metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.133D14, C14.132- 1+4, C14.1122+ 1+4, C28⋊Q8⋊17C2, (C4×Q8)⋊15D7, (C4×D28)⋊41C2, (Q8×C28)⋊17C2, C4⋊C4.300D14, D14⋊3Q8⋊10C2, D14⋊Q8⋊12C2, D14.5D4⋊9C2, C4.49(C4○D28), C4.D28⋊29C2, C28.23D4⋊9C2, C4⋊D28.10C2, C42⋊2D7⋊12C2, C42⋊D7⋊18C2, D14⋊C4.7C22, (C2×Q8).181D14, C28.120(C4○D4), (C2×C14).126C24, (C2×C28).171C23, (C4×C28).178C22, C2.24(D4⋊8D14), (C2×D28).263C22, Dic7⋊C4.77C22, C4⋊Dic7.369C22, (Q8×C14).226C22, (C4×Dic7).86C22, (C2×Dic7).57C23, (C22×D7).48C23, C22.147(C23×D7), C7⋊3(C22.36C24), (C2×Dic14).32C22, C2.14(Q8.10D14), C14.56(C2×C4○D4), C2.65(C2×C4○D28), (C2×C4×D7).76C22, (C7×C4⋊C4).354C22, (C2×C4).171(C22×D7), SmallGroup(448,1035)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.133D14
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=b2c13 >
Subgroups: 1060 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C22.36C24, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, Q8×C14, C42⋊D7, C4×D28, C4.D28, C42⋊2D7, C28⋊Q8, D14.5D4, C4⋊D28, D14⋊Q8, D14⋊3Q8, C28.23D4, Q8×C28, C42.133D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.36C24, C4○D28, C23×D7, C2×C4○D28, Q8.10D14, D4⋊8D14, C42.133D14
►On 224 points
Generators in S224
(1 38 15 52)(2 53 16 39)(3 40 17 54)(4 55 18 41)(5 42 19 56)(6 29 20 43)(7 44 21 30)(8 31 22 45)(9 46 23 32)(10 33 24 47)(11 48 25 34)(12 35 26 49)(13 50 27 36)(14 37 28 51)(57 99 71 85)(58 86 72 100)(59 101 73 87)(60 88 74 102)(61 103 75 89)(62 90 76 104)(63 105 77 91)(64 92 78 106)(65 107 79 93)(66 94 80 108)(67 109 81 95)(68 96 82 110)(69 111 83 97)(70 98 84 112)(113 202 127 216)(114 217 128 203)(115 204 129 218)(116 219 130 205)(117 206 131 220)(118 221 132 207)(119 208 133 222)(120 223 134 209)(121 210 135 224)(122 197 136 211)(123 212 137 198)(124 199 138 213)(125 214 139 200)(126 201 140 215)(141 192 155 178)(142 179 156 193)(143 194 157 180)(144 181 158 195)(145 196 159 182)(146 183 160 169)(147 170 161 184)(148 185 162 171)(149 172 163 186)(150 187 164 173)(151 174 165 188)(152 189 166 175)(153 176 167 190)(154 191 168 177)
(1 66 167 122)(2 67 168 123)(3 68 141 124)(4 69 142 125)(5 70 143 126)(6 71 144 127)(7 72 145 128)(8 73 146 129)(9 74 147 130)(10 75 148 131)(11 76 149 132)(12 77 150 133)(13 78 151 134)(14 79 152 135)(15 80 153 136)(16 81 154 137)(17 82 155 138)(18 83 156 139)(19 84 157 140)(20 57 158 113)(21 58 159 114)(22 59 160 115)(23 60 161 116)(24 61 162 117)(25 62 163 118)(26 63 164 119)(27 64 165 120)(28 65 166 121)(29 85 181 216)(30 86 182 217)(31 87 183 218)(32 88 184 219)(33 89 185 220)(34 90 186 221)(35 91 187 222)(36 92 188 223)(37 93 189 224)(38 94 190 197)(39 95 191 198)(40 96 192 199)(41 97 193 200)(42 98 194 201)(43 99 195 202)(44 100 196 203)(45 101 169 204)(46 102 170 205)(47 103 171 206)(48 104 172 207)(49 105 173 208)(50 106 174 209)(51 107 175 210)(52 108 176 211)(53 109 177 212)(54 110 178 213)(55 111 179 214)(56 112 180 215)
(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)
(1 114 153 72)(2 71 154 113)(3 140 155 70)(4 69 156 139)(5 138 157 68)(6 67 158 137)(7 136 159 66)(8 65 160 135)(9 134 161 64)(10 63 162 133)(11 132 163 62)(12 61 164 131)(13 130 165 60)(14 59 166 129)(15 128 167 58)(16 57 168 127)(17 126 141 84)(18 83 142 125)(19 124 143 82)(20 81 144 123)(21 122 145 80)(22 79 146 121)(23 120 147 78)(24 77 148 119)(25 118 149 76)(26 75 150 117)(27 116 151 74)(28 73 152 115)(29 95 195 212)(30 211 196 94)(31 93 169 210)(32 209 170 92)(33 91 171 208)(34 207 172 90)(35 89 173 206)(36 205 174 88)(37 87 175 204)(38 203 176 86)(39 85 177 202)(40 201 178 112)(41 111 179 200)(42 199 180 110)(43 109 181 198)(44 197 182 108)(45 107 183 224)(46 223 184 106)(47 105 185 222)(48 221 186 104)(49 103 187 220)(50 219 188 102)(51 101 189 218)(52 217 190 100)(53 99 191 216)(54 215 192 98)(55 97 193 214)(56 213 194 96)
G:=sub<Sym(224)| (1,38,15,52)(2,53,16,39)(3,40,17,54)(4,55,18,41)(5,42,19,56)(6,29,20,43)(7,44,21,30)(8,31,22,45)(9,46,23,32)(10,33,24,47)(11,48,25,34)(12,35,26,49)(13,50,27,36)(14,37,28,51)(57,99,71,85)(58,86,72,100)(59,101,73,87)(60,88,74,102)(61,103,75,89)(62,90,76,104)(63,105,77,91)(64,92,78,106)(65,107,79,93)(66,94,80,108)(67,109,81,95)(68,96,82,110)(69,111,83,97)(70,98,84,112)(113,202,127,216)(114,217,128,203)(115,204,129,218)(116,219,130,205)(117,206,131,220)(118,221,132,207)(119,208,133,222)(120,223,134,209)(121,210,135,224)(122,197,136,211)(123,212,137,198)(124,199,138,213)(125,214,139,200)(126,201,140,215)(141,192,155,178)(142,179,156,193)(143,194,157,180)(144,181,158,195)(145,196,159,182)(146,183,160,169)(147,170,161,184)(148,185,162,171)(149,172,163,186)(150,187,164,173)(151,174,165,188)(152,189,166,175)(153,176,167,190)(154,191,168,177), (1,66,167,122)(2,67,168,123)(3,68,141,124)(4,69,142,125)(5,70,143,126)(6,71,144,127)(7,72,145,128)(8,73,146,129)(9,74,147,130)(10,75,148,131)(11,76,149,132)(12,77,150,133)(13,78,151,134)(14,79,152,135)(15,80,153,136)(16,81,154,137)(17,82,155,138)(18,83,156,139)(19,84,157,140)(20,57,158,113)(21,58,159,114)(22,59,160,115)(23,60,161,116)(24,61,162,117)(25,62,163,118)(26,63,164,119)(27,64,165,120)(28,65,166,121)(29,85,181,216)(30,86,182,217)(31,87,183,218)(32,88,184,219)(33,89,185,220)(34,90,186,221)(35,91,187,222)(36,92,188,223)(37,93,189,224)(38,94,190,197)(39,95,191,198)(40,96,192,199)(41,97,193,200)(42,98,194,201)(43,99,195,202)(44,100,196,203)(45,101,169,204)(46,102,170,205)(47,103,171,206)(48,104,172,207)(49,105,173,208)(50,106,174,209)(51,107,175,210)(52,108,176,211)(53,109,177,212)(54,110,178,213)(55,111,179,214)(56,112,180,215), (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), (1,114,153,72)(2,71,154,113)(3,140,155,70)(4,69,156,139)(5,138,157,68)(6,67,158,137)(7,136,159,66)(8,65,160,135)(9,134,161,64)(10,63,162,133)(11,132,163,62)(12,61,164,131)(13,130,165,60)(14,59,166,129)(15,128,167,58)(16,57,168,127)(17,126,141,84)(18,83,142,125)(19,124,143,82)(20,81,144,123)(21,122,145,80)(22,79,146,121)(23,120,147,78)(24,77,148,119)(25,118,149,76)(26,75,150,117)(27,116,151,74)(28,73,152,115)(29,95,195,212)(30,211,196,94)(31,93,169,210)(32,209,170,92)(33,91,171,208)(34,207,172,90)(35,89,173,206)(36,205,174,88)(37,87,175,204)(38,203,176,86)(39,85,177,202)(40,201,178,112)(41,111,179,200)(42,199,180,110)(43,109,181,198)(44,197,182,108)(45,107,183,224)(46,223,184,106)(47,105,185,222)(48,221,186,104)(49,103,187,220)(50,219,188,102)(51,101,189,218)(52,217,190,100)(53,99,191,216)(54,215,192,98)(55,97,193,214)(56,213,194,96)>;
G:=Group( (1,38,15,52)(2,53,16,39)(3,40,17,54)(4,55,18,41)(5,42,19,56)(6,29,20,43)(7,44,21,30)(8,31,22,45)(9,46,23,32)(10,33,24,47)(11,48,25,34)(12,35,26,49)(13,50,27,36)(14,37,28,51)(57,99,71,85)(58,86,72,100)(59,101,73,87)(60,88,74,102)(61,103,75,89)(62,90,76,104)(63,105,77,91)(64,92,78,106)(65,107,79,93)(66,94,80,108)(67,109,81,95)(68,96,82,110)(69,111,83,97)(70,98,84,112)(113,202,127,216)(114,217,128,203)(115,204,129,218)(116,219,130,205)(117,206,131,220)(118,221,132,207)(119,208,133,222)(120,223,134,209)(121,210,135,224)(122,197,136,211)(123,212,137,198)(124,199,138,213)(125,214,139,200)(126,201,140,215)(141,192,155,178)(142,179,156,193)(143,194,157,180)(144,181,158,195)(145,196,159,182)(146,183,160,169)(147,170,161,184)(148,185,162,171)(149,172,163,186)(150,187,164,173)(151,174,165,188)(152,189,166,175)(153,176,167,190)(154,191,168,177), (1,66,167,122)(2,67,168,123)(3,68,141,124)(4,69,142,125)(5,70,143,126)(6,71,144,127)(7,72,145,128)(8,73,146,129)(9,74,147,130)(10,75,148,131)(11,76,149,132)(12,77,150,133)(13,78,151,134)(14,79,152,135)(15,80,153,136)(16,81,154,137)(17,82,155,138)(18,83,156,139)(19,84,157,140)(20,57,158,113)(21,58,159,114)(22,59,160,115)(23,60,161,116)(24,61,162,117)(25,62,163,118)(26,63,164,119)(27,64,165,120)(28,65,166,121)(29,85,181,216)(30,86,182,217)(31,87,183,218)(32,88,184,219)(33,89,185,220)(34,90,186,221)(35,91,187,222)(36,92,188,223)(37,93,189,224)(38,94,190,197)(39,95,191,198)(40,96,192,199)(41,97,193,200)(42,98,194,201)(43,99,195,202)(44,100,196,203)(45,101,169,204)(46,102,170,205)(47,103,171,206)(48,104,172,207)(49,105,173,208)(50,106,174,209)(51,107,175,210)(52,108,176,211)(53,109,177,212)(54,110,178,213)(55,111,179,214)(56,112,180,215), (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), (1,114,153,72)(2,71,154,113)(3,140,155,70)(4,69,156,139)(5,138,157,68)(6,67,158,137)(7,136,159,66)(8,65,160,135)(9,134,161,64)(10,63,162,133)(11,132,163,62)(12,61,164,131)(13,130,165,60)(14,59,166,129)(15,128,167,58)(16,57,168,127)(17,126,141,84)(18,83,142,125)(19,124,143,82)(20,81,144,123)(21,122,145,80)(22,79,146,121)(23,120,147,78)(24,77,148,119)(25,118,149,76)(26,75,150,117)(27,116,151,74)(28,73,152,115)(29,95,195,212)(30,211,196,94)(31,93,169,210)(32,209,170,92)(33,91,171,208)(34,207,172,90)(35,89,173,206)(36,205,174,88)(37,87,175,204)(38,203,176,86)(39,85,177,202)(40,201,178,112)(41,111,179,200)(42,199,180,110)(43,109,181,198)(44,197,182,108)(45,107,183,224)(46,223,184,106)(47,105,185,222)(48,221,186,104)(49,103,187,220)(50,219,188,102)(51,101,189,218)(52,217,190,100)(53,99,191,216)(54,215,192,98)(55,97,193,214)(56,213,194,96) );
G=PermutationGroup([[(1,38,15,52),(2,53,16,39),(3,40,17,54),(4,55,18,41),(5,42,19,56),(6,29,20,43),(7,44,21,30),(8,31,22,45),(9,46,23,32),(10,33,24,47),(11,48,25,34),(12,35,26,49),(13,50,27,36),(14,37,28,51),(57,99,71,85),(58,86,72,100),(59,101,73,87),(60,88,74,102),(61,103,75,89),(62,90,76,104),(63,105,77,91),(64,92,78,106),(65,107,79,93),(66,94,80,108),(67,109,81,95),(68,96,82,110),(69,111,83,97),(70,98,84,112),(113,202,127,216),(114,217,128,203),(115,204,129,218),(116,219,130,205),(117,206,131,220),(118,221,132,207),(119,208,133,222),(120,223,134,209),(121,210,135,224),(122,197,136,211),(123,212,137,198),(124,199,138,213),(125,214,139,200),(126,201,140,215),(141,192,155,178),(142,179,156,193),(143,194,157,180),(144,181,158,195),(145,196,159,182),(146,183,160,169),(147,170,161,184),(148,185,162,171),(149,172,163,186),(150,187,164,173),(151,174,165,188),(152,189,166,175),(153,176,167,190),(154,191,168,177)], [(1,66,167,122),(2,67,168,123),(3,68,141,124),(4,69,142,125),(5,70,143,126),(6,71,144,127),(7,72,145,128),(8,73,146,129),(9,74,147,130),(10,75,148,131),(11,76,149,132),(12,77,150,133),(13,78,151,134),(14,79,152,135),(15,80,153,136),(16,81,154,137),(17,82,155,138),(18,83,156,139),(19,84,157,140),(20,57,158,113),(21,58,159,114),(22,59,160,115),(23,60,161,116),(24,61,162,117),(25,62,163,118),(26,63,164,119),(27,64,165,120),(28,65,166,121),(29,85,181,216),(30,86,182,217),(31,87,183,218),(32,88,184,219),(33,89,185,220),(34,90,186,221),(35,91,187,222),(36,92,188,223),(37,93,189,224),(38,94,190,197),(39,95,191,198),(40,96,192,199),(41,97,193,200),(42,98,194,201),(43,99,195,202),(44,100,196,203),(45,101,169,204),(46,102,170,205),(47,103,171,206),(48,104,172,207),(49,105,173,208),(50,106,174,209),(51,107,175,210),(52,108,176,211),(53,109,177,212),(54,110,178,213),(55,111,179,214),(56,112,180,215)], [(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)], [(1,114,153,72),(2,71,154,113),(3,140,155,70),(4,69,156,139),(5,138,157,68),(6,67,158,137),(7,136,159,66),(8,65,160,135),(9,134,161,64),(10,63,162,133),(11,132,163,62),(12,61,164,131),(13,130,165,60),(14,59,166,129),(15,128,167,58),(16,57,168,127),(17,126,141,84),(18,83,142,125),(19,124,143,82),(20,81,144,123),(21,122,145,80),(22,79,146,121),(23,120,147,78),(24,77,148,119),(25,118,149,76),(26,75,150,117),(27,116,151,74),(28,73,152,115),(29,95,195,212),(30,211,196,94),(31,93,169,210),(32,209,170,92),(33,91,171,208),(34,207,172,90),(35,89,173,206),(36,205,174,88),(37,87,175,204),(38,203,176,86),(39,85,177,202),(40,201,178,112),(41,111,179,200),(42,199,180,110),(43,109,181,198),(44,197,182,108),(45,107,183,224),(46,223,184,106),(47,105,185,222),(48,221,186,104),(49,103,187,220),(50,219,188,102),(51,101,189,218),(52,217,190,100),(53,99,191,216),(54,215,192,98),(55,97,193,214),(56,213,194,96)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 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 | 28 | 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 | 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 | 2- 1+4 | Q8.10D14 | D4⋊8D14 |
| kernel | C42.133D14 | C42⋊D7 | C4×D28 | C4.D28 | C42⋊2D7 | C28⋊Q8 | D14.5D4 | C4⋊D28 | D14⋊Q8 | D14⋊3Q8 | C28.23D4 | Q8×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 9 | 9 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.133D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 21 | 18 | 28 |
| 0 | 0 | 8 | 1 | 1 | 11 |
| 0 | 0 | 18 | 28 | 1 | 8 |
| 0 | 0 | 1 | 11 | 21 | 28 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 15 | 0 | 0 |
| 0 | 0 | 14 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 |
| 0 | 0 | 0 | 0 | 14 | 9 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 10 |
| 0 | 0 | 0 | 0 | 19 | 22 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 10 | 7 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 21 | 0 | 0 |
| 0 | 0 | 19 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 21 |
| 0 | 0 | 0 | 0 | 19 | 21 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,8,18,1,0,0,21,1,28,11,0,0,18,1,1,21,0,0,28,11,8,28],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,20,14,0,0,0,0,15,9,0,0,0,0,0,0,20,14,0,0,0,0,15,9],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,19,10,0,0,0,0,19,7,0,0,10,19,0,0,0,0,10,22,0,0],[17,0,0,0,0,0,0,12,0,0,0,0,0,0,8,19,0,0,0,0,21,21,0,0,0,0,0,0,8,19,0,0,0,0,21,21] >;
C42.133D14 in GAP, Magma, Sage, TeX
C_4^2._{133}D_{14} % in TeX
G:=Group("C4^2.133D14"); // GroupNames label
G:=SmallGroup(448,1035);
// by ID
G=gap.SmallGroup(448,1035);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,675,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,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=b^2*c^13>;
// generators/relations