metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.154D14, C14.302- 1+4, C28⋊Q8⋊37C2, C4⋊C4.210D14, C42.C2⋊10D7, (C4×Dic14)⋊49C2, Dic7.Q8⋊35C2, D14⋊Q8.3C2, C28.3Q8⋊36C2, C42⋊2D7.1C2, Dic7⋊3Q8⋊37C2, (C2×C28).602C23, (C2×C14).240C24, (C4×C28).199C22, D14⋊C4.42C22, Dic7.13(C4○D4), C4⋊Dic7.316C22, C22.261(C23×D7), Dic7⋊C4.162C22, C7⋊4(C22.35C24), (C4×Dic7).216C22, (C2×Dic7).260C23, (C22×D7).105C23, C2.59(D4.10D14), C2.31(Q8.10D14), (C2×Dic14).252C22, C2.91(D7×C4○D4), C4⋊C4⋊D7.2C2, C4⋊C4⋊7D7.13C2, C14.202(C2×C4○D4), (C7×C42.C2)⋊13C2, (C2×C4×D7).130C22, (C7×C4⋊C4).195C22, (C2×C4).205(C22×D7), SmallGroup(448,1149)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.154D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b, dcd-1=c13 >
Subgroups: 764 in 192 conjugacy classes, 93 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic7, Dic7, C28, D14, C2×C14, C42⋊C2, C4×Q8, C22⋊Q8, C42.C2, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×C28, C22×D7, C22.35C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C4×Dic14, C42⋊2D7, Dic7⋊3Q8, C28⋊Q8, Dic7.Q8, C28.3Q8, C4⋊C4⋊7D7, D14⋊Q8, C4⋊C4⋊D7, C7×C42.C2, C42.154D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.35C24, C23×D7, Q8.10D14, D7×C4○D4, D4.10D14, C42.154D14
►On 224 points
Generators in S224
(1 42 15 56)(2 182 16 196)(3 44 17 30)(4 184 18 170)(5 46 19 32)(6 186 20 172)(7 48 21 34)(8 188 22 174)(9 50 23 36)(10 190 24 176)(11 52 25 38)(12 192 26 178)(13 54 27 40)(14 194 28 180)(29 100 43 86)(31 102 45 88)(33 104 47 90)(35 106 49 92)(37 108 51 94)(39 110 53 96)(41 112 55 98)(57 167 71 153)(58 222 72 208)(59 141 73 155)(60 224 74 210)(61 143 75 157)(62 198 76 212)(63 145 77 159)(64 200 78 214)(65 147 79 161)(66 202 80 216)(67 149 81 163)(68 204 82 218)(69 151 83 165)(70 206 84 220)(85 195 99 181)(87 169 101 183)(89 171 103 185)(91 173 105 187)(93 175 107 189)(95 177 109 191)(97 179 111 193)(113 197 127 211)(114 144 128 158)(115 199 129 213)(116 146 130 160)(117 201 131 215)(118 148 132 162)(119 203 133 217)(120 150 134 164)(121 205 135 219)(122 152 136 166)(123 207 137 221)(124 154 138 168)(125 209 139 223)(126 156 140 142)
(1 126 85 60)(2 61 86 127)(3 128 87 62)(4 63 88 129)(5 130 89 64)(6 65 90 131)(7 132 91 66)(8 67 92 133)(9 134 93 68)(10 69 94 135)(11 136 95 70)(12 71 96 137)(13 138 97 72)(14 73 98 139)(15 140 99 74)(16 75 100 113)(17 114 101 76)(18 77 102 115)(19 116 103 78)(20 79 104 117)(21 118 105 80)(22 81 106 119)(23 120 107 82)(24 83 108 121)(25 122 109 84)(26 57 110 123)(27 124 111 58)(28 59 112 125)(29 211 182 143)(30 144 183 212)(31 213 184 145)(32 146 185 214)(33 215 186 147)(34 148 187 216)(35 217 188 149)(36 150 189 218)(37 219 190 151)(38 152 191 220)(39 221 192 153)(40 154 193 222)(41 223 194 155)(42 156 195 224)(43 197 196 157)(44 158 169 198)(45 199 170 159)(46 160 171 200)(47 201 172 161)(48 162 173 202)(49 203 174 163)(50 164 175 204)(51 205 176 165)(52 166 177 206)(53 207 178 167)(54 168 179 208)(55 209 180 141)(56 142 181 210)
(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 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 179 43 193)(30 192 44 178)(31 177 45 191)(32 190 46 176)(33 175 47 189)(34 188 48 174)(35 173 49 187)(36 186 50 172)(37 171 51 185)(38 184 52 170)(39 169 53 183)(40 182 54 196)(41 195 55 181)(42 180 56 194)(57 114 71 128)(58 127 72 113)(59 140 73 126)(60 125 74 139)(61 138 75 124)(62 123 76 137)(63 136 77 122)(64 121 78 135)(65 134 79 120)(66 119 80 133)(67 132 81 118)(68 117 82 131)(69 130 83 116)(70 115 84 129)(85 98 99 112)(86 111 100 97)(87 96 101 110)(88 109 102 95)(89 94 103 108)(90 107 104 93)(91 92 105 106)(141 156 155 142)(143 154 157 168)(144 167 158 153)(145 152 159 166)(146 165 160 151)(147 150 161 164)(148 163 162 149)(197 208 211 222)(198 221 212 207)(199 206 213 220)(200 219 214 205)(201 204 215 218)(202 217 216 203)(209 224 223 210)
G:=sub<Sym(224)| (1,42,15,56)(2,182,16,196)(3,44,17,30)(4,184,18,170)(5,46,19,32)(6,186,20,172)(7,48,21,34)(8,188,22,174)(9,50,23,36)(10,190,24,176)(11,52,25,38)(12,192,26,178)(13,54,27,40)(14,194,28,180)(29,100,43,86)(31,102,45,88)(33,104,47,90)(35,106,49,92)(37,108,51,94)(39,110,53,96)(41,112,55,98)(57,167,71,153)(58,222,72,208)(59,141,73,155)(60,224,74,210)(61,143,75,157)(62,198,76,212)(63,145,77,159)(64,200,78,214)(65,147,79,161)(66,202,80,216)(67,149,81,163)(68,204,82,218)(69,151,83,165)(70,206,84,220)(85,195,99,181)(87,169,101,183)(89,171,103,185)(91,173,105,187)(93,175,107,189)(95,177,109,191)(97,179,111,193)(113,197,127,211)(114,144,128,158)(115,199,129,213)(116,146,130,160)(117,201,131,215)(118,148,132,162)(119,203,133,217)(120,150,134,164)(121,205,135,219)(122,152,136,166)(123,207,137,221)(124,154,138,168)(125,209,139,223)(126,156,140,142), (1,126,85,60)(2,61,86,127)(3,128,87,62)(4,63,88,129)(5,130,89,64)(6,65,90,131)(7,132,91,66)(8,67,92,133)(9,134,93,68)(10,69,94,135)(11,136,95,70)(12,71,96,137)(13,138,97,72)(14,73,98,139)(15,140,99,74)(16,75,100,113)(17,114,101,76)(18,77,102,115)(19,116,103,78)(20,79,104,117)(21,118,105,80)(22,81,106,119)(23,120,107,82)(24,83,108,121)(25,122,109,84)(26,57,110,123)(27,124,111,58)(28,59,112,125)(29,211,182,143)(30,144,183,212)(31,213,184,145)(32,146,185,214)(33,215,186,147)(34,148,187,216)(35,217,188,149)(36,150,189,218)(37,219,190,151)(38,152,191,220)(39,221,192,153)(40,154,193,222)(41,223,194,155)(42,156,195,224)(43,197,196,157)(44,158,169,198)(45,199,170,159)(46,160,171,200)(47,201,172,161)(48,162,173,202)(49,203,174,163)(50,164,175,204)(51,205,176,165)(52,166,177,206)(53,207,178,167)(54,168,179,208)(55,209,180,141)(56,142,181,210), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,179,43,193)(30,192,44,178)(31,177,45,191)(32,190,46,176)(33,175,47,189)(34,188,48,174)(35,173,49,187)(36,186,50,172)(37,171,51,185)(38,184,52,170)(39,169,53,183)(40,182,54,196)(41,195,55,181)(42,180,56,194)(57,114,71,128)(58,127,72,113)(59,140,73,126)(60,125,74,139)(61,138,75,124)(62,123,76,137)(63,136,77,122)(64,121,78,135)(65,134,79,120)(66,119,80,133)(67,132,81,118)(68,117,82,131)(69,130,83,116)(70,115,84,129)(85,98,99,112)(86,111,100,97)(87,96,101,110)(88,109,102,95)(89,94,103,108)(90,107,104,93)(91,92,105,106)(141,156,155,142)(143,154,157,168)(144,167,158,153)(145,152,159,166)(146,165,160,151)(147,150,161,164)(148,163,162,149)(197,208,211,222)(198,221,212,207)(199,206,213,220)(200,219,214,205)(201,204,215,218)(202,217,216,203)(209,224,223,210)>;
G:=Group( (1,42,15,56)(2,182,16,196)(3,44,17,30)(4,184,18,170)(5,46,19,32)(6,186,20,172)(7,48,21,34)(8,188,22,174)(9,50,23,36)(10,190,24,176)(11,52,25,38)(12,192,26,178)(13,54,27,40)(14,194,28,180)(29,100,43,86)(31,102,45,88)(33,104,47,90)(35,106,49,92)(37,108,51,94)(39,110,53,96)(41,112,55,98)(57,167,71,153)(58,222,72,208)(59,141,73,155)(60,224,74,210)(61,143,75,157)(62,198,76,212)(63,145,77,159)(64,200,78,214)(65,147,79,161)(66,202,80,216)(67,149,81,163)(68,204,82,218)(69,151,83,165)(70,206,84,220)(85,195,99,181)(87,169,101,183)(89,171,103,185)(91,173,105,187)(93,175,107,189)(95,177,109,191)(97,179,111,193)(113,197,127,211)(114,144,128,158)(115,199,129,213)(116,146,130,160)(117,201,131,215)(118,148,132,162)(119,203,133,217)(120,150,134,164)(121,205,135,219)(122,152,136,166)(123,207,137,221)(124,154,138,168)(125,209,139,223)(126,156,140,142), (1,126,85,60)(2,61,86,127)(3,128,87,62)(4,63,88,129)(5,130,89,64)(6,65,90,131)(7,132,91,66)(8,67,92,133)(9,134,93,68)(10,69,94,135)(11,136,95,70)(12,71,96,137)(13,138,97,72)(14,73,98,139)(15,140,99,74)(16,75,100,113)(17,114,101,76)(18,77,102,115)(19,116,103,78)(20,79,104,117)(21,118,105,80)(22,81,106,119)(23,120,107,82)(24,83,108,121)(25,122,109,84)(26,57,110,123)(27,124,111,58)(28,59,112,125)(29,211,182,143)(30,144,183,212)(31,213,184,145)(32,146,185,214)(33,215,186,147)(34,148,187,216)(35,217,188,149)(36,150,189,218)(37,219,190,151)(38,152,191,220)(39,221,192,153)(40,154,193,222)(41,223,194,155)(42,156,195,224)(43,197,196,157)(44,158,169,198)(45,199,170,159)(46,160,171,200)(47,201,172,161)(48,162,173,202)(49,203,174,163)(50,164,175,204)(51,205,176,165)(52,166,177,206)(53,207,178,167)(54,168,179,208)(55,209,180,141)(56,142,181,210), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,179,43,193)(30,192,44,178)(31,177,45,191)(32,190,46,176)(33,175,47,189)(34,188,48,174)(35,173,49,187)(36,186,50,172)(37,171,51,185)(38,184,52,170)(39,169,53,183)(40,182,54,196)(41,195,55,181)(42,180,56,194)(57,114,71,128)(58,127,72,113)(59,140,73,126)(60,125,74,139)(61,138,75,124)(62,123,76,137)(63,136,77,122)(64,121,78,135)(65,134,79,120)(66,119,80,133)(67,132,81,118)(68,117,82,131)(69,130,83,116)(70,115,84,129)(85,98,99,112)(86,111,100,97)(87,96,101,110)(88,109,102,95)(89,94,103,108)(90,107,104,93)(91,92,105,106)(141,156,155,142)(143,154,157,168)(144,167,158,153)(145,152,159,166)(146,165,160,151)(147,150,161,164)(148,163,162,149)(197,208,211,222)(198,221,212,207)(199,206,213,220)(200,219,214,205)(201,204,215,218)(202,217,216,203)(209,224,223,210) );
G=PermutationGroup([[(1,42,15,56),(2,182,16,196),(3,44,17,30),(4,184,18,170),(5,46,19,32),(6,186,20,172),(7,48,21,34),(8,188,22,174),(9,50,23,36),(10,190,24,176),(11,52,25,38),(12,192,26,178),(13,54,27,40),(14,194,28,180),(29,100,43,86),(31,102,45,88),(33,104,47,90),(35,106,49,92),(37,108,51,94),(39,110,53,96),(41,112,55,98),(57,167,71,153),(58,222,72,208),(59,141,73,155),(60,224,74,210),(61,143,75,157),(62,198,76,212),(63,145,77,159),(64,200,78,214),(65,147,79,161),(66,202,80,216),(67,149,81,163),(68,204,82,218),(69,151,83,165),(70,206,84,220),(85,195,99,181),(87,169,101,183),(89,171,103,185),(91,173,105,187),(93,175,107,189),(95,177,109,191),(97,179,111,193),(113,197,127,211),(114,144,128,158),(115,199,129,213),(116,146,130,160),(117,201,131,215),(118,148,132,162),(119,203,133,217),(120,150,134,164),(121,205,135,219),(122,152,136,166),(123,207,137,221),(124,154,138,168),(125,209,139,223),(126,156,140,142)], [(1,126,85,60),(2,61,86,127),(3,128,87,62),(4,63,88,129),(5,130,89,64),(6,65,90,131),(7,132,91,66),(8,67,92,133),(9,134,93,68),(10,69,94,135),(11,136,95,70),(12,71,96,137),(13,138,97,72),(14,73,98,139),(15,140,99,74),(16,75,100,113),(17,114,101,76),(18,77,102,115),(19,116,103,78),(20,79,104,117),(21,118,105,80),(22,81,106,119),(23,120,107,82),(24,83,108,121),(25,122,109,84),(26,57,110,123),(27,124,111,58),(28,59,112,125),(29,211,182,143),(30,144,183,212),(31,213,184,145),(32,146,185,214),(33,215,186,147),(34,148,187,216),(35,217,188,149),(36,150,189,218),(37,219,190,151),(38,152,191,220),(39,221,192,153),(40,154,193,222),(41,223,194,155),(42,156,195,224),(43,197,196,157),(44,158,169,198),(45,199,170,159),(46,160,171,200),(47,201,172,161),(48,162,173,202),(49,203,174,163),(50,164,175,204),(51,205,176,165),(52,166,177,206),(53,207,178,167),(54,168,179,208),(55,209,180,141),(56,142,181,210)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,179,43,193),(30,192,44,178),(31,177,45,191),(32,190,46,176),(33,175,47,189),(34,188,48,174),(35,173,49,187),(36,186,50,172),(37,171,51,185),(38,184,52,170),(39,169,53,183),(40,182,54,196),(41,195,55,181),(42,180,56,194),(57,114,71,128),(58,127,72,113),(59,140,73,126),(60,125,74,139),(61,138,75,124),(62,123,76,137),(63,136,77,122),(64,121,78,135),(65,134,79,120),(66,119,80,133),(67,132,81,118),(68,117,82,131),(69,130,83,116),(70,115,84,129),(85,98,99,112),(86,111,100,97),(87,96,101,110),(88,109,102,95),(89,94,103,108),(90,107,104,93),(91,92,105,106),(141,156,155,142),(143,154,157,168),(144,167,158,153),(145,152,159,166),(146,165,160,151),(147,150,161,164),(148,163,162,149),(197,208,211,222),(198,221,212,207),(199,206,213,220),(200,219,214,205),(201,204,215,218),(202,217,216,203),(209,224,223,210)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 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 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2- 1+4 | Q8.10D14 | D7×C4○D4 | D4.10D14 |
| kernel | C42.154D14 | C4×Dic14 | C42⋊2D7 | Dic7⋊3Q8 | C28⋊Q8 | Dic7.Q8 | C28.3Q8 | C4⋊C4⋊7D7 | D14⋊Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | Dic7 | C42 | C4⋊C4 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 3 | 1 | 1 | 2 | 3 | 1 | 3 | 4 | 3 | 18 | 2 | 6 | 6 | 6 |
Matrix representation of C42.154D14 ►in GL8(𝔽29)
| 24 | 22 | 13 | 11 | 0 | 0 | 0 | 0 |
| 4 | 0 | 6 | 9 | 0 | 0 | 0 | 0 |
| 18 | 16 | 21 | 7 | 0 | 0 | 0 | 0 |
| 16 | 28 | 6 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 24 | 25 | 7 |
| 0 | 0 | 0 | 0 | 5 | 27 | 23 | 20 |
| 0 | 0 | 0 | 0 | 23 | 16 | 11 | 10 |
| 0 | 0 | 0 | 0 | 13 | 0 | 24 | 25 |
| 2 | 26 | 18 | 13 | 0 | 0 | 0 | 0 |
| 10 | 0 | 15 | 8 | 0 | 0 | 0 | 0 |
| 16 | 11 | 9 | 3 | 0 | 0 | 0 | 0 |
| 11 | 12 | 15 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 26 | 25 |
| 0 | 0 | 0 | 0 | 0 | 0 | 2 | 3 |
| 0 | 27 | 4 | 15 | 0 | 0 | 0 | 0 |
| 24 | 5 | 17 | 17 | 0 | 0 | 0 | 0 |
| 12 | 2 | 1 | 2 | 0 | 0 | 0 | 0 |
| 13 | 6 | 2 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 1 | 19 | 8 |
| 0 | 0 | 0 | 0 | 28 | 18 | 9 | 12 |
| 0 | 0 | 0 | 0 | 4 | 22 | 15 | 27 |
| 0 | 0 | 0 | 0 | 4 | 17 | 1 | 18 |
| 9 | 18 | 14 | 25 | 0 | 0 | 0 | 0 |
| 5 | 24 | 12 | 12 | 0 | 0 | 0 | 0 |
| 2 | 10 | 27 | 28 | 0 | 0 | 0 | 0 |
| 6 | 24 | 6 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 7 | 15 | 14 |
| 0 | 0 | 0 | 0 | 18 | 28 | 16 | 10 |
| 0 | 0 | 0 | 0 | 22 | 4 | 13 | 22 |
| 0 | 0 | 0 | 0 | 17 | 4 | 6 | 16 |
G:=sub<GL(8,GF(29))| [24,4,18,16,0,0,0,0,22,0,16,28,0,0,0,0,13,6,21,6,0,0,0,0,11,9,7,13,0,0,0,0,0,0,0,0,24,5,23,13,0,0,0,0,24,27,16,0,0,0,0,0,25,23,11,24,0,0,0,0,7,20,10,25],[2,10,16,11,0,0,0,0,26,0,11,12,0,0,0,0,18,15,9,15,0,0,0,0,13,8,3,18,0,0,0,0,0,0,0,0,11,2,0,0,0,0,0,0,27,18,0,0,0,0,0,0,0,0,26,2,0,0,0,0,0,0,25,3],[0,24,12,13,0,0,0,0,27,5,2,6,0,0,0,0,4,17,1,2,0,0,0,0,15,17,2,23,0,0,0,0,0,0,0,0,7,28,4,4,0,0,0,0,1,18,22,17,0,0,0,0,19,9,15,1,0,0,0,0,8,12,27,18],[9,5,2,6,0,0,0,0,18,24,10,24,0,0,0,0,14,12,27,6,0,0,0,0,25,12,28,27,0,0,0,0,0,0,0,0,1,18,22,17,0,0,0,0,7,28,4,4,0,0,0,0,15,16,13,6,0,0,0,0,14,10,22,16] >;
C42.154D14 in GAP, Magma, Sage, TeX
C_4^2._{154}D_{14} % in TeX
G:=Group("C4^2.154D14"); // GroupNames label
G:=SmallGroup(448,1149);
// by ID
G=gap.SmallGroup(448,1149);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,555,100,1571,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations