metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.64D14, C7⋊C8⋊7D4, C7⋊2(C8⋊3D4), C4.11(D4×D7), C28⋊4D4⋊9C2, C28.25(C2×D4), (C2×C28).82D4, C4.4D4⋊2D7, (C2×D4).48D14, (C2×Q8).38D14, C2.8(C28⋊D4), C42.D7⋊9C2, C14.17(C4⋊1D4), (C2×C28).376C23, (C4×C28).107C22, (D4×C14).64C22, (Q8×C14).56C22, C2.19(D4⋊D14), C14.120(C8⋊C22), (C2×D28).101C22, (C2×D4⋊D7)⋊12C2, (C2×Q8⋊D7)⋊13C2, (C7×C4.4D4)⋊2C2, (C2×C14).507(C2×D4), (C2×C4).62(C7⋊D4), (C2×C7⋊C8).122C22, (C2×C4).476(C22×D7), C22.182(C2×C7⋊D4), SmallGroup(448,592)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.64D14
G = < a,b,c,d | a4=b4=c14=1, d2=cbc-1=b-1, ab=ba, cac-1=a-1b2, dad-1=ab2, bd=db, dcd-1=b-1c-1 >
Subgroups: 940 in 144 conjugacy classes, 43 normal (19 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, C28, C28, D14, C2×C14, C2×C14, C8⋊C4, C4.4D4, C4⋊1D4, C2×D8, C2×SD16, C7⋊C8, D28, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C8⋊3D4, C2×C7⋊C8, D4⋊D7, Q8⋊D7, C4×C28, C7×C22⋊C4, C2×D28, C2×D28, D4×C14, Q8×C14, C42.D7, C28⋊4D4, C2×D4⋊D7, C2×Q8⋊D7, C7×C4.4D4, C42.64D14
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, C28⋊D4, D4⋊D14, C42.64D14
►On 224 points
Generators in S224
(1 35 88 122)(2 61 89 178)(3 37 90 124)(4 63 91 180)(5 39 92 126)(6 65 93 182)(7 41 94 114)(8 67 95 170)(9 29 96 116)(10 69 97 172)(11 31 98 118)(12 57 85 174)(13 33 86 120)(14 59 87 176)(15 56 76 167)(16 103 77 199)(17 44 78 155)(18 105 79 201)(19 46 80 157)(20 107 81 203)(21 48 82 159)(22 109 83 205)(23 50 84 161)(24 111 71 207)(25 52 72 163)(26 99 73 209)(27 54 74 165)(28 101 75 197)(30 218 117 148)(32 220 119 150)(34 222 121 152)(36 224 123 154)(38 212 125 142)(40 214 113 144)(42 216 115 146)(43 194 168 138)(45 196 156 140)(47 184 158 128)(49 186 160 130)(51 188 162 132)(53 190 164 134)(55 192 166 136)(58 221 175 151)(60 223 177 153)(62 211 179 141)(64 213 181 143)(66 215 169 145)(68 217 171 147)(70 219 173 149)(100 191 210 135)(102 193 198 137)(104 195 200 139)(106 183 202 127)(108 185 204 129)(110 187 206 131)(112 189 208 133)
(1 187 223 23)(2 24 224 188)(3 189 211 25)(4 26 212 190)(5 191 213 27)(6 28 214 192)(7 193 215 15)(8 16 216 194)(9 195 217 17)(10 18 218 196)(11 183 219 19)(12 20 220 184)(13 185 221 21)(14 22 222 186)(29 200 171 44)(30 45 172 201)(31 202 173 46)(32 47 174 203)(33 204 175 48)(34 49 176 205)(35 206 177 50)(36 51 178 207)(37 208 179 52)(38 53 180 209)(39 210 181 54)(40 55 182 197)(41 198 169 56)(42 43 170 199)(57 107 119 158)(58 159 120 108)(59 109 121 160)(60 161 122 110)(61 111 123 162)(62 163 124 112)(63 99 125 164)(64 165 126 100)(65 101 113 166)(66 167 114 102)(67 103 115 168)(68 155 116 104)(69 105 117 156)(70 157 118 106)(71 154 132 89)(72 90 133 141)(73 142 134 91)(74 92 135 143)(75 144 136 93)(76 94 137 145)(77 146 138 95)(78 96 139 147)(79 148 140 97)(80 98 127 149)(81 150 128 85)(82 86 129 151)(83 152 130 87)(84 88 131 153)
(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 23 186 223 222 187 22)(2 21 188 221 224 185 24 13)(3 12 25 184 211 220 189 20)(4 19 190 219 212 183 26 11)(5 10 27 196 213 218 191 18)(6 17 192 217 214 195 28 9)(7 8 15 194 215 216 193 16)(29 113 44 101 171 65 200 166)(30 165 201 64 172 100 45 126)(31 125 46 99 173 63 202 164)(32 163 203 62 174 112 47 124)(33 123 48 111 175 61 204 162)(34 161 205 60 176 110 49 122)(35 121 50 109 177 59 206 160)(36 159 207 58 178 108 51 120)(37 119 52 107 179 57 208 158)(38 157 209 70 180 106 53 118)(39 117 54 105 181 69 210 156)(40 155 197 68 182 104 55 116)(41 115 56 103 169 67 198 168)(42 167 199 66 170 102 43 114)(71 86 89 82 132 151 154 129)(72 128 141 150 133 81 90 85)(73 98 91 80 134 149 142 127)(74 140 143 148 135 79 92 97)(75 96 93 78 136 147 144 139)(76 138 145 146 137 77 94 95)(83 88 87 84 130 153 152 131)
G:=sub<Sym(224)| (1,35,88,122)(2,61,89,178)(3,37,90,124)(4,63,91,180)(5,39,92,126)(6,65,93,182)(7,41,94,114)(8,67,95,170)(9,29,96,116)(10,69,97,172)(11,31,98,118)(12,57,85,174)(13,33,86,120)(14,59,87,176)(15,56,76,167)(16,103,77,199)(17,44,78,155)(18,105,79,201)(19,46,80,157)(20,107,81,203)(21,48,82,159)(22,109,83,205)(23,50,84,161)(24,111,71,207)(25,52,72,163)(26,99,73,209)(27,54,74,165)(28,101,75,197)(30,218,117,148)(32,220,119,150)(34,222,121,152)(36,224,123,154)(38,212,125,142)(40,214,113,144)(42,216,115,146)(43,194,168,138)(45,196,156,140)(47,184,158,128)(49,186,160,130)(51,188,162,132)(53,190,164,134)(55,192,166,136)(58,221,175,151)(60,223,177,153)(62,211,179,141)(64,213,181,143)(66,215,169,145)(68,217,171,147)(70,219,173,149)(100,191,210,135)(102,193,198,137)(104,195,200,139)(106,183,202,127)(108,185,204,129)(110,187,206,131)(112,189,208,133), (1,187,223,23)(2,24,224,188)(3,189,211,25)(4,26,212,190)(5,191,213,27)(6,28,214,192)(7,193,215,15)(8,16,216,194)(9,195,217,17)(10,18,218,196)(11,183,219,19)(12,20,220,184)(13,185,221,21)(14,22,222,186)(29,200,171,44)(30,45,172,201)(31,202,173,46)(32,47,174,203)(33,204,175,48)(34,49,176,205)(35,206,177,50)(36,51,178,207)(37,208,179,52)(38,53,180,209)(39,210,181,54)(40,55,182,197)(41,198,169,56)(42,43,170,199)(57,107,119,158)(58,159,120,108)(59,109,121,160)(60,161,122,110)(61,111,123,162)(62,163,124,112)(63,99,125,164)(64,165,126,100)(65,101,113,166)(66,167,114,102)(67,103,115,168)(68,155,116,104)(69,105,117,156)(70,157,118,106)(71,154,132,89)(72,90,133,141)(73,142,134,91)(74,92,135,143)(75,144,136,93)(76,94,137,145)(77,146,138,95)(78,96,139,147)(79,148,140,97)(80,98,127,149)(81,150,128,85)(82,86,129,151)(83,152,130,87)(84,88,131,153), (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), (1,14,23,186,223,222,187,22)(2,21,188,221,224,185,24,13)(3,12,25,184,211,220,189,20)(4,19,190,219,212,183,26,11)(5,10,27,196,213,218,191,18)(6,17,192,217,214,195,28,9)(7,8,15,194,215,216,193,16)(29,113,44,101,171,65,200,166)(30,165,201,64,172,100,45,126)(31,125,46,99,173,63,202,164)(32,163,203,62,174,112,47,124)(33,123,48,111,175,61,204,162)(34,161,205,60,176,110,49,122)(35,121,50,109,177,59,206,160)(36,159,207,58,178,108,51,120)(37,119,52,107,179,57,208,158)(38,157,209,70,180,106,53,118)(39,117,54,105,181,69,210,156)(40,155,197,68,182,104,55,116)(41,115,56,103,169,67,198,168)(42,167,199,66,170,102,43,114)(71,86,89,82,132,151,154,129)(72,128,141,150,133,81,90,85)(73,98,91,80,134,149,142,127)(74,140,143,148,135,79,92,97)(75,96,93,78,136,147,144,139)(76,138,145,146,137,77,94,95)(83,88,87,84,130,153,152,131)>;
G:=Group( (1,35,88,122)(2,61,89,178)(3,37,90,124)(4,63,91,180)(5,39,92,126)(6,65,93,182)(7,41,94,114)(8,67,95,170)(9,29,96,116)(10,69,97,172)(11,31,98,118)(12,57,85,174)(13,33,86,120)(14,59,87,176)(15,56,76,167)(16,103,77,199)(17,44,78,155)(18,105,79,201)(19,46,80,157)(20,107,81,203)(21,48,82,159)(22,109,83,205)(23,50,84,161)(24,111,71,207)(25,52,72,163)(26,99,73,209)(27,54,74,165)(28,101,75,197)(30,218,117,148)(32,220,119,150)(34,222,121,152)(36,224,123,154)(38,212,125,142)(40,214,113,144)(42,216,115,146)(43,194,168,138)(45,196,156,140)(47,184,158,128)(49,186,160,130)(51,188,162,132)(53,190,164,134)(55,192,166,136)(58,221,175,151)(60,223,177,153)(62,211,179,141)(64,213,181,143)(66,215,169,145)(68,217,171,147)(70,219,173,149)(100,191,210,135)(102,193,198,137)(104,195,200,139)(106,183,202,127)(108,185,204,129)(110,187,206,131)(112,189,208,133), (1,187,223,23)(2,24,224,188)(3,189,211,25)(4,26,212,190)(5,191,213,27)(6,28,214,192)(7,193,215,15)(8,16,216,194)(9,195,217,17)(10,18,218,196)(11,183,219,19)(12,20,220,184)(13,185,221,21)(14,22,222,186)(29,200,171,44)(30,45,172,201)(31,202,173,46)(32,47,174,203)(33,204,175,48)(34,49,176,205)(35,206,177,50)(36,51,178,207)(37,208,179,52)(38,53,180,209)(39,210,181,54)(40,55,182,197)(41,198,169,56)(42,43,170,199)(57,107,119,158)(58,159,120,108)(59,109,121,160)(60,161,122,110)(61,111,123,162)(62,163,124,112)(63,99,125,164)(64,165,126,100)(65,101,113,166)(66,167,114,102)(67,103,115,168)(68,155,116,104)(69,105,117,156)(70,157,118,106)(71,154,132,89)(72,90,133,141)(73,142,134,91)(74,92,135,143)(75,144,136,93)(76,94,137,145)(77,146,138,95)(78,96,139,147)(79,148,140,97)(80,98,127,149)(81,150,128,85)(82,86,129,151)(83,152,130,87)(84,88,131,153), (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), (1,14,23,186,223,222,187,22)(2,21,188,221,224,185,24,13)(3,12,25,184,211,220,189,20)(4,19,190,219,212,183,26,11)(5,10,27,196,213,218,191,18)(6,17,192,217,214,195,28,9)(7,8,15,194,215,216,193,16)(29,113,44,101,171,65,200,166)(30,165,201,64,172,100,45,126)(31,125,46,99,173,63,202,164)(32,163,203,62,174,112,47,124)(33,123,48,111,175,61,204,162)(34,161,205,60,176,110,49,122)(35,121,50,109,177,59,206,160)(36,159,207,58,178,108,51,120)(37,119,52,107,179,57,208,158)(38,157,209,70,180,106,53,118)(39,117,54,105,181,69,210,156)(40,155,197,68,182,104,55,116)(41,115,56,103,169,67,198,168)(42,167,199,66,170,102,43,114)(71,86,89,82,132,151,154,129)(72,128,141,150,133,81,90,85)(73,98,91,80,134,149,142,127)(74,140,143,148,135,79,92,97)(75,96,93,78,136,147,144,139)(76,138,145,146,137,77,94,95)(83,88,87,84,130,153,152,131) );
G=PermutationGroup([[(1,35,88,122),(2,61,89,178),(3,37,90,124),(4,63,91,180),(5,39,92,126),(6,65,93,182),(7,41,94,114),(8,67,95,170),(9,29,96,116),(10,69,97,172),(11,31,98,118),(12,57,85,174),(13,33,86,120),(14,59,87,176),(15,56,76,167),(16,103,77,199),(17,44,78,155),(18,105,79,201),(19,46,80,157),(20,107,81,203),(21,48,82,159),(22,109,83,205),(23,50,84,161),(24,111,71,207),(25,52,72,163),(26,99,73,209),(27,54,74,165),(28,101,75,197),(30,218,117,148),(32,220,119,150),(34,222,121,152),(36,224,123,154),(38,212,125,142),(40,214,113,144),(42,216,115,146),(43,194,168,138),(45,196,156,140),(47,184,158,128),(49,186,160,130),(51,188,162,132),(53,190,164,134),(55,192,166,136),(58,221,175,151),(60,223,177,153),(62,211,179,141),(64,213,181,143),(66,215,169,145),(68,217,171,147),(70,219,173,149),(100,191,210,135),(102,193,198,137),(104,195,200,139),(106,183,202,127),(108,185,204,129),(110,187,206,131),(112,189,208,133)], [(1,187,223,23),(2,24,224,188),(3,189,211,25),(4,26,212,190),(5,191,213,27),(6,28,214,192),(7,193,215,15),(8,16,216,194),(9,195,217,17),(10,18,218,196),(11,183,219,19),(12,20,220,184),(13,185,221,21),(14,22,222,186),(29,200,171,44),(30,45,172,201),(31,202,173,46),(32,47,174,203),(33,204,175,48),(34,49,176,205),(35,206,177,50),(36,51,178,207),(37,208,179,52),(38,53,180,209),(39,210,181,54),(40,55,182,197),(41,198,169,56),(42,43,170,199),(57,107,119,158),(58,159,120,108),(59,109,121,160),(60,161,122,110),(61,111,123,162),(62,163,124,112),(63,99,125,164),(64,165,126,100),(65,101,113,166),(66,167,114,102),(67,103,115,168),(68,155,116,104),(69,105,117,156),(70,157,118,106),(71,154,132,89),(72,90,133,141),(73,142,134,91),(74,92,135,143),(75,144,136,93),(76,94,137,145),(77,146,138,95),(78,96,139,147),(79,148,140,97),(80,98,127,149),(81,150,128,85),(82,86,129,151),(83,152,130,87),(84,88,131,153)], [(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)], [(1,14,23,186,223,222,187,22),(2,21,188,221,224,185,24,13),(3,12,25,184,211,220,189,20),(4,19,190,219,212,183,26,11),(5,10,27,196,213,218,191,18),(6,17,192,217,214,195,28,9),(7,8,15,194,215,216,193,16),(29,113,44,101,171,65,200,166),(30,165,201,64,172,100,45,126),(31,125,46,99,173,63,202,164),(32,163,203,62,174,112,47,124),(33,123,48,111,175,61,204,162),(34,161,205,60,176,110,49,122),(35,121,50,109,177,59,206,160),(36,159,207,58,178,108,51,120),(37,119,52,107,179,57,208,158),(38,157,209,70,180,106,53,118),(39,117,54,105,181,69,210,156),(40,155,197,68,182,104,55,116),(41,115,56,103,169,67,198,168),(42,167,199,66,170,102,43,114),(71,86,89,82,132,151,154,129),(72,128,141,150,133,81,90,85),(73,98,91,80,134,149,142,127),(74,140,143,148,135,79,92,97),(75,96,93,78,136,147,144,139),(76,138,145,146,137,77,94,95),(83,88,87,84,130,153,152,131)]])
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 | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| 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 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 56 | 56 | 2 | 2 | 4 | 4 | 8 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | D14 | D14 | D14 | C7⋊D4 | C8⋊C22 | D4×D7 | D4⋊D14 |
| kernel | C42.64D14 | C42.D7 | C28⋊4D4 | C2×D4⋊D7 | C2×Q8⋊D7 | C7×C4.4D4 | C7⋊C8 | C2×C28 | C4.4D4 | C42 | C2×D4 | C2×Q8 | C2×C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 2 | 3 | 3 | 3 | 3 | 12 | 2 | 6 | 12 |
Matrix representation of C42.64D14 ►in GL6(𝔽113)
| 12 | 112 | 0 | 0 | 0 | 0 |
| 32 | 101 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 8 |
| 0 | 0 | 0 | 0 | 105 | 96 |
| 0 | 0 | 96 | 105 | 0 | 0 |
| 0 | 0 | 8 | 17 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 89 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 89 | 89 | 36 |
| 0 | 0 | 24 | 25 | 77 | 49 |
| 0 | 0 | 89 | 36 | 77 | 24 |
| 0 | 0 | 77 | 49 | 89 | 88 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 89 | 36 | 77 | 24 |
| 0 | 0 | 25 | 24 | 64 | 36 |
| 0 | 0 | 36 | 89 | 89 | 36 |
| 0 | 0 | 49 | 77 | 25 | 24 |
G:=sub<GL(6,GF(113))| [12,32,0,0,0,0,112,101,0,0,0,0,0,0,0,0,96,8,0,0,0,0,105,17,0,0,17,105,0,0,0,0,8,96,0,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,1,0,0,0,0,0,0,1,0,0],[112,89,0,0,0,0,0,1,0,0,0,0,0,0,36,24,89,77,0,0,89,25,36,49,0,0,89,77,77,89,0,0,36,49,24,88],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,89,25,36,49,0,0,36,24,89,77,0,0,77,64,89,25,0,0,24,36,36,24] >;
C42.64D14 in GAP, Magma, Sage, TeX
C_4^2._{64}D_{14} % in TeX
G:=Group("C4^2.64D14"); // GroupNames label
G:=SmallGroup(448,592);
// by ID
G=gap.SmallGroup(448,592);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,254,555,1123,297,136,18822]);
// 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*b^2,d*a*d^-1=a*b^2,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations