metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.31D14, C4⋊C8⋊16D7, D14⋊C8.9C2, C56⋊C4⋊22C2, C28⋊C8⋊16C2, D14⋊C4.15C4, (C8×Dic7)⋊24C2, (C2×C8).218D14, C14.14(C8○D4), Dic7⋊C4.15C4, (C4×C28).66C22, C42⋊D7.2C2, C28.337(C4○D4), C2.15(D28.C4), (C2×C28).837C23, (C2×C56).216C22, C4.57(Q8⋊2D7), C4.132(D4⋊2D7), C7⋊4(C42.7C22), C14.33(C42⋊C2), C2.16(D28.2C4), (C4×Dic7).278C22, (C7×C4⋊C8)⋊21C2, (C2×C4).37(C4×D7), C22.115(C2×C4×D7), (C2×C28).182(C2×C4), (C2×C7⋊C8).197C22, (C2×C4×D7).182C22, C2.10(C4⋊C4⋊7D7), (C2×C14).92(C22×C4), (C2×Dic7).55(C2×C4), (C22×D7).17(C2×C4), (C2×C4).779(C22×D7), SmallGroup(448,374)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.31D14
G = < a,b,c,d | a4=b4=1, c14=b-1, d2=a2b, ab=ba, cac-1=a-1, dad-1=a-1b2, bc=cb, bd=db, dcd-1=a2b2c13 >
Subgroups: 388 in 96 conjugacy classes, 47 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, Dic7, C28, C28, D14, C2×C14, C4×C8, C8⋊C4, C22⋊C8, C4⋊C8, C4⋊C8, C42⋊C2, C7⋊C8, C56, C4×D7, C2×Dic7, C2×C28, C22×D7, C42.7C22, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, D14⋊C4, C4×C28, C2×C56, C2×C4×D7, C28⋊C8, C8×Dic7, C56⋊C4, D14⋊C8, C7×C4⋊C8, C42⋊D7, C42.31D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C4○D4, D14, C42⋊C2, C8○D4, C4×D7, C22×D7, C42.7C22, C2×C4×D7, D4⋊2D7, Q8⋊2D7, C4⋊C4⋊7D7, D28.2C4, D28.C4, C42.31D14
►On 224 points
Generators in S224
(1 57 147 209)(2 210 148 58)(3 59 149 211)(4 212 150 60)(5 61 151 213)(6 214 152 62)(7 63 153 215)(8 216 154 64)(9 65 155 217)(10 218 156 66)(11 67 157 219)(12 220 158 68)(13 69 159 221)(14 222 160 70)(15 71 161 223)(16 224 162 72)(17 73 163 169)(18 170 164 74)(19 75 165 171)(20 172 166 76)(21 77 167 173)(22 174 168 78)(23 79 113 175)(24 176 114 80)(25 81 115 177)(26 178 116 82)(27 83 117 179)(28 180 118 84)(29 85 119 181)(30 182 120 86)(31 87 121 183)(32 184 122 88)(33 89 123 185)(34 186 124 90)(35 91 125 187)(36 188 126 92)(37 93 127 189)(38 190 128 94)(39 95 129 191)(40 192 130 96)(41 97 131 193)(42 194 132 98)(43 99 133 195)(44 196 134 100)(45 101 135 197)(46 198 136 102)(47 103 137 199)(48 200 138 104)(49 105 139 201)(50 202 140 106)(51 107 141 203)(52 204 142 108)(53 109 143 205)(54 206 144 110)(55 111 145 207)(56 208 146 112)
(1 43 29 15)(2 44 30 16)(3 45 31 17)(4 46 32 18)(5 47 33 19)(6 48 34 20)(7 49 35 21)(8 50 36 22)(9 51 37 23)(10 52 38 24)(11 53 39 25)(12 54 40 26)(13 55 41 27)(14 56 42 28)(57 99 85 71)(58 100 86 72)(59 101 87 73)(60 102 88 74)(61 103 89 75)(62 104 90 76)(63 105 91 77)(64 106 92 78)(65 107 93 79)(66 108 94 80)(67 109 95 81)(68 110 96 82)(69 111 97 83)(70 112 98 84)(113 155 141 127)(114 156 142 128)(115 157 143 129)(116 158 144 130)(117 159 145 131)(118 160 146 132)(119 161 147 133)(120 162 148 134)(121 163 149 135)(122 164 150 136)(123 165 151 137)(124 166 152 138)(125 167 153 139)(126 168 154 140)(169 211 197 183)(170 212 198 184)(171 213 199 185)(172 214 200 186)(173 215 201 187)(174 216 202 188)(175 217 203 189)(176 218 204 190)(177 219 205 191)(178 220 206 192)(179 221 207 193)(180 222 208 194)(181 223 209 195)(182 224 210 196)
(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 42 133 118 29 14 161 146)(2 117 134 13 30 145 162 41)(3 12 135 144 31 40 163 116)(4 143 136 39 32 115 164 11)(5 38 137 114 33 10 165 142)(6 113 138 9 34 141 166 37)(7 8 139 140 35 36 167 168)(15 56 147 132 43 28 119 160)(16 131 148 27 44 159 120 55)(17 26 149 158 45 54 121 130)(18 157 150 53 46 129 122 25)(19 52 151 128 47 24 123 156)(20 127 152 23 48 155 124 51)(21 22 153 154 49 50 125 126)(57 70 195 208 85 98 223 180)(58 207 196 97 86 179 224 69)(59 96 197 178 87 68 169 206)(60 177 198 67 88 205 170 95)(61 66 199 204 89 94 171 176)(62 203 200 93 90 175 172 65)(63 92 201 174 91 64 173 202)(71 84 209 222 99 112 181 194)(72 221 210 111 100 193 182 83)(73 110 211 192 101 82 183 220)(74 191 212 81 102 219 184 109)(75 80 213 218 103 108 185 190)(76 217 214 107 104 189 186 79)(77 106 215 188 105 78 187 216)
G:=sub<Sym(224)| (1,57,147,209)(2,210,148,58)(3,59,149,211)(4,212,150,60)(5,61,151,213)(6,214,152,62)(7,63,153,215)(8,216,154,64)(9,65,155,217)(10,218,156,66)(11,67,157,219)(12,220,158,68)(13,69,159,221)(14,222,160,70)(15,71,161,223)(16,224,162,72)(17,73,163,169)(18,170,164,74)(19,75,165,171)(20,172,166,76)(21,77,167,173)(22,174,168,78)(23,79,113,175)(24,176,114,80)(25,81,115,177)(26,178,116,82)(27,83,117,179)(28,180,118,84)(29,85,119,181)(30,182,120,86)(31,87,121,183)(32,184,122,88)(33,89,123,185)(34,186,124,90)(35,91,125,187)(36,188,126,92)(37,93,127,189)(38,190,128,94)(39,95,129,191)(40,192,130,96)(41,97,131,193)(42,194,132,98)(43,99,133,195)(44,196,134,100)(45,101,135,197)(46,198,136,102)(47,103,137,199)(48,200,138,104)(49,105,139,201)(50,202,140,106)(51,107,141,203)(52,204,142,108)(53,109,143,205)(54,206,144,110)(55,111,145,207)(56,208,146,112), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,42,133,118,29,14,161,146)(2,117,134,13,30,145,162,41)(3,12,135,144,31,40,163,116)(4,143,136,39,32,115,164,11)(5,38,137,114,33,10,165,142)(6,113,138,9,34,141,166,37)(7,8,139,140,35,36,167,168)(15,56,147,132,43,28,119,160)(16,131,148,27,44,159,120,55)(17,26,149,158,45,54,121,130)(18,157,150,53,46,129,122,25)(19,52,151,128,47,24,123,156)(20,127,152,23,48,155,124,51)(21,22,153,154,49,50,125,126)(57,70,195,208,85,98,223,180)(58,207,196,97,86,179,224,69)(59,96,197,178,87,68,169,206)(60,177,198,67,88,205,170,95)(61,66,199,204,89,94,171,176)(62,203,200,93,90,175,172,65)(63,92,201,174,91,64,173,202)(71,84,209,222,99,112,181,194)(72,221,210,111,100,193,182,83)(73,110,211,192,101,82,183,220)(74,191,212,81,102,219,184,109)(75,80,213,218,103,108,185,190)(76,217,214,107,104,189,186,79)(77,106,215,188,105,78,187,216)>;
G:=Group( (1,57,147,209)(2,210,148,58)(3,59,149,211)(4,212,150,60)(5,61,151,213)(6,214,152,62)(7,63,153,215)(8,216,154,64)(9,65,155,217)(10,218,156,66)(11,67,157,219)(12,220,158,68)(13,69,159,221)(14,222,160,70)(15,71,161,223)(16,224,162,72)(17,73,163,169)(18,170,164,74)(19,75,165,171)(20,172,166,76)(21,77,167,173)(22,174,168,78)(23,79,113,175)(24,176,114,80)(25,81,115,177)(26,178,116,82)(27,83,117,179)(28,180,118,84)(29,85,119,181)(30,182,120,86)(31,87,121,183)(32,184,122,88)(33,89,123,185)(34,186,124,90)(35,91,125,187)(36,188,126,92)(37,93,127,189)(38,190,128,94)(39,95,129,191)(40,192,130,96)(41,97,131,193)(42,194,132,98)(43,99,133,195)(44,196,134,100)(45,101,135,197)(46,198,136,102)(47,103,137,199)(48,200,138,104)(49,105,139,201)(50,202,140,106)(51,107,141,203)(52,204,142,108)(53,109,143,205)(54,206,144,110)(55,111,145,207)(56,208,146,112), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,42,133,118,29,14,161,146)(2,117,134,13,30,145,162,41)(3,12,135,144,31,40,163,116)(4,143,136,39,32,115,164,11)(5,38,137,114,33,10,165,142)(6,113,138,9,34,141,166,37)(7,8,139,140,35,36,167,168)(15,56,147,132,43,28,119,160)(16,131,148,27,44,159,120,55)(17,26,149,158,45,54,121,130)(18,157,150,53,46,129,122,25)(19,52,151,128,47,24,123,156)(20,127,152,23,48,155,124,51)(21,22,153,154,49,50,125,126)(57,70,195,208,85,98,223,180)(58,207,196,97,86,179,224,69)(59,96,197,178,87,68,169,206)(60,177,198,67,88,205,170,95)(61,66,199,204,89,94,171,176)(62,203,200,93,90,175,172,65)(63,92,201,174,91,64,173,202)(71,84,209,222,99,112,181,194)(72,221,210,111,100,193,182,83)(73,110,211,192,101,82,183,220)(74,191,212,81,102,219,184,109)(75,80,213,218,103,108,185,190)(76,217,214,107,104,189,186,79)(77,106,215,188,105,78,187,216) );
G=PermutationGroup([[(1,57,147,209),(2,210,148,58),(3,59,149,211),(4,212,150,60),(5,61,151,213),(6,214,152,62),(7,63,153,215),(8,216,154,64),(9,65,155,217),(10,218,156,66),(11,67,157,219),(12,220,158,68),(13,69,159,221),(14,222,160,70),(15,71,161,223),(16,224,162,72),(17,73,163,169),(18,170,164,74),(19,75,165,171),(20,172,166,76),(21,77,167,173),(22,174,168,78),(23,79,113,175),(24,176,114,80),(25,81,115,177),(26,178,116,82),(27,83,117,179),(28,180,118,84),(29,85,119,181),(30,182,120,86),(31,87,121,183),(32,184,122,88),(33,89,123,185),(34,186,124,90),(35,91,125,187),(36,188,126,92),(37,93,127,189),(38,190,128,94),(39,95,129,191),(40,192,130,96),(41,97,131,193),(42,194,132,98),(43,99,133,195),(44,196,134,100),(45,101,135,197),(46,198,136,102),(47,103,137,199),(48,200,138,104),(49,105,139,201),(50,202,140,106),(51,107,141,203),(52,204,142,108),(53,109,143,205),(54,206,144,110),(55,111,145,207),(56,208,146,112)], [(1,43,29,15),(2,44,30,16),(3,45,31,17),(4,46,32,18),(5,47,33,19),(6,48,34,20),(7,49,35,21),(8,50,36,22),(9,51,37,23),(10,52,38,24),(11,53,39,25),(12,54,40,26),(13,55,41,27),(14,56,42,28),(57,99,85,71),(58,100,86,72),(59,101,87,73),(60,102,88,74),(61,103,89,75),(62,104,90,76),(63,105,91,77),(64,106,92,78),(65,107,93,79),(66,108,94,80),(67,109,95,81),(68,110,96,82),(69,111,97,83),(70,112,98,84),(113,155,141,127),(114,156,142,128),(115,157,143,129),(116,158,144,130),(117,159,145,131),(118,160,146,132),(119,161,147,133),(120,162,148,134),(121,163,149,135),(122,164,150,136),(123,165,151,137),(124,166,152,138),(125,167,153,139),(126,168,154,140),(169,211,197,183),(170,212,198,184),(171,213,199,185),(172,214,200,186),(173,215,201,187),(174,216,202,188),(175,217,203,189),(176,218,204,190),(177,219,205,191),(178,220,206,192),(179,221,207,193),(180,222,208,194),(181,223,209,195),(182,224,210,196)], [(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)], [(1,42,133,118,29,14,161,146),(2,117,134,13,30,145,162,41),(3,12,135,144,31,40,163,116),(4,143,136,39,32,115,164,11),(5,38,137,114,33,10,165,142),(6,113,138,9,34,141,166,37),(7,8,139,140,35,36,167,168),(15,56,147,132,43,28,119,160),(16,131,148,27,44,159,120,55),(17,26,149,158,45,54,121,130),(18,157,150,53,46,129,122,25),(19,52,151,128,47,24,123,156),(20,127,152,23,48,155,124,51),(21,22,153,154,49,50,125,126),(57,70,195,208,85,98,223,180),(58,207,196,97,86,179,224,69),(59,96,197,178,87,68,169,206),(60,177,198,67,88,205,170,95),(61,66,199,204,89,94,171,176),(62,203,200,93,90,175,172,65),(63,92,201,174,91,64,173,202),(71,84,209,222,99,112,181,194),(72,221,210,111,100,193,182,83),(73,110,211,192,101,82,183,220),(74,191,212,81,102,219,184,109),(75,80,213,218,103,108,185,190),(76,217,214,107,104,189,186,79),(77,106,215,188,105,78,187,216)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 8I | 8J | 8K | 8L | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 1 | 1 | 1 | 1 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | |||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | D7 | C4○D4 | D14 | D14 | C8○D4 | C4×D7 | D28.2C4 | D4⋊2D7 | Q8⋊2D7 | D28.C4 |
| kernel | C42.31D14 | C28⋊C8 | C8×Dic7 | C56⋊C4 | D14⋊C8 | C7×C4⋊C8 | C42⋊D7 | Dic7⋊C4 | D14⋊C4 | C4⋊C8 | C28 | C42 | C2×C8 | C14 | C2×C4 | C2 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 4 | 4 | 3 | 4 | 3 | 6 | 8 | 12 | 24 | 3 | 3 | 6 |
Matrix representation of C42.31D14 ►in GL4(𝔽113) generated by
| 79 | 68 | 0 | 0 |
| 101 | 34 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 64 | 15 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 56 | 0 | 0 |
| 30 | 56 | 0 | 0 |
| 0 | 0 | 30 | 7 |
| 0 | 0 | 33 | 83 |
| 69 | 61 | 0 | 0 |
| 0 | 44 | 0 | 0 |
| 0 | 0 | 83 | 106 |
| 0 | 0 | 48 | 30 |
G:=sub<GL(4,GF(113))| [79,101,0,0,68,34,0,0,0,0,98,64,0,0,0,15],[15,0,0,0,0,15,0,0,0,0,1,0,0,0,0,1],[0,30,0,0,56,56,0,0,0,0,30,33,0,0,7,83],[69,0,0,0,61,44,0,0,0,0,83,48,0,0,106,30] >;
C42.31D14 in GAP, Magma, Sage, TeX
C_4^2._{31}D_{14} % in TeX
G:=Group("C4^2.31D14"); // GroupNames label
G:=SmallGroup(448,374);
// by ID
G=gap.SmallGroup(448,374);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,120,422,219,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^-1,d^2=a^2*b,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a^-1*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=a^2*b^2*c^13>;
// generators/relations