metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.56D14, Q8⋊D7⋊5C4, (C4×Q8)⋊2D7, Q8⋊4(C4×D7), (Q8×C28)⋊2C2, C14.74(C4×D4), C4⋊C4.252D14, (C4×D28).15C2, D28.17(C2×C4), (C2×C28).258D4, C28.59(C4○D4), C4.41(C4○D28), Q8⋊Dic7⋊11C2, C28.Q8⋊33C2, C7⋊6(SD16⋊C4), (C4×C28).97C22, C28.26(C22×C4), (C2×Q8).159D14, C42.D7⋊7C2, C14.D8.10C2, C2.4(D4⋊D14), (C2×C28).346C23, C14.111(C8⋊C22), C2.3(C28.C23), (C2×D28).239C22, C14.87(C8.C22), C4⋊Dic7.331C22, (Q8×C14).194C22, C7⋊C8⋊10(C2×C4), C4.26(C2×C4×D7), (C7×Q8)⋊9(C2×C4), C2.20(C4×C7⋊D4), (C2×Q8⋊D7).4C2, (C2×C14).477(C2×D4), (C2×C7⋊C8).100C22, C22.80(C2×C7⋊D4), (C2×C4).221(C7⋊D4), (C7×C4⋊C4).283C22, (C2×C4).446(C22×D7), SmallGroup(448,560)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.56D14
G = < a,b,c,d | a4=b4=1, c14=b2, d2=b, ab=ba, cac-1=dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c13 >
Subgroups: 580 in 120 conjugacy classes, 51 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C8⋊C4, D4⋊C4, Q8⋊C4, C2.D8, C4×D4, C4×Q8, C2×SD16, C7⋊C8, C7⋊C8, C4×D7, D28, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×D7, SD16⋊C4, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, Q8⋊D7, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, Q8×C14, C42.D7, C28.Q8, C14.D8, Q8⋊Dic7, C4×D28, C2×Q8⋊D7, Q8×C28, C42.56D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, D14, C4×D4, C8⋊C22, C8.C22, C4×D7, C7⋊D4, C22×D7, SD16⋊C4, C2×C4×D7, C4○D28, C2×C7⋊D4, C4×C7⋊D4, C28.C23, D4⋊D14, C42.56D14
►On 224 points
Generators in S224
(1 107 66 126)(2 94 67 113)(3 109 68 128)(4 96 69 115)(5 111 70 130)(6 98 71 117)(7 85 72 132)(8 100 73 119)(9 87 74 134)(10 102 75 121)(11 89 76 136)(12 104 77 123)(13 91 78 138)(14 106 79 125)(15 93 80 140)(16 108 81 127)(17 95 82 114)(18 110 83 129)(19 97 84 116)(20 112 57 131)(21 99 58 118)(22 86 59 133)(23 101 60 120)(24 88 61 135)(25 103 62 122)(26 90 63 137)(27 105 64 124)(28 92 65 139)(29 168 202 194)(30 155 203 181)(31 142 204 196)(32 157 205 183)(33 144 206 170)(34 159 207 185)(35 146 208 172)(36 161 209 187)(37 148 210 174)(38 163 211 189)(39 150 212 176)(40 165 213 191)(41 152 214 178)(42 167 215 193)(43 154 216 180)(44 141 217 195)(45 156 218 182)(46 143 219 169)(47 158 220 184)(48 145 221 171)(49 160 222 186)(50 147 223 173)(51 162 224 188)(52 149 197 175)(53 164 198 190)(54 151 199 177)(55 166 200 192)(56 153 201 179)
(1 191 15 177)(2 178 16 192)(3 193 17 179)(4 180 18 194)(5 195 19 181)(6 182 20 196)(7 169 21 183)(8 184 22 170)(9 171 23 185)(10 186 24 172)(11 173 25 187)(12 188 26 174)(13 175 27 189)(14 190 28 176)(29 96 43 110)(30 111 44 97)(31 98 45 112)(32 85 46 99)(33 100 47 86)(34 87 48 101)(35 102 49 88)(36 89 50 103)(37 104 51 90)(38 91 52 105)(39 106 53 92)(40 93 54 107)(41 108 55 94)(42 95 56 109)(57 142 71 156)(58 157 72 143)(59 144 73 158)(60 159 74 145)(61 146 75 160)(62 161 76 147)(63 148 77 162)(64 163 78 149)(65 150 79 164)(66 165 80 151)(67 152 81 166)(68 167 82 153)(69 154 83 168)(70 141 84 155)(113 214 127 200)(114 201 128 215)(115 216 129 202)(116 203 130 217)(117 218 131 204)(118 205 132 219)(119 220 133 206)(120 207 134 221)(121 222 135 208)(122 209 136 223)(123 224 137 210)(124 211 138 197)(125 198 139 212)(126 213 140 199)
(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 79 191 164 15 65 177 150)(2 149 178 64 16 163 192 78)(3 77 193 162 17 63 179 148)(4 147 180 62 18 161 194 76)(5 75 195 160 19 61 181 146)(6 145 182 60 20 159 196 74)(7 73 169 158 21 59 183 144)(8 143 184 58 22 157 170 72)(9 71 171 156 23 57 185 142)(10 141 186 84 24 155 172 70)(11 69 173 154 25 83 187 168)(12 167 188 82 26 153 174 68)(13 67 175 152 27 81 189 166)(14 165 190 80 28 151 176 66)(29 122 96 209 43 136 110 223)(30 222 111 135 44 208 97 121)(31 120 98 207 45 134 112 221)(32 220 85 133 46 206 99 119)(33 118 100 205 47 132 86 219)(34 218 87 131 48 204 101 117)(35 116 102 203 49 130 88 217)(36 216 89 129 50 202 103 115)(37 114 104 201 51 128 90 215)(38 214 91 127 52 200 105 113)(39 140 106 199 53 126 92 213)(40 212 93 125 54 198 107 139)(41 138 108 197 55 124 94 211)(42 210 95 123 56 224 109 137)
G:=sub<Sym(224)| (1,107,66,126)(2,94,67,113)(3,109,68,128)(4,96,69,115)(5,111,70,130)(6,98,71,117)(7,85,72,132)(8,100,73,119)(9,87,74,134)(10,102,75,121)(11,89,76,136)(12,104,77,123)(13,91,78,138)(14,106,79,125)(15,93,80,140)(16,108,81,127)(17,95,82,114)(18,110,83,129)(19,97,84,116)(20,112,57,131)(21,99,58,118)(22,86,59,133)(23,101,60,120)(24,88,61,135)(25,103,62,122)(26,90,63,137)(27,105,64,124)(28,92,65,139)(29,168,202,194)(30,155,203,181)(31,142,204,196)(32,157,205,183)(33,144,206,170)(34,159,207,185)(35,146,208,172)(36,161,209,187)(37,148,210,174)(38,163,211,189)(39,150,212,176)(40,165,213,191)(41,152,214,178)(42,167,215,193)(43,154,216,180)(44,141,217,195)(45,156,218,182)(46,143,219,169)(47,158,220,184)(48,145,221,171)(49,160,222,186)(50,147,223,173)(51,162,224,188)(52,149,197,175)(53,164,198,190)(54,151,199,177)(55,166,200,192)(56,153,201,179), (1,191,15,177)(2,178,16,192)(3,193,17,179)(4,180,18,194)(5,195,19,181)(6,182,20,196)(7,169,21,183)(8,184,22,170)(9,171,23,185)(10,186,24,172)(11,173,25,187)(12,188,26,174)(13,175,27,189)(14,190,28,176)(29,96,43,110)(30,111,44,97)(31,98,45,112)(32,85,46,99)(33,100,47,86)(34,87,48,101)(35,102,49,88)(36,89,50,103)(37,104,51,90)(38,91,52,105)(39,106,53,92)(40,93,54,107)(41,108,55,94)(42,95,56,109)(57,142,71,156)(58,157,72,143)(59,144,73,158)(60,159,74,145)(61,146,75,160)(62,161,76,147)(63,148,77,162)(64,163,78,149)(65,150,79,164)(66,165,80,151)(67,152,81,166)(68,167,82,153)(69,154,83,168)(70,141,84,155)(113,214,127,200)(114,201,128,215)(115,216,129,202)(116,203,130,217)(117,218,131,204)(118,205,132,219)(119,220,133,206)(120,207,134,221)(121,222,135,208)(122,209,136,223)(123,224,137,210)(124,211,138,197)(125,198,139,212)(126,213,140,199), (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), (1,79,191,164,15,65,177,150)(2,149,178,64,16,163,192,78)(3,77,193,162,17,63,179,148)(4,147,180,62,18,161,194,76)(5,75,195,160,19,61,181,146)(6,145,182,60,20,159,196,74)(7,73,169,158,21,59,183,144)(8,143,184,58,22,157,170,72)(9,71,171,156,23,57,185,142)(10,141,186,84,24,155,172,70)(11,69,173,154,25,83,187,168)(12,167,188,82,26,153,174,68)(13,67,175,152,27,81,189,166)(14,165,190,80,28,151,176,66)(29,122,96,209,43,136,110,223)(30,222,111,135,44,208,97,121)(31,120,98,207,45,134,112,221)(32,220,85,133,46,206,99,119)(33,118,100,205,47,132,86,219)(34,218,87,131,48,204,101,117)(35,116,102,203,49,130,88,217)(36,216,89,129,50,202,103,115)(37,114,104,201,51,128,90,215)(38,214,91,127,52,200,105,113)(39,140,106,199,53,126,92,213)(40,212,93,125,54,198,107,139)(41,138,108,197,55,124,94,211)(42,210,95,123,56,224,109,137)>;
G:=Group( (1,107,66,126)(2,94,67,113)(3,109,68,128)(4,96,69,115)(5,111,70,130)(6,98,71,117)(7,85,72,132)(8,100,73,119)(9,87,74,134)(10,102,75,121)(11,89,76,136)(12,104,77,123)(13,91,78,138)(14,106,79,125)(15,93,80,140)(16,108,81,127)(17,95,82,114)(18,110,83,129)(19,97,84,116)(20,112,57,131)(21,99,58,118)(22,86,59,133)(23,101,60,120)(24,88,61,135)(25,103,62,122)(26,90,63,137)(27,105,64,124)(28,92,65,139)(29,168,202,194)(30,155,203,181)(31,142,204,196)(32,157,205,183)(33,144,206,170)(34,159,207,185)(35,146,208,172)(36,161,209,187)(37,148,210,174)(38,163,211,189)(39,150,212,176)(40,165,213,191)(41,152,214,178)(42,167,215,193)(43,154,216,180)(44,141,217,195)(45,156,218,182)(46,143,219,169)(47,158,220,184)(48,145,221,171)(49,160,222,186)(50,147,223,173)(51,162,224,188)(52,149,197,175)(53,164,198,190)(54,151,199,177)(55,166,200,192)(56,153,201,179), (1,191,15,177)(2,178,16,192)(3,193,17,179)(4,180,18,194)(5,195,19,181)(6,182,20,196)(7,169,21,183)(8,184,22,170)(9,171,23,185)(10,186,24,172)(11,173,25,187)(12,188,26,174)(13,175,27,189)(14,190,28,176)(29,96,43,110)(30,111,44,97)(31,98,45,112)(32,85,46,99)(33,100,47,86)(34,87,48,101)(35,102,49,88)(36,89,50,103)(37,104,51,90)(38,91,52,105)(39,106,53,92)(40,93,54,107)(41,108,55,94)(42,95,56,109)(57,142,71,156)(58,157,72,143)(59,144,73,158)(60,159,74,145)(61,146,75,160)(62,161,76,147)(63,148,77,162)(64,163,78,149)(65,150,79,164)(66,165,80,151)(67,152,81,166)(68,167,82,153)(69,154,83,168)(70,141,84,155)(113,214,127,200)(114,201,128,215)(115,216,129,202)(116,203,130,217)(117,218,131,204)(118,205,132,219)(119,220,133,206)(120,207,134,221)(121,222,135,208)(122,209,136,223)(123,224,137,210)(124,211,138,197)(125,198,139,212)(126,213,140,199), (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), (1,79,191,164,15,65,177,150)(2,149,178,64,16,163,192,78)(3,77,193,162,17,63,179,148)(4,147,180,62,18,161,194,76)(5,75,195,160,19,61,181,146)(6,145,182,60,20,159,196,74)(7,73,169,158,21,59,183,144)(8,143,184,58,22,157,170,72)(9,71,171,156,23,57,185,142)(10,141,186,84,24,155,172,70)(11,69,173,154,25,83,187,168)(12,167,188,82,26,153,174,68)(13,67,175,152,27,81,189,166)(14,165,190,80,28,151,176,66)(29,122,96,209,43,136,110,223)(30,222,111,135,44,208,97,121)(31,120,98,207,45,134,112,221)(32,220,85,133,46,206,99,119)(33,118,100,205,47,132,86,219)(34,218,87,131,48,204,101,117)(35,116,102,203,49,130,88,217)(36,216,89,129,50,202,103,115)(37,114,104,201,51,128,90,215)(38,214,91,127,52,200,105,113)(39,140,106,199,53,126,92,213)(40,212,93,125,54,198,107,139)(41,138,108,197,55,124,94,211)(42,210,95,123,56,224,109,137) );
G=PermutationGroup([[(1,107,66,126),(2,94,67,113),(3,109,68,128),(4,96,69,115),(5,111,70,130),(6,98,71,117),(7,85,72,132),(8,100,73,119),(9,87,74,134),(10,102,75,121),(11,89,76,136),(12,104,77,123),(13,91,78,138),(14,106,79,125),(15,93,80,140),(16,108,81,127),(17,95,82,114),(18,110,83,129),(19,97,84,116),(20,112,57,131),(21,99,58,118),(22,86,59,133),(23,101,60,120),(24,88,61,135),(25,103,62,122),(26,90,63,137),(27,105,64,124),(28,92,65,139),(29,168,202,194),(30,155,203,181),(31,142,204,196),(32,157,205,183),(33,144,206,170),(34,159,207,185),(35,146,208,172),(36,161,209,187),(37,148,210,174),(38,163,211,189),(39,150,212,176),(40,165,213,191),(41,152,214,178),(42,167,215,193),(43,154,216,180),(44,141,217,195),(45,156,218,182),(46,143,219,169),(47,158,220,184),(48,145,221,171),(49,160,222,186),(50,147,223,173),(51,162,224,188),(52,149,197,175),(53,164,198,190),(54,151,199,177),(55,166,200,192),(56,153,201,179)], [(1,191,15,177),(2,178,16,192),(3,193,17,179),(4,180,18,194),(5,195,19,181),(6,182,20,196),(7,169,21,183),(8,184,22,170),(9,171,23,185),(10,186,24,172),(11,173,25,187),(12,188,26,174),(13,175,27,189),(14,190,28,176),(29,96,43,110),(30,111,44,97),(31,98,45,112),(32,85,46,99),(33,100,47,86),(34,87,48,101),(35,102,49,88),(36,89,50,103),(37,104,51,90),(38,91,52,105),(39,106,53,92),(40,93,54,107),(41,108,55,94),(42,95,56,109),(57,142,71,156),(58,157,72,143),(59,144,73,158),(60,159,74,145),(61,146,75,160),(62,161,76,147),(63,148,77,162),(64,163,78,149),(65,150,79,164),(66,165,80,151),(67,152,81,166),(68,167,82,153),(69,154,83,168),(70,141,84,155),(113,214,127,200),(114,201,128,215),(115,216,129,202),(116,203,130,217),(117,218,131,204),(118,205,132,219),(119,220,133,206),(120,207,134,221),(121,222,135,208),(122,209,136,223),(123,224,137,210),(124,211,138,197),(125,198,139,212),(126,213,140,199)], [(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)], [(1,79,191,164,15,65,177,150),(2,149,178,64,16,163,192,78),(3,77,193,162,17,63,179,148),(4,147,180,62,18,161,194,76),(5,75,195,160,19,61,181,146),(6,145,182,60,20,159,196,74),(7,73,169,158,21,59,183,144),(8,143,184,58,22,157,170,72),(9,71,171,156,23,57,185,142),(10,141,186,84,24,155,172,70),(11,69,173,154,25,83,187,168),(12,167,188,82,26,153,174,68),(13,67,175,152,27,81,189,166),(14,165,190,80,28,151,176,66),(29,122,96,209,43,136,110,223),(30,222,111,135,44,208,97,121),(31,120,98,207,45,134,112,221),(32,220,85,133,46,206,99,119),(33,118,100,205,47,132,86,219),(34,218,87,131,48,204,101,117),(35,116,102,203,49,130,88,217),(36,216,89,129,50,202,103,115),(37,114,104,201,51,128,90,215),(38,214,91,127,52,200,105,113),(39,140,106,199,53,126,92,213),(40,212,93,125,54,198,107,139),(41,138,108,197,55,124,94,211),(42,210,95,123,56,224,109,137)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | C4×D7 | C4○D28 | C8⋊C22 | C8.C22 | C28.C23 | D4⋊D14 |
| kernel | C42.56D14 | C42.D7 | C28.Q8 | C14.D8 | Q8⋊Dic7 | C4×D28 | C2×Q8⋊D7 | Q8×C28 | Q8⋊D7 | C2×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C2×C4 | Q8 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 2 | 3 | 2 | 3 | 3 | 3 | 12 | 12 | 12 | 1 | 1 | 6 | 6 |
Matrix representation of C42.56D14 ►in GL6(𝔽113)
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 79 | 108 | 45 | 103 |
| 0 | 0 | 5 | 34 | 10 | 68 |
| 0 | 0 | 34 | 5 | 34 | 5 |
| 0 | 0 | 108 | 79 | 108 | 79 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 111 | 0 |
| 0 | 0 | 0 | 112 | 0 | 111 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 |
| 52 | 41 | 0 | 0 | 0 | 0 |
| 14 | 61 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 81 | 1 | 50 |
| 0 | 0 | 32 | 83 | 63 | 112 |
| 0 | 0 | 25 | 57 | 81 | 32 |
| 0 | 0 | 56 | 86 | 81 | 30 |
| 52 | 41 | 0 | 0 | 0 | 0 |
| 36 | 61 | 0 | 0 | 0 | 0 |
| 0 | 0 | 82 | 82 | 50 | 1 |
| 0 | 0 | 29 | 31 | 112 | 63 |
| 0 | 0 | 88 | 56 | 32 | 81 |
| 0 | 0 | 57 | 25 | 30 | 81 |
G:=sub<GL(6,GF(113))| [98,0,0,0,0,0,0,98,0,0,0,0,0,0,79,5,34,108,0,0,108,34,5,79,0,0,45,10,34,108,0,0,103,68,5,79],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,1,0,0,0,0,112,0,1,0,0,111,0,1,0,0,0,0,111,0,1],[52,14,0,0,0,0,41,61,0,0,0,0,0,0,32,32,25,56,0,0,81,83,57,86,0,0,1,63,81,81,0,0,50,112,32,30],[52,36,0,0,0,0,41,61,0,0,0,0,0,0,82,29,88,57,0,0,82,31,56,25,0,0,50,112,32,30,0,0,1,63,81,81] >;
C42.56D14 in GAP, Magma, Sage, TeX
C_4^2._{56}D_{14} % in TeX
G:=Group("C4^2.56D14"); // GroupNames label
G:=SmallGroup(448,560);
// by ID
G=gap.SmallGroup(448,560);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,387,58,1684,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,d^2=b,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^13>;
// generators/relations