metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.135D14, C14.672- 1+4, (C4×Q8)⋊17D7, (Q8×C28)⋊19C2, C4⋊C4.302D14, C28⋊2Q8⋊29C2, (C4×D28).23C2, D14⋊3Q8⋊11C2, (C4×Dic14)⋊41C2, C4.69(C4○D28), (C2×Q8).183D14, C28.122(C4○D4), (C4×C28).180C22, (C2×C14).128C24, (C2×C28).591C23, D14⋊C4.56C22, C4.50(Q8⋊2D7), C4.D28.11C2, (C2×D28).219C22, C4⋊Dic7.400C22, (Q8×C14).228C22, (C22×D7).50C23, C22.149(C23×D7), Dic7⋊C4.157C22, C7⋊4(C22.50C24), (C4×Dic7).210C22, (C2×Dic7).218C23, C2.25(D4.10D14), (C2×Dic14).243C22, C4⋊C4⋊D7⋊11C2, C4⋊C4⋊7D7⋊18C2, C2.67(C2×C4○D28), (C2×C4×D7).78C22, C14.113(C2×C4○D4), C2.13(C2×Q8⋊2D7), (C7×C4⋊C4).356C22, (C2×C4).172(C22×D7), SmallGroup(448,1037)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.135D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, ac=ca, dad-1=a-1, cbc-1=a2b-1, bd=db, dcd-1=c13 >
Subgroups: 900 in 212 conjugacy classes, 99 normal (29 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×Q8, C22⋊Q8, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.50C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C4×Dic14, C28⋊2Q8, C4×D28, C4.D28, C4⋊C4⋊7D7, C4⋊C4⋊D7, D14⋊3Q8, Q8×C28, C42.135D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.50C24, C4○D28, Q8⋊2D7, C23×D7, C2×C4○D28, C2×Q8⋊2D7, D4.10D14, C42.135D14
►On 224 points
Generators in S224
(1 125 163 210)(2 126 164 211)(3 127 165 212)(4 128 166 213)(5 129 167 214)(6 130 168 215)(7 131 141 216)(8 132 142 217)(9 133 143 218)(10 134 144 219)(11 135 145 220)(12 136 146 221)(13 137 147 222)(14 138 148 223)(15 139 149 224)(16 140 150 197)(17 113 151 198)(18 114 152 199)(19 115 153 200)(20 116 154 201)(21 117 155 202)(22 118 156 203)(23 119 157 204)(24 120 158 205)(25 121 159 206)(26 122 160 207)(27 123 161 208)(28 124 162 209)(29 99 181 60)(30 100 182 61)(31 101 183 62)(32 102 184 63)(33 103 185 64)(34 104 186 65)(35 105 187 66)(36 106 188 67)(37 107 189 68)(38 108 190 69)(39 109 191 70)(40 110 192 71)(41 111 193 72)(42 112 194 73)(43 85 195 74)(44 86 196 75)(45 87 169 76)(46 88 170 77)(47 89 171 78)(48 90 172 79)(49 91 173 80)(50 92 174 81)(51 93 175 82)(52 94 176 83)(53 95 177 84)(54 96 178 57)(55 97 179 58)(56 98 180 59)
(1 51 149 189)(2 38 150 176)(3 53 151 191)(4 40 152 178)(5 55 153 193)(6 42 154 180)(7 29 155 195)(8 44 156 182)(9 31 157 169)(10 46 158 184)(11 33 159 171)(12 48 160 186)(13 35 161 173)(14 50 162 188)(15 37 163 175)(16 52 164 190)(17 39 165 177)(18 54 166 192)(19 41 167 179)(20 56 168 194)(21 43 141 181)(22 30 142 196)(23 45 143 183)(24 32 144 170)(25 47 145 185)(26 34 146 172)(27 49 147 187)(28 36 148 174)(57 128 110 199)(58 115 111 214)(59 130 112 201)(60 117 85 216)(61 132 86 203)(62 119 87 218)(63 134 88 205)(64 121 89 220)(65 136 90 207)(66 123 91 222)(67 138 92 209)(68 125 93 224)(69 140 94 211)(70 127 95 198)(71 114 96 213)(72 129 97 200)(73 116 98 215)(74 131 99 202)(75 118 100 217)(76 133 101 204)(77 120 102 219)(78 135 103 206)(79 122 104 221)(80 137 105 208)(81 124 106 223)(82 139 107 210)(83 126 108 197)(84 113 109 212)
(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)
(1 223 15 209)(2 208 16 222)(3 221 17 207)(4 206 18 220)(5 219 19 205)(6 204 20 218)(7 217 21 203)(8 202 22 216)(9 215 23 201)(10 200 24 214)(11 213 25 199)(12 198 26 212)(13 211 27 197)(14 224 28 210)(29 75 43 61)(30 60 44 74)(31 73 45 59)(32 58 46 72)(33 71 47 57)(34 84 48 70)(35 69 49 83)(36 82 50 68)(37 67 51 81)(38 80 52 66)(39 65 53 79)(40 78 54 64)(41 63 55 77)(42 76 56 62)(85 182 99 196)(86 195 100 181)(87 180 101 194)(88 193 102 179)(89 178 103 192)(90 191 104 177)(91 176 105 190)(92 189 106 175)(93 174 107 188)(94 187 108 173)(95 172 109 186)(96 185 110 171)(97 170 111 184)(98 183 112 169)(113 160 127 146)(114 145 128 159)(115 158 129 144)(116 143 130 157)(117 156 131 142)(118 141 132 155)(119 154 133 168)(120 167 134 153)(121 152 135 166)(122 165 136 151)(123 150 137 164)(124 163 138 149)(125 148 139 162)(126 161 140 147)
G:=sub<Sym(224)| (1,125,163,210)(2,126,164,211)(3,127,165,212)(4,128,166,213)(5,129,167,214)(6,130,168,215)(7,131,141,216)(8,132,142,217)(9,133,143,218)(10,134,144,219)(11,135,145,220)(12,136,146,221)(13,137,147,222)(14,138,148,223)(15,139,149,224)(16,140,150,197)(17,113,151,198)(18,114,152,199)(19,115,153,200)(20,116,154,201)(21,117,155,202)(22,118,156,203)(23,119,157,204)(24,120,158,205)(25,121,159,206)(26,122,160,207)(27,123,161,208)(28,124,162,209)(29,99,181,60)(30,100,182,61)(31,101,183,62)(32,102,184,63)(33,103,185,64)(34,104,186,65)(35,105,187,66)(36,106,188,67)(37,107,189,68)(38,108,190,69)(39,109,191,70)(40,110,192,71)(41,111,193,72)(42,112,194,73)(43,85,195,74)(44,86,196,75)(45,87,169,76)(46,88,170,77)(47,89,171,78)(48,90,172,79)(49,91,173,80)(50,92,174,81)(51,93,175,82)(52,94,176,83)(53,95,177,84)(54,96,178,57)(55,97,179,58)(56,98,180,59), (1,51,149,189)(2,38,150,176)(3,53,151,191)(4,40,152,178)(5,55,153,193)(6,42,154,180)(7,29,155,195)(8,44,156,182)(9,31,157,169)(10,46,158,184)(11,33,159,171)(12,48,160,186)(13,35,161,173)(14,50,162,188)(15,37,163,175)(16,52,164,190)(17,39,165,177)(18,54,166,192)(19,41,167,179)(20,56,168,194)(21,43,141,181)(22,30,142,196)(23,45,143,183)(24,32,144,170)(25,47,145,185)(26,34,146,172)(27,49,147,187)(28,36,148,174)(57,128,110,199)(58,115,111,214)(59,130,112,201)(60,117,85,216)(61,132,86,203)(62,119,87,218)(63,134,88,205)(64,121,89,220)(65,136,90,207)(66,123,91,222)(67,138,92,209)(68,125,93,224)(69,140,94,211)(70,127,95,198)(71,114,96,213)(72,129,97,200)(73,116,98,215)(74,131,99,202)(75,118,100,217)(76,133,101,204)(77,120,102,219)(78,135,103,206)(79,122,104,221)(80,137,105,208)(81,124,106,223)(82,139,107,210)(83,126,108,197)(84,113,109,212), (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), (1,223,15,209)(2,208,16,222)(3,221,17,207)(4,206,18,220)(5,219,19,205)(6,204,20,218)(7,217,21,203)(8,202,22,216)(9,215,23,201)(10,200,24,214)(11,213,25,199)(12,198,26,212)(13,211,27,197)(14,224,28,210)(29,75,43,61)(30,60,44,74)(31,73,45,59)(32,58,46,72)(33,71,47,57)(34,84,48,70)(35,69,49,83)(36,82,50,68)(37,67,51,81)(38,80,52,66)(39,65,53,79)(40,78,54,64)(41,63,55,77)(42,76,56,62)(85,182,99,196)(86,195,100,181)(87,180,101,194)(88,193,102,179)(89,178,103,192)(90,191,104,177)(91,176,105,190)(92,189,106,175)(93,174,107,188)(94,187,108,173)(95,172,109,186)(96,185,110,171)(97,170,111,184)(98,183,112,169)(113,160,127,146)(114,145,128,159)(115,158,129,144)(116,143,130,157)(117,156,131,142)(118,141,132,155)(119,154,133,168)(120,167,134,153)(121,152,135,166)(122,165,136,151)(123,150,137,164)(124,163,138,149)(125,148,139,162)(126,161,140,147)>;
