metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.139D14, C14.882- 1+4, (Q8×Dic7)⋊18C2, C4.4D4.8D7, (C4×Dic14)⋊44C2, (C2×D4).169D14, (C2×C28).77C23, (C2×Q8).135D14, C22⋊C4.33D14, (D4×Dic7).14C2, Dic7⋊Q8⋊22C2, C28.124(C4○D4), C4.15(D4⋊2D7), (C2×C14).215C24, (C4×C28).184C22, C28.17D4.9C2, C23.37(C22×D7), Dic7.28(C4○D4), C22⋊Dic14⋊38C2, (D4×C14).151C22, C23.D14⋊37C2, Dic7⋊C4.48C22, C4⋊Dic7.233C22, (C22×C14).45C23, (Q8×C14).124C22, C22.236(C23×D7), C23.D7.52C22, C23.11D14⋊18C2, C7⋊6(C22.50C24), (C4×Dic7).131C22, (C2×Dic7).252C23, C2.49(D4.10D14), (C2×Dic14).296C22, (C22×Dic7).140C22, C2.74(D7×C4○D4), C14.93(C2×C4○D4), C2.55(C2×D4⋊2D7), (C7×C4.4D4).6C2, (C2×C4).299(C22×D7), (C7×C22⋊C4).62C22, SmallGroup(448,1124)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.139D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, bd=db, dcd-1=c-1 >
Subgroups: 780 in 212 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C4.4D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C2×Dic7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C22.50C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C22×Dic7, D4×C14, Q8×C14, C4×Dic14, C23.11D14, C22⋊Dic14, C23.D14, D4×Dic7, C28.17D4, Dic7⋊Q8, Q8×Dic7, C7×C4.4D4, C42.139D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.50C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, D7×C4○D4, D4.10D14, C42.139D14
►On 224 points
Generators in S224
(1 101 26 108)(2 109 27 102)(3 103 28 110)(4 111 22 104)(5 105 23 112)(6 99 24 106)(7 107 25 100)(8 119 19 126)(9 113 20 120)(10 121 21 114)(11 115 15 122)(12 123 16 116)(13 117 17 124)(14 125 18 118)(29 140 49 133)(30 134 43 127)(31 128 44 135)(32 136 45 129)(33 130 46 137)(34 138 47 131)(35 132 48 139)(36 156 50 163)(37 164 51 157)(38 158 52 165)(39 166 53 159)(40 160 54 167)(41 168 55 161)(42 162 56 155)(57 171 186 212)(58 213 187 172)(59 173 188 214)(60 215 189 174)(61 175 190 216)(62 217 191 176)(63 177 192 218)(64 219 193 178)(65 179 194 220)(66 221 195 180)(67 181 196 222)(68 223 183 182)(69 169 184 224)(70 211 185 170)(71 197 147 97)(72 98 148 198)(73 199 149 85)(74 86 150 200)(75 201 151 87)(76 88 152 202)(77 203 153 89)(78 90 154 204)(79 205 141 91)(80 92 142 206)(81 207 143 93)(82 94 144 208)(83 209 145 95)(84 96 146 210)
(1 71 16 154)(2 79 17 148)(3 73 18 142)(4 81 19 150)(5 75 20 144)(6 83 21 152)(7 77 15 146)(8 74 22 143)(9 82 23 151)(10 76 24 145)(11 84 25 153)(12 78 26 147)(13 72 27 141)(14 80 28 149)(29 218 50 170)(30 212 51 178)(31 220 52 172)(32 214 53 180)(33 222 54 174)(34 216 55 182)(35 224 56 176)(36 211 49 177)(37 219 43 171)(38 213 44 179)(39 221 45 173)(40 215 46 181)(41 223 47 175)(42 217 48 169)(57 157 64 134)(58 128 65 165)(59 159 66 136)(60 130 67 167)(61 161 68 138)(62 132 69 155)(63 163 70 140)(85 125 92 110)(86 104 93 119)(87 113 94 112)(88 106 95 121)(89 115 96 100)(90 108 97 123)(91 117 98 102)(99 209 114 202)(101 197 116 204)(103 199 118 206)(105 201 120 208)(107 203 122 210)(109 205 124 198)(111 207 126 200)(127 186 164 193)(129 188 166 195)(131 190 168 183)(133 192 156 185)(135 194 158 187)(137 196 160 189)(139 184 162 191)
