,212,97)(43,187,213,98)(44,188,214,99)(45,189,215,100)(46,190,216,101)(47,191,217,102)(48,192,218,103)(49,193,219,104)(50,194,220,105)(51,195,221,106)(52,196,222,107)(53,169,223,108)(54,170,224,109)(55,171,197,110)(56,172,198,111), (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), (1,14,124,137)(2,136,125,13)(3,12,126,135)(4,134,127,11)(5,10,128,133)(6,132,129,9)(7,8,130,131)(15,28,138,123)(16,122,139,27)(17,26,140,121)(18,120,113,25)(19,24,114,119)(20,118,115,23)(21,22,116,117)(29,40,213,224)(30,223,214,39)(31,38,215,222)(32,221,216,37)(33,36,217,220)(34,219,218,35)(41,56,197,212)(42,211,198,55)(43,54,199,210)(44,209,200,53)(45,52,201,208)(46,207,202,51)(47,50,203,206)(48,205,204,49)(57,60,161,164)(58,163,162,59)(61,84,165,160)(62,159,166,83)(63,82,167,158)(64,157,168,81)(65,80,141,156)(66,155,142,79)(67,78,143,154)(68,153,144,77)(69,76,145,152)(70,151,146,75)(71,74,147,150)(72,149,148,73)(85,94,188,169)(86,196,189,93)(87,92,190,195)(88,194,191,91)(89,90,192,193)(95,112,170,187)(96,186,171,111)(97,110,172,185)(98,184,173,109)(99,108,174,183)(100,182,175,107)(101,106,176,181)(102,180,177,105)(103,104,178,179)>;
G:=Group( (1,172,124,97)(2,98,125,173)(3,174,126,99)(4,100,127,175)(5,176,128,101)(6,102,129,177)(7,178,130,103)(8,104,131,179)(9,180,132,105)(10,106,133,181)(11,182,134,107)(12,108,135,183)(13,184,136,109)(14,110,137,185)(15,186,138,111)(16,112,139,187)(17,188,140,85)(18,86,113,189)(19,190,114,87)(20,88,115,191)(21,192,116,89)(22,90,117,193)(23,194,118,91)(24,92,119,195)(25,196,120,93)(26,94,121,169)(27,170,122,95)(28,96,123,171)(29,143,213,67)(30,68,214,144)(31,145,215,69)(32,70,216,146)(33,147,217,71)(34,72,218,148)(35,149,219,73)(36,74,220,150)(37,151,221,75)(38,76,222,152)(39,153,223,77)(40,78,224,154)(41,155,197,79)(42,80,198,156)(43,157,199,81)(44,82,200,158)(45,159,201,83)(46,84,202,160)(47,161,203,57)(48,58,204,162)(49,163,205,59)(50,60,206,164)(51,165,207,61)(52,62,208,166)(53,167,209,63)(54,64,210,168)(55,141,211,65)(56,66,212,142), (1,80,138,142)(2,81,139,143)(3,82,140,144)(4,83,113,145)(5,84,114,146)(6,57,115,147)(7,58,116,148)(8,59,117,149)(9,60,118,150)(10,61,119,151)(11,62,120,152)(12,63,121,153)(13,64,122,154)(14,65,123,155)(15,66,124,156)(16,67,125,157)(17,68,126,158)(18,69,127,159)(19,70,128,160)(20,71,129,161)(21,72,130,162)(22,73,131,163)(23,74,132,164)(24,75,133,165)(25,76,134,166)(26,77,135,167)(27,78,136,168)(28,79,137,141)(29,173,199,112)(30,174,200,85)(31,175,201,86)(32,176,202,87)(33,177,203,88)(34,178,204,89)(35,179,205,90)(36,180,206,91)(37,181,207,92)(38,182,208,93)(39,183,209,94)(40,184,210,95)(41,185,211,96)(42,186,212,97)(43,187,213,98)(44,188,214,99)(45,189,215,100)(46,190,216,101)(47,191,217,102)(48,192,218,103)(49,193,219,104)(50,194,220,105)(51,195,221,106)(52,196,222,107)(53,169,223,108)(54,170,224,109)(55,171,197,110)(56,172,198,111), (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), (1,14,124,137)(2,136,125,13)(3,12,126,135)(4,134,127,11)(5,10,128,133)(6,132,129,9)(7,8,130,131)(15,28,138,123)(16,122,139,27)(17,26,140,121)(18,120,113,25)(19,24,114,119)(20,118,115,23)(21,22,116,117)(29,40,213,224)(30,223,214,39)(31,38,215,222)(32,221,216,37)(33,36,217,220)(34,219,218,35)(41,56,197,212)(42,211,198,55)(43,54,199,210)(44,209,200,53)(45,52,201,208)(46,207,202,51)(47,50,203,206)(48,205,204,49)(57,60,161,164)(58,163,162,59)(61,84,165,160)(62,159,166,83)(63,82,167,158)(64,157,168,81)(65,80,141,156)(66,155,142,79)(67,78,143,154)(68,153,144,77)(69,76,145,152)(70,151,146,75)(71,74,147,150)(72,149,148,73)(85,94,188,169)(86,196,189,93)(87,92,190,195)(88,194,191,91)(89,90,192,193)(95,112,170,187)(96,186,171,111)(97,110,172,185)(98,184,173,109)(99,108,174,183)(100,182,175,107)(101,106,176,181)(102,180,177,105)(103,104,178,179) );
G=PermutationGroup([[(1,172,124,97),(2,98,125,173),(3,174,126,99),(4,100,127,175),(5,176,128,101),(6,102,129,177),(7,178,130,103),(8,104,131,179),(9,180,132,105),(10,106,133,181),(11,182,134,107),(12,108,135,183),(13,184,136,109),(14,110,137,185),(15,186,138,111),(16,112,139,187),(17,188,140,85),(18,86,113,189),(19,190,114,87),(20,88,115,191),(21,192,116,89),(22,90,117,193),(23,194,118,91),(24,92,119,195),(25,196,120,93),(26,94,121,169),(27,170,122,95),(28,96,123,171),(29,143,213,67),(30,68,214,144),(31,145,215,69),(32,70,216,146),(33,147,217,71),(34,72,218,148),(35,149,219,73),(36,74,220,150),(37,151,221,75),(38,76,222,152),(39,153,223,77),(40,78,224,154),(41,155,197,79),(42,80,198,156),(43,157,199,81),(44,82,200,158),(45,159,201,83),(46,84,202,160),(47,161,203,57),(48,58,204,162),(49,163,205,59),(50,60,206,164),(51,165,207,61),(52,62,208,166),(53,167,209,63),(54,64,210,168),(55,141,211,65),(56,66,212,142)], [(1,80,138,142),(2,81,139,143),(3,82,140,144),(4,83,113,145),(5,84,114,146),(6,57,115,147),(7,58,116,148),(8,59,117,149),(9,60,118,150),(10,61,119,151),(11,62,120,152),(12,63,121,153),(13,64,122,154),(14,65,123,155),(15,66,124,156),(16,67,125,157),(17,68,126,158),(18,69,127,159),(19,70,128,160),(20,71,129,161),(21,72,130,162),(22,73,131,163),(23,74,132,164),(24,75,133,165),(25,76,134,166),(26,77,135,167),(27,78,136,168),(28,79,137,141),(29,173,199,112),(30,174,200,85),(31,175,201,86),(32,176,202,87),(33,177,203,88),(34,178,204,89),(35,179,205,90),(36,180,206,91),(37,181,207,92),(38,182,208,93),(39,183,209,94),(40,184,210,95),(41,185,211,96),(42,186,212,97),(43,187,213,98),(44,188,214,99),(45,189,215,100),(46,190,216,101),(47,191,217,102),(48,192,218,103),(49,193,219,104),(50,194,220,105),(51,195,221,106),(52,196,222,107),(53,169,223,108),(54,170,224,109),(55,171,197,110),(56,172,198,111)], [(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)], [(1,14,124,137),(2,136,125,13),(3,12,126,135),(4,134,127,11),(5,10,128,133),(6,132,129,9),(7,8,130,131),(15,28,138,123),(16,122,139,27),(17,26,140,121),(18,120,113,25),(19,24,114,119),(20,118,115,23),(21,22,116,117),(29,40,213,224),(30,223,214,39),(31,38,215,222),(32,221,216,37),(33,36,217,220),(34,219,218,35),(41,56,197,212),(42,211,198,55),(43,54,199,210),(44,209,200,53),(45,52,201,208),(46,207,202,51),(47,50,203,206),(48,205,204,49),(57,60,161,164),(58,163,162,59),(61,84,165,160),(62,159,166,83),(63,82,167,158),(64,157,168,81),(65,80,141,156),(66,155,142,79),(67,78,143,154),(68,153,144,77),(69,76,145,152),(70,151,146,75),(71,74,147,150),(72,149,148,73),(85,94,188,169),(86,196,189,93),(87,92,190,195),(88,194,191,91),(89,90,192,193),(95,112,170,187),(96,186,171,111),(97,110,172,185),(98,184,173,109),(99,108,174,183),(100,182,175,107),(101,106,176,181),(102,180,177,105),(103,104,178,179)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | D14 | D14 | D14 | C4○D28 | 2- 1+4 | Q8.10D14 | D4.10D14 |
| kernel | C42.134D14 | C4×Dic14 | C28.6Q8 | C42⋊D7 | C42⋊2D7 | Dic7.Q8 | C28.3Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | Dic7⋊Q8 | D14⋊3Q8 | Q8×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 9 | 9 | 3 | 24 | 2 | 6 | 6 |
Matrix representation of C42.134D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 17 | 26 | 5 |
| 0 | 0 | 12 | 0 | 24 | 3 |
| 0 | 0 | 3 | 12 | 3 | 12 |
| 0 | 0 | 17 | 0 | 17 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 6 | 0 | 0 |
| 0 | 0 | 23 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 6 |
| 0 | 0 | 0 | 0 | 23 | 21 |
| 16 | 20 | 0 | 0 | 0 | 0 |
| 28 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 9 | 9 |
| 0 | 0 | 10 | 7 | 20 | 14 |
| 0 | 0 | 0 | 0 | 10 | 10 |
| 0 | 0 | 0 | 0 | 19 | 22 |
| 3 | 8 | 0 | 0 | 0 | 0 |
| 28 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 20 | 20 |
| 0 | 0 | 22 | 19 | 15 | 9 |
| 0 | 0 | 19 | 19 | 19 | 19 |
| 0 | 0 | 7 | 10 | 7 | 10 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,26,12,3,17,0,0,17,0,12,0,0,0,26,24,3,17,0,0,5,3,12,0],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,8,23,0,0,0,0,6,21,0,0,0,0,0,0,8,23,0,0,0,0,6,21],[16,28,0,0,0,0,20,26,0,0,0,0,0,0,19,10,0,0,0,0,19,7,0,0,0,0,9,20,10,19,0,0,9,14,10,22],[3,28,0,0,0,0,8,26,0,0,0,0,0,0,10,22,19,7,0,0,10,19,19,10,0,0,20,15,19,7,0,0,20,9,19,10] >;
C42.134D14 in GAP, Magma, Sage, TeX
C_4^2._{134}D_{14} % in TeX
G:=Group("C4^2.134D14"); // GroupNames label
G:=SmallGroup(448,1036);
// by ID
G=gap.SmallGroup(448,1036);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,675,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2*b^2,d^2=a^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=b^2*c^13>;
// generators/relations