G:=Group( (1,125,163,210)(2,126,164,211)(3,127,165,212)(4,128,166,213)(5,129,167,214)(6,130,168,215)(7,131,141,216)(8,132,142,217)(9,133,143,218)(10,134,144,219)(11,135,145,220)(12,136,146,221)(13,137,147,222)(14,138,148,223)(15,139,149,224)(16,140,150,197)(17,113,151,198)(18,114,152,199)(19,115,153,200)(20,116,154,201)(21,117,155,202)(22,118,156,203)(23,119,157,204)(24,120,158,205)(25,121,159,206)(26,122,160,207)(27,123,161,208)(28,124,162,209)(29,99,181,60)(30,100,182,61)(31,101,183,62)(32,102,184,63)(33,103,185,64)(34,104,186,65)(35,105,187,66)(36,106,188,67)(37,107,189,68)(38,108,190,69)(39,109,191,70)(40,110,192,71)(41,111,193,72)(42,112,194,73)(43,85,195,74)(44,86,196,75)(45,87,169,76)(46,88,170,77)(47,89,171,78)(48,90,172,79)(49,91,173,80)(50,92,174,81)(51,93,175,82)(52,94,176,83)(53,95,177,84)(54,96,178,57)(55,97,179,58)(56,98,180,59), (1,51,149,189)(2,38,150,176)(3,53,151,191)(4,40,152,178)(5,55,153,193)(6,42,154,180)(7,29,155,195)(8,44,156,182)(9,31,157,169)(10,46,158,184)(11,33,159,171)(12,48,160,186)(13,35,161,173)(14,50,162,188)(15,37,163,175)(16,52,164,190)(17,39,165,177)(18,54,166,192)(19,41,167,179)(20,56,168,194)(21,43,141,181)(22,30,142,196)(23,45,143,183)(24,32,144,170)(25,47,145,185)(26,34,146,172)(27,49,147,187)(28,36,148,174)(57,128,110,199)(58,115,111,214)(59,130,112,201)(60,117,85,216)(61,132,86,203)(62,119,87,218)(63,134,88,205)(64,121,89,220)(65,136,90,207)(66,123,91,222)(67,138,92,209)(68,125,93,224)(69,140,94,211)(70,127,95,198)(71,114,96,213)(72,129,97,200)(73,116,98,215)(74,131,99,202)(75,118,100,217)(76,133,101,204)(77,120,102,219)(78,135,103,206)(79,122,104,221)(80,137,105,208)(81,124,106,223)(82,139,107,210)(83,126,108,197)(84,113,109,212), (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), (1,223,15,209)(2,208,16,222)(3,221,17,207)(4,206,18,220)(5,219,19,205)(6,204,20,218)(7,217,21,203)(8,202,22,216)(9,215,23,201)(10,200,24,214)(11,213,25,199)(12,198,26,212)(13,211,27,197)(14,224,28,210)(29,75,43,61)(30,60,44,74)(31,73,45,59)(32,58,46,72)(33,71,47,57)(34,84,48,70)(35,69,49,83)(36,82,50,68)(37,67,51,81)(38,80,52,66)(39,65,53,79)(40,78,54,64)(41,63,55,77)(42,76,56,62)(85,182,99,196)(86,195,100,181)(87,180,101,194)(88,193,102,179)(89,178,103,192)(90,191,104,177)(91,176,105,190)(92,189,106,175)(93,174,107,188)(94,187,108,173)(95,172,109,186)(96,185,110,171)(97,170,111,184)(98,183,112,169)(113,160,127,146)(114,145,128,159)(115,158,129,144)(116,143,130,157)(117,156,131,142)(118,141,132,155)(119,154,133,168)(120,167,134,153)(121,152,135,166)(122,165,136,151)(123,150,137,164)(124,163,138,149)(125,148,139,162)(126,161,140,147) );
G=PermutationGroup([[(1,125,163,210),(2,126,164,211),(3,127,165,212),(4,128,166,213),(5,129,167,214),(6,130,168,215),(7,131,141,216),(8,132,142,217),(9,133,143,218),(10,134,144,219),(11,135,145,220),(12,136,146,221),(13,137,147,222),(14,138,148,223),(15,139,149,224),(16,140,150,197),(17,113,151,198),(18,114,152,199),(19,115,153,200),(20,116,154,201),(21,117,155,202),(22,118,156,203),(23,119,157,204),(24,120,158,205),(25,121,159,206),(26,122,160,207),(27,123,161,208),(28,124,162,209),(29,99,181,60),(30,100,182,61),(31,101,183,62),(32,102,184,63),(33,103,185,64),(34,104,186,65),(35,105,187,66),(36,106,188,67),(37,107,189,68),(38,108,190,69),(39,109,191,70),(40,110,192,71),(41,111,193,72),(42,112,194,73),(43,85,195,74),(44,86,196,75),(45,87,169,76),(46,88,170,77),(47,89,171,78),(48,90,172,79),(49,91,173,80),(50,92,174,81),(51,93,175,82),(52,94,176,83),(53,95,177,84),(54,96,178,57),(55,97,179,58),(56,98,180,59)], [(1,51,149,189),(2,38,150,176),(3,53,151,191),(4,40,152,178),(5,55,153,193),(6,42,154,180),(7,29,155,195),(8,44,156,182),(9,31,157,169),(10,46,158,184),(11,33,159,171),(12,48,160,186),(13,35,161,173),(14,50,162,188),(15,37,163,175),(16,52,164,190),(17,39,165,177),(18,54,166,192),(19,41,167,179),(20,56,168,194),(21,43,141,181),(22,30,142,196),(23,45,143,183),(24,32,144,170),(25,47,145,185),(26,34,146,172),(27,49,147,187),(28,36,148,174),(57,128,110,199),(58,115,111,214),(59,130,112,201),(60,117,85,216),(61,132,86,203),(62,119,87,218),(63,134,88,205),(64,121,89,220),(65,136,90,207),(66,123,91,222),(67,138,92,209),(68,125,93,224),(69,140,94,211),(70,127,95,198),(71,114,96,213),(72,129,97,200),(73,116,98,215),(74,131,99,202),(75,118,100,217),(76,133,101,204),(77,120,102,219),(78,135,103,206),(79,122,104,221),(80,137,105,208),(81,124,106,223),(82,139,107,210),(83,126,108,197),(84,113,109,212)], [(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)], [(1,223,15,209),(2,208,16,222),(3,221,17,207),(4,206,18,220),(5,219,19,205),(6,204,20,218),(7,217,21,203),(8,202,22,216),(9,215,23,201),(10,200,24,214),(11,213,25,199),(12,198,26,212),(13,211,27,197),(14,224,28,210),(29,75,43,61),(30,60,44,74),(31,73,45,59),(32,58,46,72),(33,71,47,57),(34,84,48,70),(35,69,49,83),(36,82,50,68),(37,67,51,81),(38,80,52,66),(39,65,53,79),(40,78,54,64),(41,63,55,77),(42,76,56,62),(85,182,99,196),(86,195,100,181),(87,180,101,194),(88,193,102,179),(89,178,103,192),(90,191,104,177),(91,176,105,190),(92,189,106,175),(93,174,107,188),(94,187,108,173),(95,172,109,186),(96,185,110,171),(97,170,111,184),(98,183,112,169),(113,160,127,146),(114,145,128,159),(115,158,129,144),(116,143,130,157),(117,156,131,142),(118,141,132,155),(119,154,133,168),(120,167,134,153),(121,152,135,166),(122,165,136,151),(123,150,137,164),(124,163,138,149),(125,148,139,162),(126,161,140,147)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 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 | D7 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2- 1+4 | Q8⋊2D7 | D4.10D14 |
| kernel | C42.135D14 | C4×Dic14 | C28⋊2Q8 | C4×D28 | C4.D28 | C4⋊C4⋊7D7 | C4⋊C4⋊D7 | D14⋊3Q8 | Q8×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C4 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 2 | 4 | 2 | 1 | 3 | 8 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.135D14 ►in GL4(𝔽29) generated by
| 13 | 5 | 0 | 0 |
| 24 | 16 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 28 | 26 |
| 0 | 0 | 20 | 1 |
| 4 | 4 | 0 | 0 |
| 25 | 18 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 8 | 12 |
| 3 | 26 | 0 | 0 |
| 22 | 26 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
G:=sub<GL(4,GF(29))| [13,24,0,0,5,16,0,0,0,0,1,0,0,0,0,1],[17,0,0,0,0,17,0,0,0,0,28,20,0,0,26,1],[4,25,0,0,4,18,0,0,0,0,17,8,0,0,0,12],[3,22,0,0,26,26,0,0,0,0,17,0,0,0,0,17] >;
C42.135D14 in GAP, Magma, Sage, TeX
C_4^2._{135}D_{14} % in TeX
G:=Group("C4^2.135D14"); // GroupNames label
G:=SmallGroup(448,1037);
// by ID
G=gap.SmallGroup(448,1037);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,675,185,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,b*d=d*b,d*c*d^-1=c^13>;
// generators/relations