metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.213D14, (C2×D4).46D14, (C2×C28).270D4, (C2×Q8).36D14, C4.4D4.6D7, C28.67(C4○D4), Q8⋊Dic7⋊21C2, C28.6Q8⋊12C2, C14.104(C4○D8), C4.21(D4⋊2D7), (C2×C28).374C23, (C4×C28).105C22, D4⋊Dic7.13C2, (D4×C14).62C22, (Q8×C14).54C22, C14.42(C4.4D4), C2.9(C28.17D4), C4⋊Dic7.151C22, C2.23(D4.8D14), C7⋊4(C42.78C22), (C4×C7⋊C8)⋊11C2, (C2×C14).505(C2×D4), (C2×C7⋊C8).252C22, (C7×C4.4D4).4C2, (C2×C4).109(C7⋊D4), (C2×C4).474(C22×D7), C22.180(C2×C7⋊D4), SmallGroup(448,590)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.213D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=dbd-1=b-1, dcd-1=a2bc-1 >
Subgroups: 364 in 96 conjugacy classes, 39 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C4×C8, D4⋊C4, Q8⋊C4, C4.4D4, C42.C2, C7⋊C8, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C42.78C22, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C4×C28, C7×C22⋊C4, D4×C14, Q8×C14, C4×C7⋊C8, D4⋊Dic7, Q8⋊Dic7, C28.6Q8, C7×C4.4D4, C42.213D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C4○D8, C7⋊D4, C22×D7, C42.78C22, D4⋊2D7, C2×C7⋊D4, C28.17D4, D4.8D14, C42.213D14
►On 224 points
Generators in S224
(1 88 25 172)(2 96 26 180)(3 90 27 174)(4 98 28 182)(5 92 22 176)(6 86 23 170)(7 94 24 178)(8 181 21 97)(9 175 15 91)(10 169 16 85)(11 177 17 93)(12 171 18 87)(13 179 19 95)(14 173 20 89)(29 220 36 133)(30 127 37 214)(31 222 38 135)(32 129 39 216)(33 224 40 137)(34 131 41 218)(35 212 42 139)(43 132 50 219)(44 213 51 140)(45 134 52 221)(46 215 53 128)(47 136 54 223)(48 217 55 130)(49 138 56 211)(57 111 117 158)(58 189 118 150)(59 99 119 160)(60 191 120 152)(61 101 121 162)(62 193 122 154)(63 103 123 164)(64 195 124 142)(65 105 125 166)(66 183 126 144)(67 107 113 168)(68 185 114 146)(69 109 115 156)(70 187 116 148)(71 161 202 100)(72 153 203 192)(73 163 204 102)(74 141 205 194)(75 165 206 104)(76 143 207 196)(77 167 208 106)(78 145 209 184)(79 155 210 108)(80 147 197 186)(81 157 198 110)(82 149 199 188)(83 159 200 112)(84 151 201 190)
(1 136 13 129)(2 130 14 137)(3 138 8 131)(4 132 9 139)(5 140 10 133)(6 134 11 127)(7 128 12 135)(15 212 28 219)(16 220 22 213)(17 214 23 221)(18 222 24 215)(19 216 25 223)(20 224 26 217)(21 218 27 211)(29 92 44 169)(30 170 45 93)(31 94 46 171)(32 172 47 95)(33 96 48 173)(34 174 49 97)(35 98 50 175)(36 176 51 85)(37 86 52 177)(38 178 53 87)(39 88 54 179)(40 180 55 89)(41 90 56 181)(42 182 43 91)(57 124 82 206)(58 207 83 125)(59 126 84 208)(60 209 71 113)(61 114 72 210)(62 197 73 115)(63 116 74 198)(64 199 75 117)(65 118 76 200)(66 201 77 119)(67 120 78 202)(68 203 79 121)(69 122 80 204)(70 205 81 123)(99 144 151 106)(100 107 152 145)(101 146 153 108)(102 109 154 147)(103 148 141 110)(104 111 142 149)(105 150 143 112)(155 162 185 192)(156 193 186 163)(157 164 187 194)(158 195 188 165)(159 166 189 196)(160 183 190 167)(161 168 191 184)
(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)
(1 207 25 76)(2 199 26 82)(3 205 27 74)(4 197 28 80)(5 203 22 72)(6 209 23 78)(7 201 24 84)(8 123 21 63)(9 115 15 69)(10 121 16 61)(11 113 17 67)(12 119 18 59)(13 125 19 65)(14 117 20 57)(29 146 36 185)(30 191 37 152)(31 144 38 183)(32 189 39 150)(33 142 40 195)(34 187 41 148)(35 154 42 193)(43 163 50 102)(44 108 51 155)(45 161 52 100)(46 106 53 167)(47 159 54 112)(48 104 55 165)(49 157 56 110)(58 223 118 136)(60 221 120 134)(62 219 122 132)(64 217 124 130)(66 215 126 128)(68 213 114 140)(70 211 116 138)(71 214 202 127)(73 212 204 139)(75 224 206 137)(77 222 208 135)(79 220 210 133)(81 218 198 131)(83 216 200 129)(85 192 169 153)(86 107 170 168)(87 190 171 151)(88 105 172 166)(89 188 173 149)(90 103 174 164)(91 186 175 147)(92 101 176 162)(93 184 177 145)(94 99 178 160)(95 196 179 143)(96 111 180 158)(97 194 181 141)(98 109 182 156)
G:=sub<Sym(224)| (1,88,25,172)(2,96,26,180)(3,90,27,174)(4,98,28,182)(5,92,22,176)(6,86,23,170)(7,94,24,178)(8,181,21,97)(9,175,15,91)(10,169,16,85)(11,177,17,93)(12,171,18,87)(13,179,19,95)(14,173,20,89)(29,220,36,133)(30,127,37,214)(31,222,38,135)(32,129,39,216)(33,224,40,137)(34,131,41,218)(35,212,42,139)(43,132,50,219)(44,213,51,140)(45,134,52,221)(46,215,53,128)(47,136,54,223)(48,217,55,130)(49,138,56,211)(57,111,117,158)(58,189,118,150)(59,99,119,160)(60,191,120,152)(61,101,121,162)(62,193,122,154)(63,103,123,164)(64,195,124,142)(65,105,125,166)(66,183,126,144)(67,107,113,168)(68,185,114,146)(69,109,115,156)(70,187,116,148)(71,161,202,100)(72,153,203,192)(73,163,204,102)(74,141,205,194)(75,165,206,104)(76,143,207,196)(77,167,208,106)(78,145,209,184)(79,155,210,108)(80,147,197,186)(81,157,198,110)(82,149,199,188)(83,159,200,112)(84,151,201,190), (1,136,13,129)(2,130,14,137)(3,138,8,131)(4,132,9,139)(5,140,10,133)(6,134,11,127)(7,128,12,135)(15,212,28,219)(16,220,22,213)(17,214,23,221)(18,222,24,215)(19,216,25,223)(20,224,26,217)(21,218,27,211)(29,92,44,169)(30,170,45,93)(31,94,46,171)(32,172,47,95)(33,96,48,173)(34,174,49,97)(35,98,50,175)(36,176,51,85)(37,86,52,177)(38,178,53,87)(39,88,54,179)(40,180,55,89)(41,90,56,181)(42,182,43,91)(57,124,82,206)(58,207,83,125)(59,126,84,208)(60,209,71,113)(61,114,72,210)(62,197,73,115)(63,116,74,198)(64,199,75,117)(65,118,76,200)(66,201,77,119)(67,120,78,202)(68,203,79,121)(69,122,80,204)(70,205,81,123)(99,144,151,106)(100,107,152,145)(101,146,153,108)(102,109,154,147)(103,148,141,110)(104,111,142,149)(105,150,143,112)(155,162,185,192)(156,193,186,163)(157,164,187,194)(158,195,188,165)(159,166,189,196)(160,183,190,167)(161,168,191,184), (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), (1,207,25,76)(2,199,26,82)(3,205,27,74)(4,197,28,80)(5,203,22,72)(6,209,23,78)(7,201,24,84)(8,123,21,63)(9,115,15,69)(10,121,16,61)(11,113,17,67)(12,119,18,59)(13,125,19,65)(14,117,20,57)(29,146,36,185)(30,191,37,152)(31,144,38,183)(32,189,39,150)(33,142,40,195)(34,187,41,148)(35,154,42,193)(43,163,50,102)(44,108,51,155)(45,161,52,100)(46,106,53,167)(47,159,54,112)(48,104,55,165)(49,157,56,110)(58,223,118,136)(60,221,120,134)(62,219,122,132)(64,217,124,130)(66,215,126,128)(68,213,114,140)(70,211,116,138)(71,214,202,127)(73,212,204,139)(75,224,206,137)(77,222,208,135)(79,220,210,133)(81,218,198,131)(83,216,200,129)(85,192,169,153)(86,107,170,168)(87,190,171,151)(88,105,172,166)(89,188,173,149)(90,103,174,164)(91,186,175,147)(92,101,176,162)(93,184,177,145)(94,99,178,160)(95,196,179,143)(96,111,180,158)(97,194,181,141)(98,109,182,156)>;
G:=Group( (1,88,25,172)(2,96,26,180)(3,90,27,174)(4,98,28,182)(5,92,22,176)(6,86,23,170)(7,94,24,178)(8,181,21,97)(9,175,15,91)(10,169,16,85)(11,177,17,93)(12,171,18,87)(13,179,19,95)(14,173,20,89)(29,220,36,133)(30,127,37,214)(31,222,38,135)(32,129,39,216)(33,224,40,137)(34,131,41,218)(35,212,42,139)(43,132,50,219)(44,213,51,140)(45,134,52,221)(46,215,53,128)(47,136,54,223)(48,217,55,130)(49,138,56,211)(57,111,117,158)(58,189,118,150)(59,99,119,160)(60,191,120,152)(61,101,121,162)(62,193,122,154)(63,103,123,164)(64,195,124,142)(65,105,125,166)(66,183,126,144)(67,107,113,168)(68,185,114,146)(69,109,115,156)(70,187,116,148)(71,161,202,100)(72,153,203,192)(73,163,204,102)(74,141,205,194)(75,165,206,104)(76,143,207,196)(77,167,208,106)(78,145,209,184)(79,155,210,108)(80,147,197,186)(81,157,198,110)(82,149,199,188)(83,159,200,112)(84,151,201,190), (1,136,13,129)(2,130,14,137)(3,138,8,131)(4,132,9,139)(5,140,10,133)(6,134,11,127)(7,128,12,135)(15,212,28,219)(16,220,22,213)(17,214,23,221)(18,222,24,215)(19,216,25,223)(20,224,26,217)(21,218,27,211)(29,92,44,169)(30,170,45,93)(31,94,46,171)(32,172,47,95)(33,96,48,173)(34,174,49,97)(35,98,50,175)(36,176,51,85)(37,86,52,177)(38,178,53,87)(39,88,54,179)(40,180,55,89)(41,90,56,181)(42,182,43,91)(57,124,82,206)(58,207,83,125)(59,126,84,208)(60,209,71,113)(61,114,72,210)(62,197,73,115)(63,116,74,198)(64,199,75,117)(65,118,76,200)(66,201,77,119)(67,120,78,202)(68,203,79,121)(69,122,80,204)(70,205,81,123)(99,144,151,106)(100,107,152,145)(101,146,153,108)(102,109,154,147)(103,148,141,110)(104,111,142,149)(105,150,143,112)(155,162,185,192)(156,193,186,163)(157,164,187,194)(158,195,188,165)(159,166,189,196)(160,183,190,167)(161,168,191,184), (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), (1,207,25,76)(2,199,26,82)(3,205,27,74)(4,197,28,80)(5,203,22,72)(6,209,23,78)(7,201,24,84)(8,123,21,63)(9,115,15,69)(10,121,16,61)(11,113,17,67)(12,119,18,59)(13,125,19,65)(14,117,20,57)(29,146,36,185)(30,191,37,152)(31,144,38,183)(32,189,39,150)(33,142,40,195)(34,187,41,148)(35,154,42,193)(43,163,50,102)(44,108,51,155)(45,161,52,100)(46,106,53,167)(47,159,54,112)(48,104,55,165)(49,157,56,110)(58,223,118,136)(60,221,120,134)(62,219,122,132)(64,217,124,130)(66,215,126,128)(68,213,114,140)(70,211,116,138)(71,214,202,127)(73,212,204,139)(75,224,206,137)(77,222,208,135)(79,220,210,133)(81,218,198,131)(83,216,200,129)(85,192,169,153)(86,107,170,168)(87,190,171,151)(88,105,172,166)(89,188,173,149)(90,103,174,164)(91,186,175,147)(92,101,176,162)(93,184,177,145)(94,99,178,160)(95,196,179,143)(96,111,180,158)(97,194,181,141)(98,109,182,156) );
G=PermutationGroup([[(1,88,25,172),(2,96,26,180),(3,90,27,174),(4,98,28,182),(5,92,22,176),(6,86,23,170),(7,94,24,178),(8,181,21,97),(9,175,15,91),(10,169,16,85),(11,177,17,93),(12,171,18,87),(13,179,19,95),(14,173,20,89),(29,220,36,133),(30,127,37,214),(31,222,38,135),(32,129,39,216),(33,224,40,137),(34,131,41,218),(35,212,42,139),(43,132,50,219),(44,213,51,140),(45,134,52,221),(46,215,53,128),(47,136,54,223),(48,217,55,130),(49,138,56,211),(57,111,117,158),(58,189,118,150),(59,99,119,160),(60,191,120,152),(61,101,121,162),(62,193,122,154),(63,103,123,164),(64,195,124,142),(65,105,125,166),(66,183,126,144),(67,107,113,168),(68,185,114,146),(69,109,115,156),(70,187,116,148),(71,161,202,100),(72,153,203,192),(73,163,204,102),(74,141,205,194),(75,165,206,104),(76,143,207,196),(77,167,208,106),(78,145,209,184),(79,155,210,108),(80,147,197,186),(81,157,198,110),(82,149,199,188),(83,159,200,112),(84,151,201,190)], [(1,136,13,129),(2,130,14,137),(3,138,8,131),(4,132,9,139),(5,140,10,133),(6,134,11,127),(7,128,12,135),(15,212,28,219),(16,220,22,213),(17,214,23,221),(18,222,24,215),(19,216,25,223),(20,224,26,217),(21,218,27,211),(29,92,44,169),(30,170,45,93),(31,94,46,171),(32,172,47,95),(33,96,48,173),(34,174,49,97),(35,98,50,175),(36,176,51,85),(37,86,52,177),(38,178,53,87),(39,88,54,179),(40,180,55,89),(41,90,56,181),(42,182,43,91),(57,124,82,206),(58,207,83,125),(59,126,84,208),(60,209,71,113),(61,114,72,210),(62,197,73,115),(63,116,74,198),(64,199,75,117),(65,118,76,200),(66,201,77,119),(67,120,78,202),(68,203,79,121),(69,122,80,204),(70,205,81,123),(99,144,151,106),(100,107,152,145),(101,146,153,108),(102,109,154,147),(103,148,141,110),(104,111,142,149),(105,150,143,112),(155,162,185,192),(156,193,186,163),(157,164,187,194),(158,195,188,165),(159,166,189,196),(160,183,190,167),(161,168,191,184)], [(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)], [(1,207,25,76),(2,199,26,82),(3,205,27,74),(4,197,28,80),(5,203,22,72),(6,209,23,78),(7,201,24,84),(8,123,21,63),(9,115,15,69),(10,121,16,61),(11,113,17,67),(12,119,18,59),(13,125,19,65),(14,117,20,57),(29,146,36,185),(30,191,37,152),(31,144,38,183),(32,189,39,150),(33,142,40,195),(34,187,41,148),(35,154,42,193),(43,163,50,102),(44,108,51,155),(45,161,52,100),(46,106,53,167),(47,159,54,112),(48,104,55,165),(49,157,56,110),(58,223,118,136),(60,221,120,134),(62,219,122,132),(64,217,124,130),(66,215,126,128),(68,213,114,140),(70,211,116,138),(71,214,202,127),(73,212,204,139),(75,224,206,137),(77,222,208,135),(79,220,210,133),(81,218,198,131),(83,216,200,129),(85,192,169,153),(86,107,170,168),(87,190,171,151),(88,105,172,166),(89,188,173,149),(90,103,174,164),(91,186,175,147),(92,101,176,162),(93,184,177,145),(94,99,178,160),(95,196,179,143),(96,111,180,158),(97,194,181,141),(98,109,182,156)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | ··· | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 2 | ··· | 2 | 8 | 56 | 56 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | D4⋊2D7 | D4.8D14 |
| kernel | C42.213D14 | C4×C7⋊C8 | D4⋊Dic7 | Q8⋊Dic7 | C28.6Q8 | C7×C4.4D4 | C2×C28 | C4.4D4 | C28 | C42 | C2×D4 | C2×Q8 | C14 | C2×C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 3 | 4 | 3 | 3 | 3 | 8 | 12 | 6 | 12 |
Matrix representation of C42.213D14 ►in GL6(𝔽113)
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 98 | 104 |
| 0 | 0 | 0 | 0 | 50 | 15 |
| 1 | 85 | 0 | 0 | 0 | 0 |
| 105 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 91 |
| 0 | 0 | 0 | 0 | 72 | 112 |
| 1 | 85 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 88 | 88 | 0 | 0 |
| 0 | 0 | 25 | 34 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 72 | 112 |
| 87 | 25 | 0 | 0 | 0 | 0 |
| 104 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 105 | 0 | 0 |
| 0 | 0 | 101 | 73 | 0 | 0 |
| 0 | 0 | 0 | 0 | 51 | 4 |
| 0 | 0 | 0 | 0 | 28 | 62 |
G:=sub<GL(6,GF(113))| [98,0,0,0,0,0,0,98,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,98,50,0,0,0,0,104,15],[1,105,0,0,0,0,85,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,72,0,0,0,0,91,112],[1,0,0,0,0,0,85,112,0,0,0,0,0,0,88,25,0,0,0,0,88,34,0,0,0,0,0,0,1,72,0,0,0,0,0,112],[87,104,0,0,0,0,25,26,0,0,0,0,0,0,40,101,0,0,0,0,105,73,0,0,0,0,0,0,51,28,0,0,0,0,4,62] >;
C42.213D14 in GAP, Magma, Sage, TeX
C_4^2._{213}D_{14} % in TeX
G:=Group("C4^2.213D14"); // GroupNames label
G:=SmallGroup(448,590);
// by ID
G=gap.SmallGroup(448,590);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,64,590,471,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=a^2*b*c^-1>;
// generators/relations