metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.131D14, (C4×Q8)⋊13D7, (C4×D28)⋊40C2, (Q8×C28)⋊15C2, (D7×C42)⋊7C2, C4⋊C4.298D14, D14⋊3Q8⋊46C2, D14.3(C4○D4), C4.48(C4○D28), C4⋊D28.14C2, C42⋊D7⋊17C2, (C2×Q8).179D14, C28.3Q8⋊47C2, D14.5D4⋊50C2, C28.340(C4○D4), C28.23D4⋊33C2, (C2×C28).622C23, (C4×C28).176C22, (C2×C14).124C24, C4.60(Q8⋊2D7), D14⋊C4.104C22, (C2×D28).217C22, C4⋊Dic7.308C22, (Q8×C14).224C22, C22.145(C23×D7), Dic7⋊C4.156C22, C7⋊5(C23.36C23), (C2×Dic7).217C23, (C4×Dic7).295C22, (C22×D7).181C23, C2.31(D7×C4○D4), C4⋊C4⋊D7⋊51C2, C2.63(C2×C4○D28), C14.146(C2×C4○D4), C2.12(C2×Q8⋊2D7), (C2×C4×D7).296C22, (C7×C4⋊C4).352C22, (C2×C4).170(C22×D7), SmallGroup(448,1033)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.131D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=a-1, dad-1=ab2, bc=cb, bd=db, dcd-1=c13 >
Subgroups: 1060 in 234 conjugacy classes, 101 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, Dic7, C28, C28, D14, D14, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C23.36C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, Q8×C14, D7×C42, C42⋊D7, C4×D28, C4×D28, C28.3Q8, D14.5D4, C4⋊D28, C4⋊C4⋊D7, D14⋊3Q8, C28.23D4, Q8×C28, C42.131D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, C4○D28, Q8⋊2D7, C23×D7, C2×C4○D28, C2×Q8⋊2D7, D7×C4○D4, C42.131D14
►On 224 points
Generators in S224
(1 198 52 65)(2 66 53 199)(3 200 54 67)(4 68 55 201)(5 202 56 69)(6 70 29 203)(7 204 30 71)(8 72 31 205)(9 206 32 73)(10 74 33 207)(11 208 34 75)(12 76 35 209)(13 210 36 77)(14 78 37 211)(15 212 38 79)(16 80 39 213)(17 214 40 81)(18 82 41 215)(19 216 42 83)(20 84 43 217)(21 218 44 57)(22 58 45 219)(23 220 46 59)(24 60 47 221)(25 222 48 61)(26 62 49 223)(27 224 50 63)(28 64 51 197)(85 174 138 146)(86 147 139 175)(87 176 140 148)(88 149 113 177)(89 178 114 150)(90 151 115 179)(91 180 116 152)(92 153 117 181)(93 182 118 154)(94 155 119 183)(95 184 120 156)(96 157 121 185)(97 186 122 158)(98 159 123 187)(99 188 124 160)(100 161 125 189)(101 190 126 162)(102 163 127 191)(103 192 128 164)(104 165 129 193)(105 194 130 166)(106 167 131 195)(107 196 132 168)(108 141 133 169)(109 170 134 142)(110 143 135 171)(111 172 136 144)(112 145 137 173)
(1 93 38 132)(2 94 39 133)(3 95 40 134)(4 96 41 135)(5 97 42 136)(6 98 43 137)(7 99 44 138)(8 100 45 139)(9 101 46 140)(10 102 47 113)(11 103 48 114)(12 104 49 115)(13 105 50 116)(14 106 51 117)(15 107 52 118)(16 108 53 119)(17 109 54 120)(18 110 55 121)(19 111 56 122)(20 112 29 123)(21 85 30 124)(22 86 31 125)(23 87 32 126)(24 88 33 127)(25 89 34 128)(26 90 35 129)(27 91 36 130)(28 92 37 131)(57 146 204 188)(58 147 205 189)(59 148 206 190)(60 149 207 191)(61 150 208 192)(62 151 209 193)(63 152 210 194)(64 153 211 195)(65 154 212 196)(66 155 213 169)(67 156 214 170)(68 157 215 171)(69 158 216 172)(70 159 217 173)(71 160 218 174)(72 161 219 175)(73 162 220 176)(74 163 221 177)(75 164 222 178)(76 165 223 179)(77 166 224 180)(78 167 197 181)(79 168 198 182)(80 141 199 183)(81 142 200 184)(82 143 201 185)(83 144 202 186)(84 145 203 187)
(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 51 15 37)(2 36 16 50)(3 49 17 35)(4 34 18 48)(5 47 19 33)(6 32 20 46)(7 45 21 31)(8 30 22 44)(9 43 23 29)(10 56 24 42)(11 41 25 55)(12 54 26 40)(13 39 27 53)(14 52 28 38)(57 219 71 205)(58 204 72 218)(59 217 73 203)(60 202 74 216)(61 215 75 201)(62 200 76 214)(63 213 77 199)(64 198 78 212)(65 211 79 197)(66 224 80 210)(67 209 81 223)(68 222 82 208)(69 207 83 221)(70 220 84 206)(85 125 99 139)(86 138 100 124)(87 123 101 137)(88 136 102 122)(89 121 103 135)(90 134 104 120)(91 119 105 133)(92 132 106 118)(93 117 107 131)(94 130 108 116)(95 115 109 129)(96 128 110 114)(97 113 111 127)(98 126 112 140)(141 194 155 180)(142 179 156 193)(143 192 157 178)(144 177 158 191)(145 190 159 176)(146 175 160 189)(147 188 161 174)(148 173 162 187)(149 186 163 172)(150 171 164 185)(151 184 165 170)(152 169 166 183)(153 182 167 196)(154 195 168 181)
G:=sub<Sym(224)| (1,198,52,65)(2,66,53,199)(3,200,54,67)(4,68,55,201)(5,202,56,69)(6,70,29,203)(7,204,30,71)(8,72,31,205)(9,206,32,73)(10,74,33,207)(11,208,34,75)(12,76,35,209)(13,210,36,77)(14,78,37,211)(15,212,38,79)(16,80,39,213)(17,214,40,81)(18,82,41,215)(19,216,42,83)(20,84,43,217)(21,218,44,57)(22,58,45,219)(23,220,46,59)(24,60,47,221)(25,222,48,61)(26,62,49,223)(27,224,50,63)(28,64,51,197)(85,174,138,146)(86,147,139,175)(87,176,140,148)(88,149,113,177)(89,178,114,150)(90,151,115,179)(91,180,116,152)(92,153,117,181)(93,182,118,154)(94,155,119,183)(95,184,120,156)(96,157,121,185)(97,186,122,158)(98,159,123,187)(99,188,124,160)(100,161,125,189)(101,190,126,162)(102,163,127,191)(103,192,128,164)(104,165,129,193)(105,194,130,166)(106,167,131,195)(107,196,132,168)(108,141,133,169)(109,170,134,142)(110,143,135,171)(111,172,136,144)(112,145,137,173), (1,93,38,132)(2,94,39,133)(3,95,40,134)(4,96,41,135)(5,97,42,136)(6,98,43,137)(7,99,44,138)(8,100,45,139)(9,101,46,140)(10,102,47,113)(11,103,48,114)(12,104,49,115)(13,105,50,116)(14,106,51,117)(15,107,52,118)(16,108,53,119)(17,109,54,120)(18,110,55,121)(19,111,56,122)(20,112,29,123)(21,85,30,124)(22,86,31,125)(23,87,32,126)(24,88,33,127)(25,89,34,128)(26,90,35,129)(27,91,36,130)(28,92,37,131)(57,146,204,188)(58,147,205,189)(59,148,206,190)(60,149,207,191)(61,150,208,192)(62,151,209,193)(63,152,210,194)(64,153,211,195)(65,154,212,196)(66,155,213,169)(67,156,214,170)(68,157,215,171)(69,158,216,172)(70,159,217,173)(71,160,218,174)(72,161,219,175)(73,162,220,176)(74,163,221,177)(75,164,222,178)(76,165,223,179)(77,166,224,180)(78,167,197,181)(79,168,198,182)(80,141,199,183)(81,142,200,184)(82,143,201,185)(83,144,202,186)(84,145,203,187), (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), (1,51,15,37)(2,36,16,50)(3,49,17,35)(4,34,18,48)(5,47,19,33)(6,32,20,46)(7,45,21,31)(8,30,22,44)(9,43,23,29)(10,56,24,42)(11,41,25,55)(12,54,26,40)(13,39,27,53)(14,52,28,38)(57,219,71,205)(58,204,72,218)(59,217,73,203)(60,202,74,216)(61,215,75,201)(62,200,76,214)(63,213,77,199)(64,198,78,212)(65,211,79,197)(66,224,80,210)(67,209,81,223)(68,222,82,208)(69,207,83,221)(70,220,84,206)(85,125,99,139)(86,138,100,124)(87,123,101,137)(88,136,102,122)(89,121,103,135)(90,134,104,120)(91,119,105,133)(92,132,106,118)(93,117,107,131)(94,130,108,116)(95,115,109,129)(96,128,110,114)(97,113,111,127)(98,126,112,140)(141,194,155,180)(142,179,156,193)(143,192,157,178)(144,177,158,191)(145,190,159,176)(146,175,160,189)(147,188,161,174)(148,173,162,187)(149,186,163,172)(150,171,164,185)(151,184,165,170)(152,169,166,183)(153,182,167,196)(154,195,168,181)>;
G:=Group( (1,198,52,65)(2,66,53,199)(3,200,54,67)(4,68,55,201)(5,202,56,69)(6,70,29,203)(7,204,30,71)(8,72,31,205)(9,206,32,73)(10,74,33,207)(11,208,34,75)(12,76,35,209)(13,210,36,77)(14,78,37,211)(15,212,38,79)(16,80,39,213)(17,214,40,81)(18,82,41,215)(19,216,42,83)(20,84,43,217)(21,218,44,57)(22,58,45,219)(23,220,46,59)(24,60,47,221)(25,222,48,61)(26,62,49,223)(27,224,50,63)(28,64,51,197)(85,174,138,146)(86,147,139,175)(87,176,140,148)(88,149,113,177)(89,178,114,150)(90,151,115,179)(91,180,116,152)(92,153,117,181)(93,182,118,154)(94,155,119,183)(95,184,120,156)(96,157,121,185)(97,186,122,158)(98,159,123,187)(99,188,124,160)(100,161,125,189)(101,190,126,162)(102,163,127,191)(103,192,128,164)(104,165,129,193)(105,194,130,166)(106,167,131,195)(107,196,132,168)(108,141,133,169)(109,170,134,142)(110,143,135,171)(111,172,136,144)(112,145,137,173), (1,93,38,132)(2,94,39,133)(3,95,40,134)(4,96,41,135)(5,97,42,136)(6,98,43,137)(7,99,44,138)(8,100,45,139)(9,101,46,140)(10,102,47,113)(11,103,48,114)(12,104,49,115)(13,105,50,116)(14,106,51,117)(15,107,52,118)(16,108,53,119)(17,109,54,120)(18,110,55,121)(19,111,56,122)(20,112,29,123)(21,85,30,124)(22,86,31,125)(23,87,32,126)(24,88,33,127)(25,89,34,128)(26,90,35,129)(27,91,36,130)(28,92,37,131)(57,146,204,188)(58,147,205,189)(59,148,206,190)(60,149,207,191)(61,150,208,192)(62,151,209,193)(63,152,210,194)(64,153,211,195)(65,154,212,196)(66,155,213,169)(67,156,214,170)(68,157,215,171)(69,158,216,172)(70,159,217,173)(71,160,218,174)(72,161,219,175)(73,162,220,176)(74,163,221,177)(75,164,222,178)(76,165,223,179)(77,166,224,180)(78,167,197,181)(79,168,198,182)(80,141,199,183)(81,142,200,184)(82,143,201,185)(83,144,202,186)(84,145,203,187), (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), (1,51,15,37)(2,36,16,50)(3,49,17,35)(4,34,18,48)(5,47,19,33)(6,32,20,46)(7,45,21,31)(8,30,22,44)(9,43,23,29)(10,56,24,42)(11,41,25,55)(12,54,26,40)(13,39,27,53)(14,52,28,38)(57,219,71,205)(58,204,72,218)(59,217,73,203)(60,202,74,216)(61,215,75,201)(62,200,76,214)(63,213,77,199)(64,198,78,212)(65,211,79,197)(66,224,80,210)(67,209,81,223)(68,222,82,208)(69,207,83,221)(70,220,84,206)(85,125,99,139)(86,138,100,124)(87,123,101,137)(88,136,102,122)(89,121,103,135)(90,134,104,120)(91,119,105,133)(92,132,106,118)(93,117,107,131)(94,130,108,116)(95,115,109,129)(96,128,110,114)(97,113,111,127)(98,126,112,140)(141,194,155,180)(142,179,156,193)(143,192,157,178)(144,177,158,191)(145,190,159,176)(146,175,160,189)(147,188,161,174)(148,173,162,187)(149,186,163,172)(150,171,164,185)(151,184,165,170)(152,169,166,183)(153,182,167,196)(154,195,168,181) );
G=PermutationGroup([[(1,198,52,65),(2,66,53,199),(3,200,54,67),(4,68,55,201),(5,202,56,69),(6,70,29,203),(7,204,30,71),(8,72,31,205),(9,206,32,73),(10,74,33,207),(11,208,34,75),(12,76,35,209),(13,210,36,77),(14,78,37,211),(15,212,38,79),(16,80,39,213),(17,214,40,81),(18,82,41,215),(19,216,42,83),(20,84,43,217),(21,218,44,57),(22,58,45,219),(23,220,46,59),(24,60,47,221),(25,222,48,61),(26,62,49,223),(27,224,50,63),(28,64,51,197),(85,174,138,146),(86,147,139,175),(87,176,140,148),(88,149,113,177),(89,178,114,150),(90,151,115,179),(91,180,116,152),(92,153,117,181),(93,182,118,154),(94,155,119,183),(95,184,120,156),(96,157,121,185),(97,186,122,158),(98,159,123,187),(99,188,124,160),(100,161,125,189),(101,190,126,162),(102,163,127,191),(103,192,128,164),(104,165,129,193),(105,194,130,166),(106,167,131,195),(107,196,132,168),(108,141,133,169),(109,170,134,142),(110,143,135,171),(111,172,136,144),(112,145,137,173)], [(1,93,38,132),(2,94,39,133),(3,95,40,134),(4,96,41,135),(5,97,42,136),(6,98,43,137),(7,99,44,138),(8,100,45,139),(9,101,46,140),(10,102,47,113),(11,103,48,114),(12,104,49,115),(13,105,50,116),(14,106,51,117),(15,107,52,118),(16,108,53,119),(17,109,54,120),(18,110,55,121),(19,111,56,122),(20,112,29,123),(21,85,30,124),(22,86,31,125),(23,87,32,126),(24,88,33,127),(25,89,34,128),(26,90,35,129),(27,91,36,130),(28,92,37,131),(57,146,204,188),(58,147,205,189),(59,148,206,190),(60,149,207,191),(61,150,208,192),(62,151,209,193),(63,152,210,194),(64,153,211,195),(65,154,212,196),(66,155,213,169),(67,156,214,170),(68,157,215,171),(69,158,216,172),(70,159,217,173),(71,160,218,174),(72,161,219,175),(73,162,220,176),(74,163,221,177),(75,164,222,178),(76,165,223,179),(77,166,224,180),(78,167,197,181),(79,168,198,182),(80,141,199,183),(81,142,200,184),(82,143,201,185),(83,144,202,186),(84,145,203,187)], [(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)], [(1,51,15,37),(2,36,16,50),(3,49,17,35),(4,34,18,48),(5,47,19,33),(6,32,20,46),(7,45,21,31),(8,30,22,44),(9,43,23,29),(10,56,24,42),(11,41,25,55),(12,54,26,40),(13,39,27,53),(14,52,28,38),(57,219,71,205),(58,204,72,218),(59,217,73,203),(60,202,74,216),(61,215,75,201),(62,200,76,214),(63,213,77,199),(64,198,78,212),(65,211,79,197),(66,224,80,210),(67,209,81,223),(68,222,82,208),(69,207,83,221),(70,220,84,206),(85,125,99,139),(86,138,100,124),(87,123,101,137),(88,136,102,122),(89,121,103,135),(90,134,104,120),(91,119,105,133),(92,132,106,118),(93,117,107,131),(94,130,108,116),(95,115,109,129),(96,128,110,114),(97,113,111,127),(98,126,112,140),(141,194,155,180),(142,179,156,193),(143,192,157,178),(144,177,158,191),(145,190,159,176),(146,175,160,189),(147,188,161,174),(148,173,162,187),(149,186,163,172),(150,171,164,185),(151,184,165,170),(152,169,166,183),(153,182,167,196),(154,195,168,181)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 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 | 14 | 14 | 28 | 28 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | C4○D28 | Q8⋊2D7 | D7×C4○D4 |
| kernel | C42.131D14 | D7×C42 | C42⋊D7 | C4×D28 | C28.3Q8 | D14.5D4 | C4⋊D28 | C4⋊C4⋊D7 | D14⋊3Q8 | C28.23D4 | Q8×C28 | C4×Q8 | C28 | D14 | C42 | C4⋊C4 | C2×Q8 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 3 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 3 | 8 | 4 | 9 | 9 | 3 | 24 | 6 | 6 |
Matrix representation of C42.131D14 ►in GL6(𝔽29)
| 8 | 7 | 0 | 0 | 0 | 0 |
| 20 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 12 | 17 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 19 | 0 | 0 |
| 0 | 0 | 10 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 24 |
| 0 | 0 | 0 | 0 | 17 | 12 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 15 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 5 |
| 0 | 0 | 0 | 0 | 12 | 17 |
G:=sub<GL(6,GF(29))| [8,20,0,0,0,0,7,21,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,12,0,0,0,0,0,17],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,7,10,0,0,0,0,19,19,0,0,0,0,0,0,17,17,0,0,0,0,24,12],[17,15,0,0,0,0,0,12,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,12,12,0,0,0,0,5,17] >;
C42.131D14 in GAP, Magma, Sage, TeX
C_4^2._{131}D_{14} % in TeX
G:=Group("C4^2.131D14"); // GroupNames label
G:=SmallGroup(448,1033);
// by ID
G=gap.SmallGroup(448,1033);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,1123,794,136,18822]);
// 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=a^-1,d*a*d^-1=a*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=c^13>;
// generators/relations