(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 31 12 38)(2 30 13 37)(3 29 14 36)(4 35 8 42)(5 34 9 41)(6 33 10 40)(7 32 11 39)(15 53 25 45)(16 52 26 44)(17 51 27 43)(18 50 28 49)(19 56 22 48)(20 55 23 47)(21 54 24 46)(57 198 193 91)(58 197 194 90)(59 210 195 89)(60 209 196 88)(61 208 183 87)(62 207 184 86)(63 206 185 85)(64 205 186 98)(65 204 187 97)(66 203 188 96)(67 202 189 95)(68 201 190 94)(69 200 191 93)(70 199 192 92)(71 220 78 213)(72 219 79 212)(73 218 80 211)(74 217 81 224)(75 216 82 223)(76 215 83 222)(77 214 84 221)(99 137 121 167)(100 136 122 166)(101 135 123 165)(102 134 124 164)(103 133 125 163)(104 132 126 162)(105 131 113 161)(106 130 114 160)(107 129 115 159)(108 128 116 158)(109 127 117 157)(110 140 118 156)(111 139 119 155)(112 138 120 168)(141 171 148 178)(142 170 149 177)(143 169 150 176)(144 182 151 175)(145 181 152 174)(146 180 153 173)(147 179 154 172)
G:=sub<Sym(224)| (1,101,26,108)(2,109,27,102)(3,103,28,110)(4,111,22,104)(5,105,23,112)(6,99,24,106)(7,107,25,100)(8,119,19,126)(9,113,20,120)(10,121,21,114)(11,115,15,122)(12,123,16,116)(13,117,17,124)(14,125,18,118)(29,140,49,133)(30,134,43,127)(31,128,44,135)(32,136,45,129)(33,130,46,137)(34,138,47,131)(35,132,48,139)(36,156,50,163)(37,164,51,157)(38,158,52,165)(39,166,53,159)(40,160,54,167)(41,168,55,161)(42,162,56,155)(57,171,186,212)(58,213,187,172)(59,173,188,214)(60,215,189,174)(61,175,190,216)(62,217,191,176)(63,177,192,218)(64,219,193,178)(65,179,194,220)(66,221,195,180)(67,181,196,222)(68,223,183,182)(69,169,184,224)(70,211,185,170)(71,197,147,97)(72,98,148,198)(73,199,149,85)(74,86,150,200)(75,201,151,87)(76,88,152,202)(77,203,153,89)(78,90,154,204)(79,205,141,91)(80,92,142,206)(81,207,143,93)(82,94,144,208)(83,209,145,95)(84,96,146,210), (1,71,16,154)(2,79,17,148)(3,73,18,142)(4,81,19,150)(5,75,20,144)(6,83,21,152)(7,77,15,146)(8,74,22,143)(9,82,23,151)(10,76,24,145)(11,84,25,153)(12,78,26,147)(13,72,27,141)(14,80,28,149)(29,218,50,170)(30,212,51,178)(31,220,52,172)(32,214,53,180)(33,222,54,174)(34,216,55,182)(35,224,56,176)(36,211,49,177)(37,219,43,171)(38,213,44,179)(39,221,45,173)(40,215,46,181)(41,223,47,175)(42,217,48,169)(57,157,64,134)(58,128,65,165)(59,159,66,136)(60,130,67,167)(61,161,68,138)(62,132,69,155)(63,163,70,140)(85,125,92,110)(86,104,93,119)(87,113,94,112)(88,106,95,121)(89,115,96,100)(90,108,97,123)(91,117,98,102)(99,209,114,202)(101,197,116,204)(103,199,118,206)(105,201,120,208)(107,203,122,210)(109,205,124,198)(111,207,126,200)(127,186,164,193)(129,188,166,195)(131,190,168,183)(133,192,156,185)(135,194,158,187)(137,196,160,189)(139,184,162,191), (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), (1,31,12,38)(2,30,13,37)(3,29,14,36)(4,35,8,42)(5,34,9,41)(6,33,10,40)(7,32,11,39)(15,53,25,45)(16,52,26,44)(17,51,27,43)(18,50,28,49)(19,56,22,48)(20,55,23,47)(21,54,24,46)(57,198,193,91)(58,197,194,90)(59,210,195,89)(60,209,196,88)(61,208,183,87)(62,207,184,86)(63,206,185,85)(64,205,186,98)(65,204,187,97)(66,203,188,96)(67,202,189,95)(68,201,190,94)(69,200,191,93)(70,199,192,92)(71,220,78,213)(72,219,79,212)(73,218,80,211)(74,217,81,224)(75,216,82,223)(76,215,83,222)(77,214,84,221)(99,137,121,167)(100,136,122,166)(101,135,123,165)(102,134,124,164)(103,133,125,163)(104,132,126,162)(105,131,113,161)(106,130,114,160)(107,129,115,159)(108,128,116,158)(109,127,117,157)(110,140,118,156)(111,139,119,155)(112,138,120,168)(141,171,148,178)(142,170,149,177)(143,169,150,176)(144,182,151,175)(145,181,152,174)(146,180,153,173)(147,179,154,172)>;
G:=Group( (1,101,26,108)(2,109,27,102)(3,103,28,110)(4,111,22,104)(5,105,23,112)(6,99,24,106)(7,107,25,100)(8,119,19,126)(9,113,20,120)(10,121,21,114)(11,115,15,122)(12,123,16,116)(13,117,17,124)(14,125,18,118)(29,140,49,133)(30,134,43,127)(31,128,44,135)(32,136,45,129)(33,130,46,137)(34,138,47,131)(35,132,48,139)(36,156,50,163)(37,164,51,157)(38,158,52,165)(39,166,53,159)(40,160,54,167)(41,168,55,161)(42,162,56,155)(57,171,186,212)(58,213,187,172)(59,173,188,214)(60,215,189,174)(61,175,190,216)(62,217,191,176)(63,177,192,218)(64,219,193,178)(65,179,194,220)(66,221,195,180)(67,181,196,222)(68,223,183,182)(69,169,184,224)(70,211,185,170)(71,197,147,97)(72,98,148,198)(73,199,149,85)(74,86,150,200)(75,201,151,87)(76,88,152,202)(77,203,153,89)(78,90,154,204)(79,205,141,91)(80,92,142,206)(81,207,143,93)(82,94,144,208)(83,209,145,95)(84,96,146,210), (1,71,16,154)(2,79,17,148)(3,73,18,142)(4,81,19,150)(5,75,20,144)(6,83,21,152)(7,77,15,146)(8,74,22,143)(9,82,23,151)(10,76,24,145)(11,84,25,153)(12,78,26,147)(13,72,27,141)(14,80,28,149)(29,218,50,170)(30,212,51,178)(31,220,52,172)(32,214,53,180)(33,222,54,174)(34,216,55,182)(35,224,56,176)(36,211,49,177)(37,219,43,171)(38,213,44,179)(39,221,45,173)(40,215,46,181)(41,223,47,175)(42,217,48,169)(57,157,64,134)(58,128,65,165)(59,159,66,136)(60,130,67,167)(61,161,68,138)(62,132,69,155)(63,163,70,140)(85,125,92,110)(86,104,93,119)(87,113,94,112)(88,106,95,121)(89,115,96,100)(90,108,97,123)(91,117,98,102)(99,209,114,202)(101,197,116,204)(103,199,118,206)(105,201,120,208)(107,203,122,210)(109,205,124,198)(111,207,126,200)(127,186,164,193)(129,188,166,195)(131,190,168,183)(133,192,156,185)(135,194,158,187)(137,196,160,189)(139,184,162,191), (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), (1,31,12,38)(2,30,13,37)(3,29,14,36)(4,35,8,42)(5,34,9,41)(6,33,10,40)(7,32,11,39)(15,53,25,45)(16,52,26,44)(17,51,27,43)(18,50,28,49)(19,56,22,48)(20,55,23,47)(21,54,24,46)(57,198,193,91)(58,197,194,90)(59,210,195,89)(60,209,196,88)(61,208,183,87)(62,207,184,86)(63,206,185,85)(64,205,186,98)(65,204,187,97)(66,203,188,96)(67,202,189,95)(68,201,190,94)(69,200,191,93)(70,199,192,92)(71,220,78,213)(72,219,79,212)(73,218,80,211)(74,217,81,224)(75,216,82,223)(76,215,83,222)(77,214,84,221)(99,137,121,167)(100,136,122,166)(101,135,123,165)(102,134,124,164)(103,133,125,163)(104,132,126,162)(105,131,113,161)(106,130,114,160)(107,129,115,159)(108,128,116,158)(109,127,117,157)(110,140,118,156)(111,139,119,155)(112,138,120,168)(141,171,148,178)(142,170,149,177)(143,169,150,176)(144,182,151,175)(145,181,152,174)(146,180,153,173)(147,179,154,172) );
G=PermutationGroup([[(1,101,26,108),(2,109,27,102),(3,103,28,110),(4,111,22,104),(5,105,23,112),(6,99,24,106),(7,107,25,100),(8,119,19,126),(9,113,20,120),(10,121,21,114),(11,115,15,122),(12,123,16,116),(13,117,17,124),(14,125,18,118),(29,140,49,133),(30,134,43,127),(31,128,44,135),(32,136,45,129),(33,130,46,137),(34,138,47,131),(35,132,48,139),(36,156,50,163),(37,164,51,157),(38,158,52,165),(39,166,53,159),(40,160,54,167),(41,168,55,161),(42,162,56,155),(57,171,186,212),(58,213,187,172),(59,173,188,214),(60,215,189,174),(61,175,190,216),(62,217,191,176),(63,177,192,218),(64,219,193,178),(65,179,194,220),(66,221,195,180),(67,181,196,222),(68,223,183,182),(69,169,184,224),(70,211,185,170),(71,197,147,97),(72,98,148,198),(73,199,149,85),(74,86,150,200),(75,201,151,87),(76,88,152,202),(77,203,153,89),(78,90,154,204),(79,205,141,91),(80,92,142,206),(81,207,143,93),(82,94,144,208),(83,209,145,95),(84,96,146,210)], [(1,71,16,154),(2,79,17,148),(3,73,18,142),(4,81,19,150),(5,75,20,144),(6,83,21,152),(7,77,15,146),(8,74,22,143),(9,82,23,151),(10,76,24,145),(11,84,25,153),(12,78,26,147),(13,72,27,141),(14,80,28,149),(29,218,50,170),(30,212,51,178),(31,220,52,172),(32,214,53,180),(33,222,54,174),(34,216,55,182),(35,224,56,176),(36,211,49,177),(37,219,43,171),(38,213,44,179),(39,221,45,173),(40,215,46,181),(41,223,47,175),(42,217,48,169),(57,157,64,134),(58,128,65,165),(59,159,66,136),(60,130,67,167),(61,161,68,138),(62,132,69,155),(63,163,70,140),(85,125,92,110),(86,104,93,119),(87,113,94,112),(88,106,95,121),(89,115,96,100),(90,108,97,123),(91,117,98,102),(99,209,114,202),(101,197,116,204),(103,199,118,206),(105,201,120,208),(107,203,122,210),(109,205,124,198),(111,207,126,200),(127,186,164,193),(129,188,166,195),(131,190,168,183),(133,192,156,185),(135,194,158,187),(137,196,160,189),(139,184,162,191)], [(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)], [(1,31,12,38),(2,30,13,37),(3,29,14,36),(4,35,8,42),(5,34,9,41),(6,33,10,40),(7,32,11,39),(15,53,25,45),(16,52,26,44),(17,51,27,43),(18,50,28,49),(19,56,22,48),(20,55,23,47),(21,54,24,46),(57,198,193,91),(58,197,194,90),(59,210,195,89),(60,209,196,88),(61,208,183,87),(62,207,184,86),(63,206,185,85),(64,205,186,98),(65,204,187,97),(66,203,188,96),(67,202,189,95),(68,201,190,94),(69,200,191,93),(70,199,192,92),(71,220,78,213),(72,219,79,212),(73,218,80,211),(74,217,81,224),(75,216,82,223),(76,215,83,222),(77,214,84,221),(99,137,121,167),(100,136,122,166),(101,135,123,165),(102,134,124,164),(103,133,125,163),(104,132,126,162),(105,131,113,161),(106,130,114,160),(107,129,115,159),(108,128,116,158),(109,127,117,157),(110,140,118,156),(111,139,119,155),(112,138,120,168),(141,171,148,178),(142,170,149,177),(143,169,150,176),(144,182,151,175),(145,181,152,174),(146,180,153,173),(147,179,154,172)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4O | 4P | 4Q | 4R | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| 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 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | 2- 1+4 | D4⋊2D7 | D7×C4○D4 | D4.10D14 |
| kernel | C42.139D14 | C4×Dic14 | C23.11D14 | C22⋊Dic14 | C23.D14 | D4×Dic7 | C28.17D4 | Dic7⋊Q8 | Q8×Dic7 | C7×C4.4D4 | C4.4D4 | Dic7 | C28 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 4 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 12 | 3 | 3 | 1 | 6 | 6 | 6 |
Matrix representation of C42.139D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 7 | 0 | 0 | 0 | 0 | 0 |
| 10 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 19 | 11 | 0 | 0 | 0 | 0 |
| 20 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,1,0,0,0,0,28,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[7,10,0,0,0,0,0,25,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28],[19,20,0,0,0,0,11,10,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,28] >;
C42.139D14 in GAP, Magma, Sage, TeX
C_4^2._{139}D_{14} % in TeX
G:=Group("C4^2.139D14"); // GroupNames label
G:=SmallGroup(448,1124);
// by ID
G=gap.SmallGroup(448,1124);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,387,100,794,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations