metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.74D14, C7⋊C8⋊8D4, C4⋊1D4⋊3D7, C7⋊3(C8⋊3D4), C4.15(D4×D7), C28.32(C2×D4), (C2×D4).57D14, (C2×C28).292D4, C4.D28⋊15C2, C2.12(C28⋊D4), C14.21(C4⋊1D4), C14.95(C8⋊C22), (C2×C28).392C23, (C4×C28).122C22, (D4×C14).73C22, C42.D7⋊13C2, (C2×D28).106C22, C2.16(D4.D14), (C2×Dic14).111C22, (C2×D4⋊D7)⋊15C2, (C7×C4⋊1D4)⋊3C2, (C2×D4.D7)⋊13C2, (C2×C14).523(C2×D4), (C2×C4).70(C7⋊D4), (C2×C7⋊C8).131C22, (C2×C4).490(C22×D7), C22.196(C2×C7⋊D4), SmallGroup(448,608)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.74D14
G = < a,b,c,d | a4=b4=c14=1, d2=cbc-1=b-1, ab=ba, cac-1=a-1, dad-1=ab2, bd=db, dcd-1=b-1c-1 >
Subgroups: 748 in 144 conjugacy classes, 43 normal (17 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C14, C42, C22⋊C4, C2×C8, D8, SD16, C2×D4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, C8⋊C4, C4.4D4, C4⋊1D4, C2×D8, C2×SD16, C7⋊C8, Dic14, D28, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C8⋊3D4, C2×C7⋊C8, D14⋊C4, D4⋊D7, D4.D7, C4×C28, C2×Dic14, C2×D28, D4×C14, D4×C14, C42.D7, C4.D28, C2×D4⋊D7, C2×D4.D7, C7×C4⋊1D4, C42.74D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C4⋊1D4, C8⋊C22, C7⋊D4, C22×D7, C8⋊3D4, D4×D7, C2×C7⋊D4, D4.D14, C28⋊D4, C42.74D14
►On 224 points
Generators in S224
(1 150 217 23)(2 24 218 151)(3 152 219 25)(4 26 220 153)(5 154 221 27)(6 28 222 141)(7 142 223 15)(8 16 224 143)(9 144 211 17)(10 18 212 145)(11 146 213 19)(12 20 214 147)(13 148 215 21)(14 22 216 149)(29 83 127 199)(30 200 128 84)(31 71 129 201)(32 202 130 72)(33 73 131 203)(34 204 132 74)(35 75 133 205)(36 206 134 76)(37 77 135 207)(38 208 136 78)(39 79 137 209)(40 210 138 80)(41 81 139 197)(42 198 140 82)(43 124 164 96)(44 97 165 125)(45 126 166 98)(46 85 167 113)(47 114 168 86)(48 87 155 115)(49 116 156 88)(50 89 157 117)(51 118 158 90)(52 91 159 119)(53 120 160 92)(54 93 161 121)(55 122 162 94)(56 95 163 123)(57 106 183 176)(58 177 184 107)(59 108 185 178)(60 179 186 109)(61 110 187 180)(62 181 188 111)(63 112 189 182)(64 169 190 99)(65 100 191 170)(66 171 192 101)(67 102 193 172)(68 173 194 103)(69 104 195 174)(70 175 196 105)
(1 184 44 209)(2 210 45 185)(3 186 46 197)(4 198 47 187)(5 188 48 199)(6 200 49 189)(7 190 50 201)(8 202 51 191)(9 192 52 203)(10 204 53 193)(11 194 54 205)(12 206 55 195)(13 196 56 207)(14 208 43 183)(15 169 117 129)(16 130 118 170)(17 171 119 131)(18 132 120 172)(19 173 121 133)(20 134 122 174)(21 175 123 135)(22 136 124 176)(23 177 125 137)(24 138 126 178)(25 179 113 139)(26 140 114 180)(27 181 115 127)(28 128 116 182)(29 154 111 87)(30 88 112 141)(31 142 99 89)(32 90 100 143)(33 144 101 91)(34 92 102 145)(35 146 103 93)(36 94 104 147)(37 148 105 95)(38 96 106 149)(39 150 107 97)(40 98 108 151)(41 152 109 85)(42 86 110 153)(57 216 78 164)(58 165 79 217)(59 218 80 166)(60 167 81 219)(61 220 82 168)(62 155 83 221)(63 222 84 156)(64 157 71 223)(65 224 72 158)(66 159 73 211)(67 212 74 160)(68 161 75 213)(69 214 76 162)(70 163 77 215)
(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 14 209 183 44 43 184 208)(2 207 185 56 45 196 210 13)(3 12 197 195 46 55 186 206)(4 205 187 54 47 194 198 11)(5 10 199 193 48 53 188 204)(6 203 189 52 49 192 200 9)(7 8 201 191 50 51 190 202)(15 90 129 32 117 143 169 100)(16 99 170 142 118 31 130 89)(17 88 131 30 119 141 171 112)(18 111 172 154 120 29 132 87)(19 86 133 42 121 153 173 110)(20 109 174 152 122 41 134 85)(21 98 135 40 123 151 175 108)(22 107 176 150 124 39 136 97)(23 96 137 38 125 149 177 106)(24 105 178 148 126 37 138 95)(25 94 139 36 113 147 179 104)(26 103 180 146 114 35 140 93)(27 92 127 34 115 145 181 102)(28 101 182 144 116 33 128 91)(57 165 164 58 78 217 216 79)(59 163 166 70 80 215 218 77)(60 76 219 214 81 69 167 162)(61 161 168 68 82 213 220 75)(62 74 221 212 83 67 155 160)(63 159 156 66 84 211 222 73)(64 72 223 224 71 65 157 158)
G:=sub<Sym(224)| (1,150,217,23)(2,24,218,151)(3,152,219,25)(4,26,220,153)(5,154,221,27)(6,28,222,141)(7,142,223,15)(8,16,224,143)(9,144,211,17)(10,18,212,145)(11,146,213,19)(12,20,214,147)(13,148,215,21)(14,22,216,149)(29,83,127,199)(30,200,128,84)(31,71,129,201)(32,202,130,72)(33,73,131,203)(34,204,132,74)(35,75,133,205)(36,206,134,76)(37,77,135,207)(38,208,136,78)(39,79,137,209)(40,210,138,80)(41,81,139,197)(42,198,140,82)(43,124,164,96)(44,97,165,125)(45,126,166,98)(46,85,167,113)(47,114,168,86)(48,87,155,115)(49,116,156,88)(50,89,157,117)(51,118,158,90)(52,91,159,119)(53,120,160,92)(54,93,161,121)(55,122,162,94)(56,95,163,123)(57,106,183,176)(58,177,184,107)(59,108,185,178)(60,179,186,109)(61,110,187,180)(62,181,188,111)(63,112,189,182)(64,169,190,99)(65,100,191,170)(66,171,192,101)(67,102,193,172)(68,173,194,103)(69,104,195,174)(70,175,196,105), (1,184,44,209)(2,210,45,185)(3,186,46,197)(4,198,47,187)(5,188,48,199)(6,200,49,189)(7,190,50,201)(8,202,51,191)(9,192,52,203)(10,204,53,193)(11,194,54,205)(12,206,55,195)(13,196,56,207)(14,208,43,183)(15,169,117,129)(16,130,118,170)(17,171,119,131)(18,132,120,172)(19,173,121,133)(20,134,122,174)(21,175,123,135)(22,136,124,176)(23,177,125,137)(24,138,126,178)(25,179,113,139)(26,140,114,180)(27,181,115,127)(28,128,116,182)(29,154,111,87)(30,88,112,141)(31,142,99,89)(32,90,100,143)(33,144,101,91)(34,92,102,145)(35,146,103,93)(36,94,104,147)(37,148,105,95)(38,96,106,149)(39,150,107,97)(40,98,108,151)(41,152,109,85)(42,86,110,153)(57,216,78,164)(58,165,79,217)(59,218,80,166)(60,167,81,219)(61,220,82,168)(62,155,83,221)(63,222,84,156)(64,157,71,223)(65,224,72,158)(66,159,73,211)(67,212,74,160)(68,161,75,213)(69,214,76,162)(70,163,77,215), (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), (1,14,209,183,44,43,184,208)(2,207,185,56,45,196,210,13)(3,12,197,195,46,55,186,206)(4,205,187,54,47,194,198,11)(5,10,199,193,48,53,188,204)(6,203,189,52,49,192,200,9)(7,8,201,191,50,51,190,202)(15,90,129,32,117,143,169,100)(16,99,170,142,118,31,130,89)(17,88,131,30,119,141,171,112)(18,111,172,154,120,29,132,87)(19,86,133,42,121,153,173,110)(20,109,174,152,122,41,134,85)(21,98,135,40,123,151,175,108)(22,107,176,150,124,39,136,97)(23,96,137,38,125,149,177,106)(24,105,178,148,126,37,138,95)(25,94,139,36,113,147,179,104)(26,103,180,146,114,35,140,93)(27,92,127,34,115,145,181,102)(28,101,182,144,116,33,128,91)(57,165,164,58,78,217,216,79)(59,163,166,70,80,215,218,77)(60,76,219,214,81,69,167,162)(61,161,168,68,82,213,220,75)(62,74,221,212,83,67,155,160)(63,159,156,66,84,211,222,73)(64,72,223,224,71,65,157,158)>;
G:=Group( (1,150,217,23)(2,24,218,151)(3,152,219,25)(4,26,220,153)(5,154,221,27)(6,28,222,141)(7,142,223,15)(8,16,224,143)(9,144,211,17)(10,18,212,145)(11,146,213,19)(12,20,214,147)(13,148,215,21)(14,22,216,149)(29,83,127,199)(30,200,128,84)(31,71,129,201)(32,202,130,72)(33,73,131,203)(34,204,132,74)(35,75,133,205)(36,206,134,76)(37,77,135,207)(38,208,136,78)(39,79,137,209)(40,210,138,80)(41,81,139,197)(42,198,140,82)(43,124,164,96)(44,97,165,125)(45,126,166,98)(46,85,167,113)(47,114,168,86)(48,87,155,115)(49,116,156,88)(50,89,157,117)(51,118,158,90)(52,91,159,119)(53,120,160,92)(54,93,161,121)(55,122,162,94)(56,95,163,123)(57,106,183,176)(58,177,184,107)(59,108,185,178)(60,179,186,109)(61,110,187,180)(62,181,188,111)(63,112,189,182)(64,169,190,99)(65,100,191,170)(66,171,192,101)(67,102,193,172)(68,173,194,103)(69,104,195,174)(70,175,196,105), (1,184,44,209)(2,210,45,185)(3,186,46,197)(4,198,47,187)(5,188,48,199)(6,200,49,189)(7,190,50,201)(8,202,51,191)(9,192,52,203)(10,204,53,193)(11,194,54,205)(12,206,55,195)(13,196,56,207)(14,208,43,183)(15,169,117,129)(16,130,118,170)(17,171,119,131)(18,132,120,172)(19,173,121,133)(20,134,122,174)(21,175,123,135)(22,136,124,176)(23,177,125,137)(24,138,126,178)(25,179,113,139)(26,140,114,180)(27,181,115,127)(28,128,116,182)(29,154,111,87)(30,88,112,141)(31,142,99,89)(32,90,100,143)(33,144,101,91)(34,92,102,145)(35,146,103,93)(36,94,104,147)(37,148,105,95)(38,96,106,149)(39,150,107,97)(40,98,108,151)(41,152,109,85)(42,86,110,153)(57,216,78,164)(58,165,79,217)(59,218,80,166)(60,167,81,219)(61,220,82,168)(62,155,83,221)(63,222,84,156)(64,157,71,223)(65,224,72,158)(66,159,73,211)(67,212,74,160)(68,161,75,213)(69,214,76,162)(70,163,77,215), (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), (1,14,209,183,44,43,184,208)(2,207,185,56,45,196,210,13)(3,12,197,195,46,55,186,206)(4,205,187,54,47,194,198,11)(5,10,199,193,48,53,188,204)(6,203,189,52,49,192,200,9)(7,8,201,191,50,51,190,202)(15,90,129,32,117,143,169,100)(16,99,170,142,118,31,130,89)(17,88,131,30,119,141,171,112)(18,111,172,154,120,29,132,87)(19,86,133,42,121,153,173,110)(20,109,174,152,122,41,134,85)(21,98,135,40,123,151,175,108)(22,107,176,150,124,39,136,97)(23,96,137,38,125,149,177,106)(24,105,178,148,126,37,138,95)(25,94,139,36,113,147,179,104)(26,103,180,146,114,35,140,93)(27,92,127,34,115,145,181,102)(28,101,182,144,116,33,128,91)(57,165,164,58,78,217,216,79)(59,163,166,70,80,215,218,77)(60,76,219,214,81,69,167,162)(61,161,168,68,82,213,220,75)(62,74,221,212,83,67,155,160)(63,159,156,66,84,211,222,73)(64,72,223,224,71,65,157,158) );
G=PermutationGroup([[(1,150,217,23),(2,24,218,151),(3,152,219,25),(4,26,220,153),(5,154,221,27),(6,28,222,141),(7,142,223,15),(8,16,224,143),(9,144,211,17),(10,18,212,145),(11,146,213,19),(12,20,214,147),(13,148,215,21),(14,22,216,149),(29,83,127,199),(30,200,128,84),(31,71,129,201),(32,202,130,72),(33,73,131,203),(34,204,132,74),(35,75,133,205),(36,206,134,76),(37,77,135,207),(38,208,136,78),(39,79,137,209),(40,210,138,80),(41,81,139,197),(42,198,140,82),(43,124,164,96),(44,97,165,125),(45,126,166,98),(46,85,167,113),(47,114,168,86),(48,87,155,115),(49,116,156,88),(50,89,157,117),(51,118,158,90),(52,91,159,119),(53,120,160,92),(54,93,161,121),(55,122,162,94),(56,95,163,123),(57,106,183,176),(58,177,184,107),(59,108,185,178),(60,179,186,109),(61,110,187,180),(62,181,188,111),(63,112,189,182),(64,169,190,99),(65,100,191,170),(66,171,192,101),(67,102,193,172),(68,173,194,103),(69,104,195,174),(70,175,196,105)], [(1,184,44,209),(2,210,45,185),(3,186,46,197),(4,198,47,187),(5,188,48,199),(6,200,49,189),(7,190,50,201),(8,202,51,191),(9,192,52,203),(10,204,53,193),(11,194,54,205),(12,206,55,195),(13,196,56,207),(14,208,43,183),(15,169,117,129),(16,130,118,170),(17,171,119,131),(18,132,120,172),(19,173,121,133),(20,134,122,174),(21,175,123,135),(22,136,124,176),(23,177,125,137),(24,138,126,178),(25,179,113,139),(26,140,114,180),(27,181,115,127),(28,128,116,182),(29,154,111,87),(30,88,112,141),(31,142,99,89),(32,90,100,143),(33,144,101,91),(34,92,102,145),(35,146,103,93),(36,94,104,147),(37,148,105,95),(38,96,106,149),(39,150,107,97),(40,98,108,151),(41,152,109,85),(42,86,110,153),(57,216,78,164),(58,165,79,217),(59,218,80,166),(60,167,81,219),(61,220,82,168),(62,155,83,221),(63,222,84,156),(64,157,71,223),(65,224,72,158),(66,159,73,211),(67,212,74,160),(68,161,75,213),(69,214,76,162),(70,163,77,215)], [(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)], [(1,14,209,183,44,43,184,208),(2,207,185,56,45,196,210,13),(3,12,197,195,46,55,186,206),(4,205,187,54,47,194,198,11),(5,10,199,193,48,53,188,204),(6,203,189,52,49,192,200,9),(7,8,201,191,50,51,190,202),(15,90,129,32,117,143,169,100),(16,99,170,142,118,31,130,89),(17,88,131,30,119,141,171,112),(18,111,172,154,120,29,132,87),(19,86,133,42,121,153,173,110),(20,109,174,152,122,41,134,85),(21,98,135,40,123,151,175,108),(22,107,176,150,124,39,136,97),(23,96,137,38,125,149,177,106),(24,105,178,148,126,37,138,95),(25,94,139,36,113,147,179,104),(26,103,180,146,114,35,140,93),(27,92,127,34,115,145,181,102),(28,101,182,144,116,33,128,91),(57,165,164,58,78,217,216,79),(59,163,166,70,80,215,218,77),(60,76,219,214,81,69,167,162),(61,161,168,68,82,213,220,75),(62,74,221,212,83,67,155,160),(63,159,156,66,84,211,222,73),(64,72,223,224,71,65,157,158)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 56 | 2 | 2 | 4 | 4 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | D14 | D14 | C7⋊D4 | C8⋊C22 | D4×D7 | D4.D14 |
| kernel | C42.74D14 | C42.D7 | C4.D28 | C2×D4⋊D7 | C2×D4.D7 | C7×C4⋊1D4 | C7⋊C8 | C2×C28 | C4⋊1D4 | C42 | C2×D4 | C2×C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 2 | 3 | 3 | 6 | 12 | 2 | 6 | 12 |
Matrix representation of C42.74D14 ►in GL6(𝔽113)
| 105 | 77 | 0 | 0 | 0 | 0 |
| 74 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 84 | 101 | 0 | 0 |
| 0 | 0 | 70 | 29 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 101 |
| 0 | 0 | 0 | 0 | 12 | 91 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 55 |
| 0 | 0 | 0 | 1 | 58 | 15 |
| 0 | 0 | 62 | 74 | 112 | 0 |
| 0 | 0 | 39 | 0 | 0 | 112 |
| 105 | 77 | 0 | 0 | 0 | 0 |
| 30 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 95 | 45 | 51 | 79 |
| 0 | 0 | 20 | 47 | 15 | 52 |
| 0 | 0 | 51 | 30 | 68 | 68 |
| 0 | 0 | 70 | 90 | 45 | 16 |
| 105 | 77 | 0 | 0 | 0 | 0 |
| 74 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 109 | 99 | 34 | 62 |
| 0 | 0 | 13 | 4 | 61 | 98 |
| 0 | 0 | 62 | 83 | 45 | 45 |
| 0 | 0 | 109 | 93 | 97 | 68 |
G:=sub<GL(6,GF(113))| [105,74,0,0,0,0,77,8,0,0,0,0,0,0,84,70,0,0,0,0,101,29,0,0,0,0,0,0,22,12,0,0,0,0,101,91],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,62,39,0,0,0,1,74,0,0,0,0,58,112,0,0,0,55,15,0,112],[105,30,0,0,0,0,77,8,0,0,0,0,0,0,95,20,51,70,0,0,45,47,30,90,0,0,51,15,68,45,0,0,79,52,68,16],[105,74,0,0,0,0,77,8,0,0,0,0,0,0,109,13,62,109,0,0,99,4,83,93,0,0,34,61,45,97,0,0,62,98,45,68] >;
C42.74D14 in GAP, Magma, Sage, TeX
C_4^2._{74}D_{14} % in TeX
G:=Group("C4^2.74D14"); // GroupNames label
G:=SmallGroup(448,608);
// by ID
G=gap.SmallGroup(448,608);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,555,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=c*b*c^-1=b^-1,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a*b^2,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations