metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.277D14, (C4×D28)⋊4C2, (C2×C42)⋊12D7, (C4×Dic14)⋊4C2, C4.D28⋊34C2, C28⋊7D4.20C2, C42⋊2D7⋊21C2, C42⋊D7⋊27C2, (C2×C14).23C24, C28.6Q8⋊32C2, C4.118(C4○D28), C28.234(C4○D4), C28.48D4⋊50C2, (C2×C28).696C23, (C4×C28).316C22, D14⋊C4.82C22, (C22×C4).410D14, (C2×Dic7).7C23, (C22×D7).5C23, C22.66(C23×D7), (C2×D28).204C22, C22.22(C4○D28), Dic7⋊C4.96C22, C4⋊Dic7.290C22, C23.219(C22×D7), C23.D7.81C22, C23.23D14⋊32C2, (C22×C28).565C22, (C22×C14).385C23, C7⋊1(C23.36C23), (C4×Dic7).191C22, (C2×Dic14).225C22, (C2×C4×C28)⋊14C2, (C4×C7⋊D4)⋊32C2, C2.12(C2×C4○D28), C14.10(C2×C4○D4), (C2×C4×D7).188C22, (C2×C14).99(C4○D4), (C2×C4).651(C22×D7), (C2×C7⋊D4).86C22, SmallGroup(448,932)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.277D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, ac=ca, dad-1=ab2, bc=cb, dbd-1=a2b, dcd-1=b2c-1 >
Subgroups: 964 in 234 conjugacy classes, 103 normal (51 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C23.36C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, C4×Dic14, C28.6Q8, C42⋊D7, C4×D28, C4.D28, C42⋊2D7, C28.48D4, C4×C7⋊D4, C23.23D14, C28⋊7D4, C2×C4×C28, C42.277D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, C4○D28, C23×D7, C2×C4○D28, C42.277D14
►On 224 points
Generators in S224
(1 80 8 73)(2 81 9 74)(3 82 10 75)(4 83 11 76)(5 84 12 77)(6 71 13 78)(7 72 14 79)(15 193 103 41)(16 194 104 42)(17 195 105 29)(18 196 106 30)(19 183 107 31)(20 184 108 32)(21 185 109 33)(22 186 110 34)(23 187 111 35)(24 188 112 36)(25 189 99 37)(26 190 100 38)(27 191 101 39)(28 192 102 40)(43 146 128 96)(44 147 129 97)(45 148 130 98)(46 149 131 85)(47 150 132 86)(48 151 133 87)(49 152 134 88)(50 153 135 89)(51 154 136 90)(52 141 137 91)(53 142 138 92)(54 143 139 93)(55 144 140 94)(56 145 127 95)(57 163 64 156)(58 164 65 157)(59 165 66 158)(60 166 67 159)(61 167 68 160)(62 168 69 161)(63 155 70 162)(113 208 120 201)(114 209 121 202)(115 210 122 203)(116 197 123 204)(117 198 124 205)(118 199 125 206)(119 200 126 207)(169 222 176 215)(170 223 177 216)(171 224 178 217)(172 211 179 218)(173 212 180 219)(174 213 181 220)(175 214 182 221)
(1 159 169 113)(2 160 170 114)(3 161 171 115)(4 162 172 116)(5 163 173 117)(6 164 174 118)(7 165 175 119)(8 166 176 120)(9 167 177 121)(10 168 178 122)(11 155 179 123)(12 156 180 124)(13 157 181 125)(14 158 182 126)(15 50 110 128)(16 51 111 129)(17 52 112 130)(18 53 99 131)(19 54 100 132)(20 55 101 133)(21 56 102 134)(22 43 103 135)(23 44 104 136)(24 45 105 137)(25 46 106 138)(26 47 107 139)(27 48 108 140)(28 49 109 127)(29 91 188 148)(30 92 189 149)(31 93 190 150)(32 94 191 151)(33 95 192 152)(34 96 193 153)(35 97 194 154)(36 98 195 141)(37 85 196 142)(38 86 183 143)(39 87 184 144)(40 88 185 145)(41 89 186 146)(42 90 187 147)(57 219 205 77)(58 220 206 78)(59 221 207 79)(60 222 208 80)(61 223 209 81)(62 224 210 82)(63 211 197 83)(64 212 198 84)(65 213 199 71)(66 214 200 72)(67 215 201 73)(68 216 202 74)(69 217 203 75)(70 218 204 76)
(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)
(1 141 169 98)(2 97 170 154)(3 153 171 96)(4 95 172 152)(5 151 173 94)(6 93 174 150)(7 149 175 92)(8 91 176 148)(9 147 177 90)(10 89 178 146)(11 145 179 88)(12 87 180 144)(13 143 181 86)(14 85 182 142)(15 210 110 62)(16 61 111 209)(17 208 112 60)(18 59 99 207)(19 206 100 58)(20 57 101 205)(21 204 102 70)(22 69 103 203)(23 202 104 68)(24 67 105 201)(25 200 106 66)(26 65 107 199)(27 198 108 64)(28 63 109 197)(29 159 188 113)(30 126 189 158)(31 157 190 125)(32 124 191 156)(33 155 192 123)(34 122 193 168)(35 167 194 121)(36 120 195 166)(37 165 196 119)(38 118 183 164)(39 163 184 117)(40 116 185 162)(41 161 186 115)(42 114 187 160)(43 224 135 82)(44 81 136 223)(45 222 137 80)(46 79 138 221)(47 220 139 78)(48 77 140 219)(49 218 127 76)(50 75 128 217)(51 216 129 74)(52 73 130 215)(53 214 131 72)(54 71 132 213)(55 212 133 84)(56 83 134 211)
G:=sub<Sym(224)| (1,80,8,73)(2,81,9,74)(3,82,10,75)(4,83,11,76)(5,84,12,77)(6,71,13,78)(7,72,14,79)(15,193,103,41)(16,194,104,42)(17,195,105,29)(18,196,106,30)(19,183,107,31)(20,184,108,32)(21,185,109,33)(22,186,110,34)(23,187,111,35)(24,188,112,36)(25,189,99,37)(26,190,100,38)(27,191,101,39)(28,192,102,40)(43,146,128,96)(44,147,129,97)(45,148,130,98)(46,149,131,85)(47,150,132,86)(48,151,133,87)(49,152,134,88)(50,153,135,89)(51,154,136,90)(52,141,137,91)(53,142,138,92)(54,143,139,93)(55,144,140,94)(56,145,127,95)(57,163,64,156)(58,164,65,157)(59,165,66,158)(60,166,67,159)(61,167,68,160)(62,168,69,161)(63,155,70,162)(113,208,120,201)(114,209,121,202)(115,210,122,203)(116,197,123,204)(117,198,124,205)(118,199,125,206)(119,200,126,207)(169,222,176,215)(170,223,177,216)(171,224,178,217)(172,211,179,218)(173,212,180,219)(174,213,181,220)(175,214,182,221), (1,159,169,113)(2,160,170,114)(3,161,171,115)(4,162,172,116)(5,163,173,117)(6,164,174,118)(7,165,175,119)(8,166,176,120)(9,167,177,121)(10,168,178,122)(11,155,179,123)(12,156,180,124)(13,157,181,125)(14,158,182,126)(15,50,110,128)(16,51,111,129)(17,52,112,130)(18,53,99,131)(19,54,100,132)(20,55,101,133)(21,56,102,134)(22,43,103,135)(23,44,104,136)(24,45,105,137)(25,46,106,138)(26,47,107,139)(27,48,108,140)(28,49,109,127)(29,91,188,148)(30,92,189,149)(31,93,190,150)(32,94,191,151)(33,95,192,152)(34,96,193,153)(35,97,194,154)(36,98,195,141)(37,85,196,142)(38,86,183,143)(39,87,184,144)(40,88,185,145)(41,89,186,146)(42,90,187,147)(57,219,205,77)(58,220,206,78)(59,221,207,79)(60,222,208,80)(61,223,209,81)(62,224,210,82)(63,211,197,83)(64,212,198,84)(65,213,199,71)(66,214,200,72)(67,215,201,73)(68,216,202,74)(69,217,203,75)(70,218,204,76), (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), (1,141,169,98)(2,97,170,154)(3,153,171,96)(4,95,172,152)(5,151,173,94)(6,93,174,150)(7,149,175,92)(8,91,176,148)(9,147,177,90)(10,89,178,146)(11,145,179,88)(12,87,180,144)(13,143,181,86)(14,85,182,142)(15,210,110,62)(16,61,111,209)(17,208,112,60)(18,59,99,207)(19,206,100,58)(20,57,101,205)(21,204,102,70)(22,69,103,203)(23,202,104,68)(24,67,105,201)(25,200,106,66)(26,65,107,199)(27,198,108,64)(28,63,109,197)(29,159,188,113)(30,126,189,158)(31,157,190,125)(32,124,191,156)(33,155,192,123)(34,122,193,168)(35,167,194,121)(36,120,195,166)(37,165,196,119)(38,118,183,164)(39,163,184,117)(40,116,185,162)(41,161,186,115)(42,114,187,160)(43,224,135,82)(44,81,136,223)(45,222,137,80)(46,79,138,221)(47,220,139,78)(48,77,140,219)(49,218,127,76)(50,75,128,217)(51,216,129,74)(52,73,130,215)(53,214,131,72)(54,71,132,213)(55,212,133,84)(56,83,134,211)>;
G:=Group( (1,80,8,73)(2,81,9,74)(3,82,10,75)(4,83,11,76)(5,84,12,77)(6,71,13,78)(7,72,14,79)(15,193,103,41)(16,194,104,42)(17,195,105,29)(18,196,106,30)(19,183,107,31)(20,184,108,32)(21,185,109,33)(22,186,110,34)(23,187,111,35)(24,188,112,36)(25,189,99,37)(26,190,100,38)(27,191,101,39)(28,192,102,40)(43,146,128,96)(44,147,129,97)(45,148,130,98)(46,149,131,85)(47,150,132,86)(48,151,133,87)(49,152,134,88)(50,153,135,89)(51,154,136,90)(52,141,137,91)(53,142,138,92)(54,143,139,93)(55,144,140,94)(56,145,127,95)(57,163,64,156)(58,164,65,157)(59,165,66,158)(60,166,67,159)(61,167,68,160)(62,168,69,161)(63,155,70,162)(113,208,120,201)(114,209,121,202)(115,210,122,203)(116,197,123,204)(117,198,124,205)(118,199,125,206)(119,200,126,207)(169,222,176,215)(170,223,177,216)(171,224,178,217)(172,211,179,218)(173,212,180,219)(174,213,181,220)(175,214,182,221), (1,159,169,113)(2,160,170,114)(3,161,171,115)(4,162,172,116)(5,163,173,117)(6,164,174,118)(7,165,175,119)(8,166,176,120)(9,167,177,121)(10,168,178,122)(11,155,179,123)(12,156,180,124)(13,157,181,125)(14,158,182,126)(15,50,110,128)(16,51,111,129)(17,52,112,130)(18,53,99,131)(19,54,100,132)(20,55,101,133)(21,56,102,134)(22,43,103,135)(23,44,104,136)(24,45,105,137)(25,46,106,138)(26,47,107,139)(27,48,108,140)(28,49,109,127)(29,91,188,148)(30,92,189,149)(31,93,190,150)(32,94,191,151)(33,95,192,152)(34,96,193,153)(35,97,194,154)(36,98,195,141)(37,85,196,142)(38,86,183,143)(39,87,184,144)(40,88,185,145)(41,89,186,146)(42,90,187,147)(57,219,205,77)(58,220,206,78)(59,221,207,79)(60,222,208,80)(61,223,209,81)(62,224,210,82)(63,211,197,83)(64,212,198,84)(65,213,199,71)(66,214,200,72)(67,215,201,73)(68,216,202,74)(69,217,203,75)(70,218,204,76), (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), (1,141,169,98)(2,97,170,154)(3,153,171,96)(4,95,172,152)(5,151,173,94)(6,93,174,150)(7,149,175,92)(8,91,176,148)(9,147,177,90)(10,89,178,146)(11,145,179,88)(12,87,180,144)(13,143,181,86)(14,85,182,142)(15,210,110,62)(16,61,111,209)(17,208,112,60)(18,59,99,207)(19,206,100,58)(20,57,101,205)(21,204,102,70)(22,69,103,203)(23,202,104,68)(24,67,105,201)(25,200,106,66)(26,65,107,199)(27,198,108,64)(28,63,109,197)(29,159,188,113)(30,126,189,158)(31,157,190,125)(32,124,191,156)(33,155,192,123)(34,122,193,168)(35,167,194,121)(36,120,195,166)(37,165,196,119)(38,118,183,164)(39,163,184,117)(40,116,185,162)(41,161,186,115)(42,114,187,160)(43,224,135,82)(44,81,136,223)(45,222,137,80)(46,79,138,221)(47,220,139,78)(48,77,140,219)(49,218,127,76)(50,75,128,217)(51,216,129,74)(52,73,130,215)(53,214,131,72)(54,71,132,213)(55,212,133,84)(56,83,134,211) );
G=PermutationGroup([[(1,80,8,73),(2,81,9,74),(3,82,10,75),(4,83,11,76),(5,84,12,77),(6,71,13,78),(7,72,14,79),(15,193,103,41),(16,194,104,42),(17,195,105,29),(18,196,106,30),(19,183,107,31),(20,184,108,32),(21,185,109,33),(22,186,110,34),(23,187,111,35),(24,188,112,36),(25,189,99,37),(26,190,100,38),(27,191,101,39),(28,192,102,40),(43,146,128,96),(44,147,129,97),(45,148,130,98),(46,149,131,85),(47,150,132,86),(48,151,133,87),(49,152,134,88),(50,153,135,89),(51,154,136,90),(52,141,137,91),(53,142,138,92),(54,143,139,93),(55,144,140,94),(56,145,127,95),(57,163,64,156),(58,164,65,157),(59,165,66,158),(60,166,67,159),(61,167,68,160),(62,168,69,161),(63,155,70,162),(113,208,120,201),(114,209,121,202),(115,210,122,203),(116,197,123,204),(117,198,124,205),(118,199,125,206),(119,200,126,207),(169,222,176,215),(170,223,177,216),(171,224,178,217),(172,211,179,218),(173,212,180,219),(174,213,181,220),(175,214,182,221)], [(1,159,169,113),(2,160,170,114),(3,161,171,115),(4,162,172,116),(5,163,173,117),(6,164,174,118),(7,165,175,119),(8,166,176,120),(9,167,177,121),(10,168,178,122),(11,155,179,123),(12,156,180,124),(13,157,181,125),(14,158,182,126),(15,50,110,128),(16,51,111,129),(17,52,112,130),(18,53,99,131),(19,54,100,132),(20,55,101,133),(21,56,102,134),(22,43,103,135),(23,44,104,136),(24,45,105,137),(25,46,106,138),(26,47,107,139),(27,48,108,140),(28,49,109,127),(29,91,188,148),(30,92,189,149),(31,93,190,150),(32,94,191,151),(33,95,192,152),(34,96,193,153),(35,97,194,154),(36,98,195,141),(37,85,196,142),(38,86,183,143),(39,87,184,144),(40,88,185,145),(41,89,186,146),(42,90,187,147),(57,219,205,77),(58,220,206,78),(59,221,207,79),(60,222,208,80),(61,223,209,81),(62,224,210,82),(63,211,197,83),(64,212,198,84),(65,213,199,71),(66,214,200,72),(67,215,201,73),(68,216,202,74),(69,217,203,75),(70,218,204,76)], [(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)], [(1,141,169,98),(2,97,170,154),(3,153,171,96),(4,95,172,152),(5,151,173,94),(6,93,174,150),(7,149,175,92),(8,91,176,148),(9,147,177,90),(10,89,178,146),(11,145,179,88),(12,87,180,144),(13,143,181,86),(14,85,182,142),(15,210,110,62),(16,61,111,209),(17,208,112,60),(18,59,99,207),(19,206,100,58),(20,57,101,205),(21,204,102,70),(22,69,103,203),(23,202,104,68),(24,67,105,201),(25,200,106,66),(26,65,107,199),(27,198,108,64),(28,63,109,197),(29,159,188,113),(30,126,189,158),(31,157,190,125),(32,124,191,156),(33,155,192,123),(34,122,193,168),(35,167,194,121),(36,120,195,166),(37,165,196,119),(38,118,183,164),(39,163,184,117),(40,116,185,162),(41,161,186,115),(42,114,187,160),(43,224,135,82),(44,81,136,223),(45,222,137,80),(46,79,138,221),(47,220,139,78),(48,77,140,219),(49,218,127,76),(50,75,128,217),(51,216,129,74),(52,73,130,215),(53,214,131,72),(54,71,132,213),(55,212,133,84),(56,83,134,211)]])
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4N | 4O | ··· | 4T | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | C4○D28 | C4○D28 |
| kernel | C42.277D14 | C4×Dic14 | C28.6Q8 | C42⋊D7 | C4×D28 | C4.D28 | C42⋊2D7 | C28.48D4 | C4×C7⋊D4 | C23.23D14 | C28⋊7D4 | C2×C4×C28 | C2×C42 | C28 | C2×C14 | C42 | C22×C4 | C4 | C22 |
| # reps | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 3 | 8 | 4 | 12 | 9 | 48 | 24 |
Matrix representation of C42.277D14 ►in GL4(𝔽29) generated by
| 17 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 1 |
| 17 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 9 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 |
| 0 | 0 | 23 | 0 |
| 0 | 0 | 0 | 5 |
| 0 | 13 | 0 | 0 |
| 20 | 0 | 0 | 0 |
| 0 | 0 | 0 | 24 |
| 0 | 0 | 6 | 0 |
G:=sub<GL(4,GF(29))| [17,0,0,0,0,12,0,0,0,0,28,0,0,0,0,1],[17,0,0,0,0,12,0,0,0,0,12,0,0,0,0,12],[9,0,0,0,0,16,0,0,0,0,23,0,0,0,0,5],[0,20,0,0,13,0,0,0,0,0,0,6,0,0,24,0] >;
C42.277D14 in GAP, Magma, Sage, TeX
C_4^2._{277}D_{14} % in TeX
G:=Group("C4^2.277D14"); // GroupNames label
G:=SmallGroup(448,932);
// by ID
G=gap.SmallGroup(448,932);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,100,675,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a*b^2,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^-1>;
// generators/relations