metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.43D14, C28⋊C8⋊6C2, C4.82(C2×D28), C4⋊C4.5Dic7, C28.18(C4⋊C4), (C2×C28).23Q8, C28.84(C2×Q8), (C2×C28).143D4, (C2×C4).145D28, C28.302(C2×D4), C4.5(C4⋊Dic7), C14.36(C8○D4), (C4×C28).18C22, (C2×C4).33Dic14, C4.49(C2×Dic14), C42⋊C2.7D7, C22⋊C4.2Dic7, (C2×C28).846C23, (C22×C4).338D14, C2.4(Q8.Dic7), C22.5(C4⋊Dic7), C23.15(C2×Dic7), C7⋊2(C42.6C22), (C22×C28).149C22, C22.43(C22×Dic7), (C7×C4⋊C4).8C4, C14.41(C2×C4⋊C4), (C22×C7⋊C8).8C2, C2.9(C2×C4⋊Dic7), (C2×C28).90(C2×C4), (C7×C22⋊C4).3C4, (C2×C14).13(C4⋊C4), (C2×C7⋊C8).313C22, (C2×C4).43(C2×Dic7), (C22×C14).57(C2×C4), (C7×C42⋊C2).8C2, (C2×C4).788(C22×D7), (C2×C4.Dic7).18C2, (C2×C14).183(C22×C4), SmallGroup(448,533)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.43D14
G = < a,b,c,d | a4=b4=c14=1, d2=b, ab=ba, cac-1=ab2, dad-1=a-1, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 308 in 114 conjugacy classes, 71 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C23, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, M4(2), C22×C4, C28, C28, C28, C2×C14, C2×C14, C2×C14, C4⋊C8, C42⋊C2, C22×C8, C2×M4(2), C7⋊C8, C2×C28, C2×C28, C22×C14, C42.6C22, C2×C7⋊C8, C2×C7⋊C8, C4.Dic7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C22×C28, C28⋊C8, C22×C7⋊C8, C2×C4.Dic7, C7×C42⋊C2, C42.43D14
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, D14, C2×C4⋊C4, C8○D4, Dic14, D28, C2×Dic7, C22×D7, C42.6C22, C4⋊Dic7, C2×Dic14, C2×D28, C22×Dic7, C2×C4⋊Dic7, Q8.Dic7, C42.43D14
►On 224 points
Generators in S224
(1 163 22 210)(2 157 23 204)(3 165 24 198)(4 159 25 206)(5 167 26 200)(6 161 27 208)(7 155 28 202)(8 166 88 199)(9 160 89 207)(10 168 90 201)(11 162 91 209)(12 156 85 203)(13 164 86 197)(14 158 87 205)(15 218 97 128)(16 212 98 136)(17 220 92 130)(18 214 93 138)(19 222 94 132)(20 216 95 140)(21 224 96 134)(29 182 50 150)(30 176 51 144)(31 170 52 152)(32 178 53 146)(33 172 54 154)(34 180 55 148)(35 174 56 142)(36 175 43 143)(37 169 44 151)(38 177 45 145)(39 171 46 153)(40 179 47 147)(41 173 48 141)(42 181 49 149)(57 186 70 116)(58 194 64 124)(59 188 65 118)(60 196 66 126)(61 190 67 120)(62 184 68 114)(63 192 69 122)(71 211 82 135)(72 219 83 129)(73 213 84 137)(74 221 78 131)(75 215 79 139)(76 223 80 133)(77 217 81 127)(99 183 110 113)(100 191 111 121)(101 185 112 115)(102 193 106 123)(103 187 107 117)(104 195 108 125)(105 189 109 119)
(1 36 12 29)(2 37 13 30)(3 38 14 31)(4 39 8 32)(5 40 9 33)(6 41 10 34)(7 42 11 35)(15 101 71 63)(16 102 72 57)(17 103 73 58)(18 104 74 59)(19 105 75 60)(20 99 76 61)(21 100 77 62)(22 43 85 50)(23 44 86 51)(24 45 87 52)(25 46 88 53)(26 47 89 54)(27 48 90 55)(28 49 91 56)(64 92 107 84)(65 93 108 78)(66 94 109 79)(67 95 110 80)(68 96 111 81)(69 97 112 82)(70 98 106 83)(113 133 120 140)(114 134 121 127)(115 135 122 128)(116 136 123 129)(117 137 124 130)(118 138 125 131)(119 139 126 132)(141 201 148 208)(142 202 149 209)(143 203 150 210)(144 204 151 197)(145 205 152 198)(146 206 153 199)(147 207 154 200)(155 181 162 174)(156 182 163 175)(157 169 164 176)(158 170 165 177)(159 171 166 178)(160 172 167 179)(161 173 168 180)(183 223 190 216)(184 224 191 217)(185 211 192 218)(186 212 193 219)(187 213 194 220)(188 214 195 221)(189 215 196 222)
(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 99 36 76 12 61 29 20)(2 105 37 75 13 60 30 19)(3 104 38 74 14 59 31 18)(4 103 39 73 8 58 32 17)(5 102 40 72 9 57 33 16)(6 101 41 71 10 63 34 15)(7 100 42 77 11 62 35 21)(22 110 43 80 85 67 50 95)(23 109 44 79 86 66 51 94)(24 108 45 78 87 65 52 93)(25 107 46 84 88 64 53 92)(26 106 47 83 89 70 54 98)(27 112 48 82 90 69 55 97)(28 111 49 81 91 68 56 96)(113 175 133 156 120 182 140 163)(114 174 134 155 121 181 127 162)(115 173 135 168 122 180 128 161)(116 172 136 167 123 179 129 160)(117 171 137 166 124 178 130 159)(118 170 138 165 125 177 131 158)(119 169 139 164 126 176 132 157)(141 211 201 192 148 218 208 185)(142 224 202 191 149 217 209 184)(143 223 203 190 150 216 210 183)(144 222 204 189 151 215 197 196)(145 221 205 188 152 214 198 195)(146 220 206 187 153 213 199 194)(147 219 207 186 154 212 200 193)
G:=sub<Sym(224)| (1,163,22,210)(2,157,23,204)(3,165,24,198)(4,159,25,206)(5,167,26,200)(6,161,27,208)(7,155,28,202)(8,166,88,199)(9,160,89,207)(10,168,90,201)(11,162,91,209)(12,156,85,203)(13,164,86,197)(14,158,87,205)(15,218,97,128)(16,212,98,136)(17,220,92,130)(18,214,93,138)(19,222,94,132)(20,216,95,140)(21,224,96,134)(29,182,50,150)(30,176,51,144)(31,170,52,152)(32,178,53,146)(33,172,54,154)(34,180,55,148)(35,174,56,142)(36,175,43,143)(37,169,44,151)(38,177,45,145)(39,171,46,153)(40,179,47,147)(41,173,48,141)(42,181,49,149)(57,186,70,116)(58,194,64,124)(59,188,65,118)(60,196,66,126)(61,190,67,120)(62,184,68,114)(63,192,69,122)(71,211,82,135)(72,219,83,129)(73,213,84,137)(74,221,78,131)(75,215,79,139)(76,223,80,133)(77,217,81,127)(99,183,110,113)(100,191,111,121)(101,185,112,115)(102,193,106,123)(103,187,107,117)(104,195,108,125)(105,189,109,119), (1,36,12,29)(2,37,13,30)(3,38,14,31)(4,39,8,32)(5,40,9,33)(6,41,10,34)(7,42,11,35)(15,101,71,63)(16,102,72,57)(17,103,73,58)(18,104,74,59)(19,105,75,60)(20,99,76,61)(21,100,77,62)(22,43,85,50)(23,44,86,51)(24,45,87,52)(25,46,88,53)(26,47,89,54)(27,48,90,55)(28,49,91,56)(64,92,107,84)(65,93,108,78)(66,94,109,79)(67,95,110,80)(68,96,111,81)(69,97,112,82)(70,98,106,83)(113,133,120,140)(114,134,121,127)(115,135,122,128)(116,136,123,129)(117,137,124,130)(118,138,125,131)(119,139,126,132)(141,201,148,208)(142,202,149,209)(143,203,150,210)(144,204,151,197)(145,205,152,198)(146,206,153,199)(147,207,154,200)(155,181,162,174)(156,182,163,175)(157,169,164,176)(158,170,165,177)(159,171,166,178)(160,172,167,179)(161,173,168,180)(183,223,190,216)(184,224,191,217)(185,211,192,218)(186,212,193,219)(187,213,194,220)(188,214,195,221)(189,215,196,222), (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), (1,99,36,76,12,61,29,20)(2,105,37,75,13,60,30,19)(3,104,38,74,14,59,31,18)(4,103,39,73,8,58,32,17)(5,102,40,72,9,57,33,16)(6,101,41,71,10,63,34,15)(7,100,42,77,11,62,35,21)(22,110,43,80,85,67,50,95)(23,109,44,79,86,66,51,94)(24,108,45,78,87,65,52,93)(25,107,46,84,88,64,53,92)(26,106,47,83,89,70,54,98)(27,112,48,82,90,69,55,97)(28,111,49,81,91,68,56,96)(113,175,133,156,120,182,140,163)(114,174,134,155,121,181,127,162)(115,173,135,168,122,180,128,161)(116,172,136,167,123,179,129,160)(117,171,137,166,124,178,130,159)(118,170,138,165,125,177,131,158)(119,169,139,164,126,176,132,157)(141,211,201,192,148,218,208,185)(142,224,202,191,149,217,209,184)(143,223,203,190,150,216,210,183)(144,222,204,189,151,215,197,196)(145,221,205,188,152,214,198,195)(146,220,206,187,153,213,199,194)(147,219,207,186,154,212,200,193)>;
G:=Group( (1,163,22,210)(2,157,23,204)(3,165,24,198)(4,159,25,206)(5,167,26,200)(6,161,27,208)(7,155,28,202)(8,166,88,199)(9,160,89,207)(10,168,90,201)(11,162,91,209)(12,156,85,203)(13,164,86,197)(14,158,87,205)(15,218,97,128)(16,212,98,136)(17,220,92,130)(18,214,93,138)(19,222,94,132)(20,216,95,140)(21,224,96,134)(29,182,50,150)(30,176,51,144)(31,170,52,152)(32,178,53,146)(33,172,54,154)(34,180,55,148)(35,174,56,142)(36,175,43,143)(37,169,44,151)(38,177,45,145)(39,171,46,153)(40,179,47,147)(41,173,48,141)(42,181,49,149)(57,186,70,116)(58,194,64,124)(59,188,65,118)(60,196,66,126)(61,190,67,120)(62,184,68,114)(63,192,69,122)(71,211,82,135)(72,219,83,129)(73,213,84,137)(74,221,78,131)(75,215,79,139)(76,223,80,133)(77,217,81,127)(99,183,110,113)(100,191,111,121)(101,185,112,115)(102,193,106,123)(103,187,107,117)(104,195,108,125)(105,189,109,119), (1,36,12,29)(2,37,13,30)(3,38,14,31)(4,39,8,32)(5,40,9,33)(6,41,10,34)(7,42,11,35)(15,101,71,63)(16,102,72,57)(17,103,73,58)(18,104,74,59)(19,105,75,60)(20,99,76,61)(21,100,77,62)(22,43,85,50)(23,44,86,51)(24,45,87,52)(25,46,88,53)(26,47,89,54)(27,48,90,55)(28,49,91,56)(64,92,107,84)(65,93,108,78)(66,94,109,79)(67,95,110,80)(68,96,111,81)(69,97,112,82)(70,98,106,83)(113,133,120,140)(114,134,121,127)(115,135,122,128)(116,136,123,129)(117,137,124,130)(118,138,125,131)(119,139,126,132)(141,201,148,208)(142,202,149,209)(143,203,150,210)(144,204,151,197)(145,205,152,198)(146,206,153,199)(147,207,154,200)(155,181,162,174)(156,182,163,175)(157,169,164,176)(158,170,165,177)(159,171,166,178)(160,172,167,179)(161,173,168,180)(183,223,190,216)(184,224,191,217)(185,211,192,218)(186,212,193,219)(187,213,194,220)(188,214,195,221)(189,215,196,222), (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), (1,99,36,76,12,61,29,20)(2,105,37,75,13,60,30,19)(3,104,38,74,14,59,31,18)(4,103,39,73,8,58,32,17)(5,102,40,72,9,57,33,16)(6,101,41,71,10,63,34,15)(7,100,42,77,11,62,35,21)(22,110,43,80,85,67,50,95)(23,109,44,79,86,66,51,94)(24,108,45,78,87,65,52,93)(25,107,46,84,88,64,53,92)(26,106,47,83,89,70,54,98)(27,112,48,82,90,69,55,97)(28,111,49,81,91,68,56,96)(113,175,133,156,120,182,140,163)(114,174,134,155,121,181,127,162)(115,173,135,168,122,180,128,161)(116,172,136,167,123,179,129,160)(117,171,137,166,124,178,130,159)(118,170,138,165,125,177,131,158)(119,169,139,164,126,176,132,157)(141,211,201,192,148,218,208,185)(142,224,202,191,149,217,209,184)(143,223,203,190,150,216,210,183)(144,222,204,189,151,215,197,196)(145,221,205,188,152,214,198,195)(146,220,206,187,153,213,199,194)(147,219,207,186,154,212,200,193) );
G=PermutationGroup([[(1,163,22,210),(2,157,23,204),(3,165,24,198),(4,159,25,206),(5,167,26,200),(6,161,27,208),(7,155,28,202),(8,166,88,199),(9,160,89,207),(10,168,90,201),(11,162,91,209),(12,156,85,203),(13,164,86,197),(14,158,87,205),(15,218,97,128),(16,212,98,136),(17,220,92,130),(18,214,93,138),(19,222,94,132),(20,216,95,140),(21,224,96,134),(29,182,50,150),(30,176,51,144),(31,170,52,152),(32,178,53,146),(33,172,54,154),(34,180,55,148),(35,174,56,142),(36,175,43,143),(37,169,44,151),(38,177,45,145),(39,171,46,153),(40,179,47,147),(41,173,48,141),(42,181,49,149),(57,186,70,116),(58,194,64,124),(59,188,65,118),(60,196,66,126),(61,190,67,120),(62,184,68,114),(63,192,69,122),(71,211,82,135),(72,219,83,129),(73,213,84,137),(74,221,78,131),(75,215,79,139),(76,223,80,133),(77,217,81,127),(99,183,110,113),(100,191,111,121),(101,185,112,115),(102,193,106,123),(103,187,107,117),(104,195,108,125),(105,189,109,119)], [(1,36,12,29),(2,37,13,30),(3,38,14,31),(4,39,8,32),(5,40,9,33),(6,41,10,34),(7,42,11,35),(15,101,71,63),(16,102,72,57),(17,103,73,58),(18,104,74,59),(19,105,75,60),(20,99,76,61),(21,100,77,62),(22,43,85,50),(23,44,86,51),(24,45,87,52),(25,46,88,53),(26,47,89,54),(27,48,90,55),(28,49,91,56),(64,92,107,84),(65,93,108,78),(66,94,109,79),(67,95,110,80),(68,96,111,81),(69,97,112,82),(70,98,106,83),(113,133,120,140),(114,134,121,127),(115,135,122,128),(116,136,123,129),(117,137,124,130),(118,138,125,131),(119,139,126,132),(141,201,148,208),(142,202,149,209),(143,203,150,210),(144,204,151,197),(145,205,152,198),(146,206,153,199),(147,207,154,200),(155,181,162,174),(156,182,163,175),(157,169,164,176),(158,170,165,177),(159,171,166,178),(160,172,167,179),(161,173,168,180),(183,223,190,216),(184,224,191,217),(185,211,192,218),(186,212,193,219),(187,213,194,220),(188,214,195,221),(189,215,196,222)], [(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)], [(1,99,36,76,12,61,29,20),(2,105,37,75,13,60,30,19),(3,104,38,74,14,59,31,18),(4,103,39,73,8,58,32,17),(5,102,40,72,9,57,33,16),(6,101,41,71,10,63,34,15),(7,100,42,77,11,62,35,21),(22,110,43,80,85,67,50,95),(23,109,44,79,86,66,51,94),(24,108,45,78,87,65,52,93),(25,107,46,84,88,64,53,92),(26,106,47,83,89,70,54,98),(27,112,48,82,90,69,55,97),(28,111,49,81,91,68,56,96),(113,175,133,156,120,182,140,163),(114,174,134,155,121,181,127,162),(115,173,135,168,122,180,128,161),(116,172,136,167,123,179,129,160),(117,171,137,166,124,178,130,159),(118,170,138,165,125,177,131,158),(119,169,139,164,126,176,132,157),(141,211,201,192,148,218,208,185),(142,224,202,191,149,217,209,184),(143,223,203,190,150,216,210,183),(144,222,204,189,151,215,197,196),(145,221,205,188,152,214,198,195),(146,220,206,187,153,213,199,194),(147,219,207,186,154,212,200,193)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | - | + | + | - | - | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | D4 | Q8 | D7 | D14 | Dic7 | Dic7 | D14 | C8○D4 | Dic14 | D28 | Q8.Dic7 |
| kernel | C42.43D14 | C28⋊C8 | C22×C7⋊C8 | C2×C4.Dic7 | C7×C42⋊C2 | C7×C22⋊C4 | C7×C4⋊C4 | C2×C28 | C2×C28 | C42⋊C2 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C14 | C2×C4 | C2×C4 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 3 | 6 | 6 | 6 | 3 | 8 | 12 | 12 | 12 |
Matrix representation of C42.43D14 ►in GL4(𝔽113) generated by
| 0 | 112 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 17 | 8 |
| 0 | 0 | 105 | 96 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 103 | 103 |
| 0 | 0 | 10 | 89 |
| 69 | 0 | 0 | 0 |
| 0 | 44 | 0 | 0 |
| 0 | 0 | 66 | 85 |
| 0 | 0 | 87 | 47 |
G:=sub<GL(4,GF(113))| [0,1,0,0,112,0,0,0,0,0,17,105,0,0,8,96],[15,0,0,0,0,15,0,0,0,0,112,0,0,0,0,112],[1,0,0,0,0,112,0,0,0,0,103,10,0,0,103,89],[69,0,0,0,0,44,0,0,0,0,66,87,0,0,85,47] >;
C42.43D14 in GAP, Magma, Sage, TeX
C_4^2._{43}D_{14} % in TeX
G:=Group("C4^2.43D14"); // GroupNames label
G:=SmallGroup(448,533);
// by ID
G=gap.SmallGroup(448,533);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,422,387,100,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b,a*b=b*a,c*a*c^-1=a*b^2,d*a*d^-1=a^-1,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations