metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.214D14, C7⋊C8.17D4, C4.12(D4×D7), C28.26(C2×D4), C4.4D4⋊3D7, (C2×D4).49D14, (C2×C28).272D4, C7⋊2(C8.12D4), (C2×Q8).39D14, C4.D28⋊14C2, C2.9(C28⋊D4), C14.106(C4○D8), C14.18(C4⋊1D4), (C4×C28).108C22, (C2×C28).377C23, (D4×C14).65C22, (Q8×C14).57C22, (C2×D28).102C22, C2.25(D4.8D14), (C2×Dic14).107C22, (C4×C7⋊C8)⋊12C2, (C2×Q8⋊D7)⋊14C2, (C2×D4⋊D7).7C2, (C2×D4.D7)⋊12C2, (C2×C7⋊Q16)⋊13C2, (C7×C4.4D4)⋊3C2, (C2×C14).508(C2×D4), (C2×C7⋊C8).253C22, (C2×C4).110(C7⋊D4), (C2×C4).477(C22×D7), C22.183(C2×C7⋊D4), SmallGroup(448,593)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.214D14
G = < a,b,c,d | a4=b4=c14=1, d2=cbc-1=b-1, ab=ba, cac-1=a-1b2, ad=da, bd=db, dcd-1=b-1c-1 >
Subgroups: 684 in 130 conjugacy classes, 43 normal (31 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, Q16, C2×D4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×C8, C4.4D4, C4.4D4, C2×D8, C2×SD16, C2×Q16, C7⋊C8, Dic14, D28, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C8.12D4, C2×C7⋊C8, D14⋊C4, D4⋊D7, D4.D7, Q8⋊D7, C7⋊Q16, C4×C28, C7×C22⋊C4, C2×Dic14, C2×D28, D4×C14, Q8×C14, C4×C7⋊C8, C4.D28, C2×D4⋊D7, C2×D4.D7, C2×Q8⋊D7, C2×C7⋊Q16, C7×C4.4D4, C42.214D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C4⋊1D4, C4○D8, C7⋊D4, C22×D7, C8.12D4, D4×D7, C2×C7⋊D4, C28⋊D4, D4.8D14, C42.214D14
►On 224 points
Generators in S224
(1 206 187 129)(2 70 188 117)(3 208 189 131)(4 58 190 119)(5 210 191 133)(6 60 192 121)(7 198 193 135)(8 62 194 123)(9 200 195 137)(10 64 196 125)(11 202 183 139)(12 66 184 113)(13 204 185 127)(14 68 186 115)(15 80 48 177)(16 88 49 38)(17 82 50 179)(18 90 51 40)(19 84 52 181)(20 92 53 42)(21 72 54 169)(22 94 55 30)(23 74 56 171)(24 96 43 32)(25 76 44 173)(26 98 45 34)(27 78 46 175)(28 86 47 36)(29 144 93 159)(31 146 95 161)(33 148 97 163)(35 150 85 165)(37 152 87 167)(39 154 89 155)(41 142 91 157)(57 102 118 217)(59 104 120 219)(61 106 122 221)(63 108 124 223)(65 110 126 211)(67 112 114 213)(69 100 116 215)(71 158 182 143)(73 160 170 145)(75 162 172 147)(77 164 174 149)(79 166 176 151)(81 168 178 153)(83 156 180 141)(99 128 214 205)(101 130 216 207)(103 132 218 209)(105 134 220 197)(107 136 222 199)(109 138 224 201)(111 140 212 203)
(1 20 100 158)(2 159 101 21)(3 22 102 160)(4 161 103 23)(5 24 104 162)(6 163 105 25)(7 26 106 164)(8 165 107 27)(9 28 108 166)(10 167 109 15)(11 16 110 168)(12 155 111 17)(13 18 112 156)(14 157 99 19)(29 130 72 70)(30 57 73 131)(31 132 74 58)(32 59 75 133)(33 134 76 60)(34 61 77 135)(35 136 78 62)(36 63 79 137)(37 138 80 64)(38 65 81 139)(39 140 82 66)(40 67 83 127)(41 128 84 68)(42 69 71 129)(43 219 147 191)(44 192 148 220)(45 221 149 193)(46 194 150 222)(47 223 151 195)(48 196 152 224)(49 211 153 183)(50 184 154 212)(51 213 141 185)(52 186 142 214)(53 215 143 187)(54 188 144 216)(55 217 145 189)(56 190 146 218)(85 199 175 123)(86 124 176 200)(87 201 177 125)(88 126 178 202)(89 203 179 113)(90 114 180 204)(91 205 181 115)(92 116 182 206)(93 207 169 117)(94 118 170 208)(95 209 171 119)(96 120 172 210)(97 197 173 121)(98 122 174 198)
(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 14 158 19 100 99 20 157)(2 156 21 112 101 18 159 13)(3 12 160 17 102 111 22 155)(4 168 23 110 103 16 161 11)(5 10 162 15 104 109 24 167)(6 166 25 108 105 28 163 9)(7 8 164 27 106 107 26 165)(29 204 70 180 72 114 130 90)(30 89 131 113 73 179 57 203)(31 202 58 178 74 126 132 88)(32 87 133 125 75 177 59 201)(33 200 60 176 76 124 134 86)(34 85 135 123 77 175 61 199)(35 198 62 174 78 122 136 98)(36 97 137 121 79 173 63 197)(37 210 64 172 80 120 138 96)(38 95 139 119 81 171 65 209)(39 208 66 170 82 118 140 94)(40 93 127 117 83 169 67 207)(41 206 68 182 84 116 128 92)(42 91 129 115 71 181 69 205)(43 152 191 196 147 48 219 224)(44 223 220 47 148 195 192 151)(45 150 193 194 149 46 221 222)(49 146 183 190 153 56 211 218)(50 217 212 55 154 189 184 145)(51 144 185 188 141 54 213 216)(52 215 214 53 142 187 186 143)
G:=sub<Sym(224)| (1,206,187,129)(2,70,188,117)(3,208,189,131)(4,58,190,119)(5,210,191,133)(6,60,192,121)(7,198,193,135)(8,62,194,123)(9,200,195,137)(10,64,196,125)(11,202,183,139)(12,66,184,113)(13,204,185,127)(14,68,186,115)(15,80,48,177)(16,88,49,38)(17,82,50,179)(18,90,51,40)(19,84,52,181)(20,92,53,42)(21,72,54,169)(22,94,55,30)(23,74,56,171)(24,96,43,32)(25,76,44,173)(26,98,45,34)(27,78,46,175)(28,86,47,36)(29,144,93,159)(31,146,95,161)(33,148,97,163)(35,150,85,165)(37,152,87,167)(39,154,89,155)(41,142,91,157)(57,102,118,217)(59,104,120,219)(61,106,122,221)(63,108,124,223)(65,110,126,211)(67,112,114,213)(69,100,116,215)(71,158,182,143)(73,160,170,145)(75,162,172,147)(77,164,174,149)(79,166,176,151)(81,168,178,153)(83,156,180,141)(99,128,214,205)(101,130,216,207)(103,132,218,209)(105,134,220,197)(107,136,222,199)(109,138,224,201)(111,140,212,203), (1,20,100,158)(2,159,101,21)(3,22,102,160)(4,161,103,23)(5,24,104,162)(6,163,105,25)(7,26,106,164)(8,165,107,27)(9,28,108,166)(10,167,109,15)(11,16,110,168)(12,155,111,17)(13,18,112,156)(14,157,99,19)(29,130,72,70)(30,57,73,131)(31,132,74,58)(32,59,75,133)(33,134,76,60)(34,61,77,135)(35,136,78,62)(36,63,79,137)(37,138,80,64)(38,65,81,139)(39,140,82,66)(40,67,83,127)(41,128,84,68)(42,69,71,129)(43,219,147,191)(44,192,148,220)(45,221,149,193)(46,194,150,222)(47,223,151,195)(48,196,152,224)(49,211,153,183)(50,184,154,212)(51,213,141,185)(52,186,142,214)(53,215,143,187)(54,188,144,216)(55,217,145,189)(56,190,146,218)(85,199,175,123)(86,124,176,200)(87,201,177,125)(88,126,178,202)(89,203,179,113)(90,114,180,204)(91,205,181,115)(92,116,182,206)(93,207,169,117)(94,118,170,208)(95,209,171,119)(96,120,172,210)(97,197,173,121)(98,122,174,198), (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), (1,14,158,19,100,99,20,157)(2,156,21,112,101,18,159,13)(3,12,160,17,102,111,22,155)(4,168,23,110,103,16,161,11)(5,10,162,15,104,109,24,167)(6,166,25,108,105,28,163,9)(7,8,164,27,106,107,26,165)(29,204,70,180,72,114,130,90)(30,89,131,113,73,179,57,203)(31,202,58,178,74,126,132,88)(32,87,133,125,75,177,59,201)(33,200,60,176,76,124,134,86)(34,85,135,123,77,175,61,199)(35,198,62,174,78,122,136,98)(36,97,137,121,79,173,63,197)(37,210,64,172,80,120,138,96)(38,95,139,119,81,171,65,209)(39,208,66,170,82,118,140,94)(40,93,127,117,83,169,67,207)(41,206,68,182,84,116,128,92)(42,91,129,115,71,181,69,205)(43,152,191,196,147,48,219,224)(44,223,220,47,148,195,192,151)(45,150,193,194,149,46,221,222)(49,146,183,190,153,56,211,218)(50,217,212,55,154,189,184,145)(51,144,185,188,141,54,213,216)(52,215,214,53,142,187,186,143)>;
G:=Group( (1,206,187,129)(2,70,188,117)(3,208,189,131)(4,58,190,119)(5,210,191,133)(6,60,192,121)(7,198,193,135)(8,62,194,123)(9,200,195,137)(10,64,196,125)(11,202,183,139)(12,66,184,113)(13,204,185,127)(14,68,186,115)(15,80,48,177)(16,88,49,38)(17,82,50,179)(18,90,51,40)(19,84,52,181)(20,92,53,42)(21,72,54,169)(22,94,55,30)(23,74,56,171)(24,96,43,32)(25,76,44,173)(26,98,45,34)(27,78,46,175)(28,86,47,36)(29,144,93,159)(31,146,95,161)(33,148,97,163)(35,150,85,165)(37,152,87,167)(39,154,89,155)(41,142,91,157)(57,102,118,217)(59,104,120,219)(61,106,122,221)(63,108,124,223)(65,110,126,211)(67,112,114,213)(69,100,116,215)(71,158,182,143)(73,160,170,145)(75,162,172,147)(77,164,174,149)(79,166,176,151)(81,168,178,153)(83,156,180,141)(99,128,214,205)(101,130,216,207)(103,132,218,209)(105,134,220,197)(107,136,222,199)(109,138,224,201)(111,140,212,203), (1,20,100,158)(2,159,101,21)(3,22,102,160)(4,161,103,23)(5,24,104,162)(6,163,105,25)(7,26,106,164)(8,165,107,27)(9,28,108,166)(10,167,109,15)(11,16,110,168)(12,155,111,17)(13,18,112,156)(14,157,99,19)(29,130,72,70)(30,57,73,131)(31,132,74,58)(32,59,75,133)(33,134,76,60)(34,61,77,135)(35,136,78,62)(36,63,79,137)(37,138,80,64)(38,65,81,139)(39,140,82,66)(40,67,83,127)(41,128,84,68)(42,69,71,129)(43,219,147,191)(44,192,148,220)(45,221,149,193)(46,194,150,222)(47,223,151,195)(48,196,152,224)(49,211,153,183)(50,184,154,212)(51,213,141,185)(52,186,142,214)(53,215,143,187)(54,188,144,216)(55,217,145,189)(56,190,146,218)(85,199,175,123)(86,124,176,200)(87,201,177,125)(88,126,178,202)(89,203,179,113)(90,114,180,204)(91,205,181,115)(92,116,182,206)(93,207,169,117)(94,118,170,208)(95,209,171,119)(96,120,172,210)(97,197,173,121)(98,122,174,198), (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), (1,14,158,19,100,99,20,157)(2,156,21,112,101,18,159,13)(3,12,160,17,102,111,22,155)(4,168,23,110,103,16,161,11)(5,10,162,15,104,109,24,167)(6,166,25,108,105,28,163,9)(7,8,164,27,106,107,26,165)(29,204,70,180,72,114,130,90)(30,89,131,113,73,179,57,203)(31,202,58,178,74,126,132,88)(32,87,133,125,75,177,59,201)(33,200,60,176,76,124,134,86)(34,85,135,123,77,175,61,199)(35,198,62,174,78,122,136,98)(36,97,137,121,79,173,63,197)(37,210,64,172,80,120,138,96)(38,95,139,119,81,171,65,209)(39,208,66,170,82,118,140,94)(40,93,127,117,83,169,67,207)(41,206,68,182,84,116,128,92)(42,91,129,115,71,181,69,205)(43,152,191,196,147,48,219,224)(44,223,220,47,148,195,192,151)(45,150,193,194,149,46,221,222)(49,146,183,190,153,56,211,218)(50,217,212,55,154,189,184,145)(51,144,185,188,141,54,213,216)(52,215,214,53,142,187,186,143) );
G=PermutationGroup([[(1,206,187,129),(2,70,188,117),(3,208,189,131),(4,58,190,119),(5,210,191,133),(6,60,192,121),(7,198,193,135),(8,62,194,123),(9,200,195,137),(10,64,196,125),(11,202,183,139),(12,66,184,113),(13,204,185,127),(14,68,186,115),(15,80,48,177),(16,88,49,38),(17,82,50,179),(18,90,51,40),(19,84,52,181),(20,92,53,42),(21,72,54,169),(22,94,55,30),(23,74,56,171),(24,96,43,32),(25,76,44,173),(26,98,45,34),(27,78,46,175),(28,86,47,36),(29,144,93,159),(31,146,95,161),(33,148,97,163),(35,150,85,165),(37,152,87,167),(39,154,89,155),(41,142,91,157),(57,102,118,217),(59,104,120,219),(61,106,122,221),(63,108,124,223),(65,110,126,211),(67,112,114,213),(69,100,116,215),(71,158,182,143),(73,160,170,145),(75,162,172,147),(77,164,174,149),(79,166,176,151),(81,168,178,153),(83,156,180,141),(99,128,214,205),(101,130,216,207),(103,132,218,209),(105,134,220,197),(107,136,222,199),(109,138,224,201),(111,140,212,203)], [(1,20,100,158),(2,159,101,21),(3,22,102,160),(4,161,103,23),(5,24,104,162),(6,163,105,25),(7,26,106,164),(8,165,107,27),(9,28,108,166),(10,167,109,15),(11,16,110,168),(12,155,111,17),(13,18,112,156),(14,157,99,19),(29,130,72,70),(30,57,73,131),(31,132,74,58),(32,59,75,133),(33,134,76,60),(34,61,77,135),(35,136,78,62),(36,63,79,137),(37,138,80,64),(38,65,81,139),(39,140,82,66),(40,67,83,127),(41,128,84,68),(42,69,71,129),(43,219,147,191),(44,192,148,220),(45,221,149,193),(46,194,150,222),(47,223,151,195),(48,196,152,224),(49,211,153,183),(50,184,154,212),(51,213,141,185),(52,186,142,214),(53,215,143,187),(54,188,144,216),(55,217,145,189),(56,190,146,218),(85,199,175,123),(86,124,176,200),(87,201,177,125),(88,126,178,202),(89,203,179,113),(90,114,180,204),(91,205,181,115),(92,116,182,206),(93,207,169,117),(94,118,170,208),(95,209,171,119),(96,120,172,210),(97,197,173,121),(98,122,174,198)], [(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)], [(1,14,158,19,100,99,20,157),(2,156,21,112,101,18,159,13),(3,12,160,17,102,111,22,155),(4,168,23,110,103,16,161,11),(5,10,162,15,104,109,24,167),(6,166,25,108,105,28,163,9),(7,8,164,27,106,107,26,165),(29,204,70,180,72,114,130,90),(30,89,131,113,73,179,57,203),(31,202,58,178,74,126,132,88),(32,87,133,125,75,177,59,201),(33,200,60,176,76,124,134,86),(34,85,135,123,77,175,61,199),(35,198,62,174,78,122,136,98),(36,97,137,121,79,173,63,197),(37,210,64,172,80,120,138,96),(38,95,139,119,81,171,65,209),(39,208,66,170,82,118,140,94),(40,93,127,117,83,169,67,207),(41,206,68,182,84,116,128,92),(42,91,129,115,71,181,69,205),(43,152,191,196,147,48,219,224),(44,223,220,47,148,195,192,151),(45,150,193,194,149,46,221,222),(49,146,183,190,153,56,211,218),(50,217,212,55,154,189,184,145),(51,144,185,188,141,54,213,216),(52,215,214,53,142,187,186,143)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | 4H | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 56 | 2 | ··· | 2 | 8 | 56 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | D4×D7 | D4.8D14 |
| kernel | C42.214D14 | C4×C7⋊C8 | C4.D28 | C2×D4⋊D7 | C2×D4.D7 | C2×Q8⋊D7 | C2×C7⋊Q16 | C7×C4.4D4 | C7⋊C8 | C2×C28 | C4.4D4 | C42 | C2×D4 | C2×Q8 | C14 | C2×C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 2 | 3 | 3 | 3 | 3 | 8 | 12 | 6 | 12 |
Matrix representation of C42.214D14 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 9 | 0 | 0 |
| 0 | 0 | 63 | 98 | 0 | 0 |
| 0 | 0 | 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 0 | 0 | 98 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 91 | 0 | 0 |
| 0 | 0 | 72 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 84 | 91 |
| 0 | 0 | 0 | 0 | 28 | 29 |
| 80 | 80 | 0 | 0 | 0 | 0 |
| 33 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 62 | 109 | 0 | 0 |
| 0 | 0 | 85 | 51 | 0 | 0 |
| 0 | 0 | 0 | 0 | 77 | 4 |
| 0 | 0 | 0 | 0 | 100 | 36 |
| 80 | 80 | 0 | 0 | 0 | 0 |
| 9 | 33 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 28 | 62 | 0 | 0 |
| 0 | 0 | 0 | 0 | 87 | 109 |
| 0 | 0 | 0 | 0 | 77 | 77 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,15,63,0,0,0,0,9,98,0,0,0,0,0,0,98,0,0,0,0,0,0,98],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,72,0,0,0,0,91,112,0,0,0,0,0,0,84,28,0,0,0,0,91,29],[80,33,0,0,0,0,80,9,0,0,0,0,0,0,62,85,0,0,0,0,109,51,0,0,0,0,0,0,77,100,0,0,0,0,4,36],[80,9,0,0,0,0,80,33,0,0,0,0,0,0,0,28,0,0,0,0,4,62,0,0,0,0,0,0,87,77,0,0,0,0,109,77] >;
C42.214D14 in GAP, Magma, Sage, TeX
C_4^2._{214}D_{14} % in TeX
G:=Group("C4^2.214D14"); // GroupNames label
G:=SmallGroup(448,593);
// by ID
G=gap.SmallGroup(448,593);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,219,1123,297,136,18822]);
// 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*b^2,a*d=d*a,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations