Copied to
clipboard

G = C42.214D14order 448 = 26·7

34th non-split extension by C42 of D14 acting via D14/D7=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C42.214D14, C7⋊C8.17D4, C4.12(D4×D7), C28.26(C2×D4), C4.4D43D7, (C2×D4).49D14, (C2×C28).272D4, C72(C8.12D4), (C2×Q8).39D14, C4.D2814C2, C2.9(C28⋊D4), C14.106(C4○D8), C14.18(C41D4), (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

C1C2×C28 — C42.214D14
C1C7C14C28C2×C28C2×D28C4.D28 — C42.214D14
C7C14C2×C28 — C42.214D14
C1C22C42C4.4D4

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 [×2], C2 [×2], C4 [×2], C4 [×4], C22, C22 [×6], C7, C8 [×4], C2×C4, C2×C4 [×2], C2×C4 [×2], D4 [×4], Q8 [×4], C23 [×2], D7, C14, C14 [×2], C14, C42, C22⋊C4 [×4], C2×C8 [×2], D8 [×2], SD16 [×4], Q16 [×2], C2×D4, C2×D4, C2×Q8, C2×Q8, Dic7, C28 [×2], C28 [×3], D14 [×3], C2×C14, C2×C14 [×3], C4×C8, C4.4D4, C4.4D4, C2×D8, C2×SD16 [×2], C2×Q16, C7⋊C8 [×4], Dic14 [×2], D28 [×2], C2×Dic7, C2×C28, C2×C28 [×2], C2×C28, C7×D4 [×2], C7×Q8 [×2], C22×D7, C22×C14, C8.12D4, C2×C7⋊C8 [×2], D14⋊C4 [×2], D4⋊D7 [×2], D4.D7 [×2], Q8⋊D7 [×2], C7⋊Q16 [×2], C4×C28, C7×C22⋊C4 [×2], 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 [×7], C22 [×7], D4 [×6], C23, D7, C2×D4 [×3], D14 [×3], C41D4, C4○D8 [×2], C7⋊D4 [×2], C22×D7, C8.12D4, D4×D7 [×2], C2×C7⋊D4, C28⋊D4, D4.8D14 [×2], C42.214D14

Smallest permutation representation of C42.214D14
On 224 points
Generators in S224
(1 192 41 134)(2 161 42 124)(3 194 29 136)(4 163 30 126)(5 196 31 138)(6 165 32 114)(7 184 33 140)(8 167 34 116)(9 186 35 128)(10 155 36 118)(11 188 37 130)(12 157 38 120)(13 190 39 132)(14 159 40 122)(15 103 197 48)(16 69 198 211)(17 105 199 50)(18 57 200 213)(19 107 201 52)(20 59 202 215)(21 109 203 54)(22 61 204 217)(23 111 205 56)(24 63 206 219)(25 99 207 44)(26 65 208 221)(27 101 209 46)(28 67 210 223)(43 143 112 93)(45 145 100 95)(47 147 102 97)(49 149 104 85)(51 151 106 87)(53 153 108 89)(55 141 110 91)(58 88 214 152)(60 90 216 154)(62 92 218 142)(64 94 220 144)(66 96 222 146)(68 98 224 148)(70 86 212 150)(71 168 177 117)(72 187 178 129)(73 156 179 119)(74 189 180 131)(75 158 181 121)(76 191 182 133)(77 160 169 123)(78 193 170 135)(79 162 171 125)(80 195 172 137)(81 164 173 113)(82 183 174 139)(83 166 175 115)(84 185 176 127)
(1 54 169 60)(2 61 170 55)(3 56 171 62)(4 63 172 43)(5 44 173 64)(6 65 174 45)(7 46 175 66)(8 67 176 47)(9 48 177 68)(10 69 178 49)(11 50 179 70)(12 57 180 51)(13 52 181 58)(14 59 182 53)(15 117 98 186)(16 187 85 118)(17 119 86 188)(18 189 87 120)(19 121 88 190)(20 191 89 122)(21 123 90 192)(22 193 91 124)(23 125 92 194)(24 195 93 126)(25 113 94 196)(26 183 95 114)(27 115 96 184)(28 185 97 116)(29 111 79 218)(30 219 80 112)(31 99 81 220)(32 221 82 100)(33 101 83 222)(34 223 84 102)(35 103 71 224)(36 211 72 104)(37 105 73 212)(38 213 74 106)(39 107 75 214)(40 215 76 108)(41 109 77 216)(42 217 78 110)(127 147 167 210)(128 197 168 148)(129 149 155 198)(130 199 156 150)(131 151 157 200)(132 201 158 152)(133 153 159 202)(134 203 160 154)(135 141 161 204)(136 205 162 142)(137 143 163 206)(138 207 164 144)(139 145 165 208)(140 209 166 146)
(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 60 53 169 182 54 59)(2 58 55 181 170 52 61 13)(3 12 62 51 171 180 56 57)(4 70 43 179 172 50 63 11)(5 10 64 49 173 178 44 69)(6 68 45 177 174 48 65 9)(7 8 66 47 175 176 46 67)(15 208 186 165 98 145 117 139)(16 138 118 144 85 164 187 207)(17 206 188 163 86 143 119 137)(18 136 120 142 87 162 189 205)(19 204 190 161 88 141 121 135)(20 134 122 154 89 160 191 203)(21 202 192 159 90 153 123 133)(22 132 124 152 91 158 193 201)(23 200 194 157 92 151 125 131)(24 130 126 150 93 156 195 199)(25 198 196 155 94 149 113 129)(26 128 114 148 95 168 183 197)(27 210 184 167 96 147 115 127)(28 140 116 146 97 166 185 209)(29 38 218 106 79 74 111 213)(30 212 112 73 80 105 219 37)(31 36 220 104 81 72 99 211)(32 224 100 71 82 103 221 35)(33 34 222 102 83 84 101 223)(39 42 214 110 75 78 107 217)(40 216 108 77 76 109 215 41)

G:=sub<Sym(224)| (1,192,41,134)(2,161,42,124)(3,194,29,136)(4,163,30,126)(5,196,31,138)(6,165,32,114)(7,184,33,140)(8,167,34,116)(9,186,35,128)(10,155,36,118)(11,188,37,130)(12,157,38,120)(13,190,39,132)(14,159,40,122)(15,103,197,48)(16,69,198,211)(17,105,199,50)(18,57,200,213)(19,107,201,52)(20,59,202,215)(21,109,203,54)(22,61,204,217)(23,111,205,56)(24,63,206,219)(25,99,207,44)(26,65,208,221)(27,101,209,46)(28,67,210,223)(43,143,112,93)(45,145,100,95)(47,147,102,97)(49,149,104,85)(51,151,106,87)(53,153,108,89)(55,141,110,91)(58,88,214,152)(60,90,216,154)(62,92,218,142)(64,94,220,144)(66,96,222,146)(68,98,224,148)(70,86,212,150)(71,168,177,117)(72,187,178,129)(73,156,179,119)(74,189,180,131)(75,158,181,121)(76,191,182,133)(77,160,169,123)(78,193,170,135)(79,162,171,125)(80,195,172,137)(81,164,173,113)(82,183,174,139)(83,166,175,115)(84,185,176,127), (1,54,169,60)(2,61,170,55)(3,56,171,62)(4,63,172,43)(5,44,173,64)(6,65,174,45)(7,46,175,66)(8,67,176,47)(9,48,177,68)(10,69,178,49)(11,50,179,70)(12,57,180,51)(13,52,181,58)(14,59,182,53)(15,117,98,186)(16,187,85,118)(17,119,86,188)(18,189,87,120)(19,121,88,190)(20,191,89,122)(21,123,90,192)(22,193,91,124)(23,125,92,194)(24,195,93,126)(25,113,94,196)(26,183,95,114)(27,115,96,184)(28,185,97,116)(29,111,79,218)(30,219,80,112)(31,99,81,220)(32,221,82,100)(33,101,83,222)(34,223,84,102)(35,103,71,224)(36,211,72,104)(37,105,73,212)(38,213,74,106)(39,107,75,214)(40,215,76,108)(41,109,77,216)(42,217,78,110)(127,147,167,210)(128,197,168,148)(129,149,155,198)(130,199,156,150)(131,151,157,200)(132,201,158,152)(133,153,159,202)(134,203,160,154)(135,141,161,204)(136,205,162,142)(137,143,163,206)(138,207,164,144)(139,145,165,208)(140,209,166,146), (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), (1,14,60,53,169,182,54,59)(2,58,55,181,170,52,61,13)(3,12,62,51,171,180,56,57)(4,70,43,179,172,50,63,11)(5,10,64,49,173,178,44,69)(6,68,45,177,174,48,65,9)(7,8,66,47,175,176,46,67)(15,208,186,165,98,145,117,139)(16,138,118,144,85,164,187,207)(17,206,188,163,86,143,119,137)(18,136,120,142,87,162,189,205)(19,204,190,161,88,141,121,135)(20,134,122,154,89,160,191,203)(21,202,192,159,90,153,123,133)(22,132,124,152,91,158,193,201)(23,200,194,157,92,151,125,131)(24,130,126,150,93,156,195,199)(25,198,196,155,94,149,113,129)(26,128,114,148,95,168,183,197)(27,210,184,167,96,147,115,127)(28,140,116,146,97,166,185,209)(29,38,218,106,79,74,111,213)(30,212,112,73,80,105,219,37)(31,36,220,104,81,72,99,211)(32,224,100,71,82,103,221,35)(33,34,222,102,83,84,101,223)(39,42,214,110,75,78,107,217)(40,216,108,77,76,109,215,41)>;

G:=Group( (1,192,41,134)(2,161,42,124)(3,194,29,136)(4,163,30,126)(5,196,31,138)(6,165,32,114)(7,184,33,140)(8,167,34,116)(9,186,35,128)(10,155,36,118)(11,188,37,130)(12,157,38,120)(13,190,39,132)(14,159,40,122)(15,103,197,48)(16,69,198,211)(17,105,199,50)(18,57,200,213)(19,107,201,52)(20,59,202,215)(21,109,203,54)(22,61,204,217)(23,111,205,56)(24,63,206,219)(25,99,207,44)(26,65,208,221)(27,101,209,46)(28,67,210,223)(43,143,112,93)(45,145,100,95)(47,147,102,97)(49,149,104,85)(51,151,106,87)(53,153,108,89)(55,141,110,91)(58,88,214,152)(60,90,216,154)(62,92,218,142)(64,94,220,144)(66,96,222,146)(68,98,224,148)(70,86,212,150)(71,168,177,117)(72,187,178,129)(73,156,179,119)(74,189,180,131)(75,158,181,121)(76,191,182,133)(77,160,169,123)(78,193,170,135)(79,162,171,125)(80,195,172,137)(81,164,173,113)(82,183,174,139)(83,166,175,115)(84,185,176,127), (1,54,169,60)(2,61,170,55)(3,56,171,62)(4,63,172,43)(5,44,173,64)(6,65,174,45)(7,46,175,66)(8,67,176,47)(9,48,177,68)(10,69,178,49)(11,50,179,70)(12,57,180,51)(13,52,181,58)(14,59,182,53)(15,117,98,186)(16,187,85,118)(17,119,86,188)(18,189,87,120)(19,121,88,190)(20,191,89,122)(21,123,90,192)(22,193,91,124)(23,125,92,194)(24,195,93,126)(25,113,94,196)(26,183,95,114)(27,115,96,184)(28,185,97,116)(29,111,79,218)(30,219,80,112)(31,99,81,220)(32,221,82,100)(33,101,83,222)(34,223,84,102)(35,103,71,224)(36,211,72,104)(37,105,73,212)(38,213,74,106)(39,107,75,214)(40,215,76,108)(41,109,77,216)(42,217,78,110)(127,147,167,210)(128,197,168,148)(129,149,155,198)(130,199,156,150)(131,151,157,200)(132,201,158,152)(133,153,159,202)(134,203,160,154)(135,141,161,204)(136,205,162,142)(137,143,163,206)(138,207,164,144)(139,145,165,208)(140,209,166,146), (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), (1,14,60,53,169,182,54,59)(2,58,55,181,170,52,61,13)(3,12,62,51,171,180,56,57)(4,70,43,179,172,50,63,11)(5,10,64,49,173,178,44,69)(6,68,45,177,174,48,65,9)(7,8,66,47,175,176,46,67)(15,208,186,165,98,145,117,139)(16,138,118,144,85,164,187,207)(17,206,188,163,86,143,119,137)(18,136,120,142,87,162,189,205)(19,204,190,161,88,141,121,135)(20,134,122,154,89,160,191,203)(21,202,192,159,90,153,123,133)(22,132,124,152,91,158,193,201)(23,200,194,157,92,151,125,131)(24,130,126,150,93,156,195,199)(25,198,196,155,94,149,113,129)(26,128,114,148,95,168,183,197)(27,210,184,167,96,147,115,127)(28,140,116,146,97,166,185,209)(29,38,218,106,79,74,111,213)(30,212,112,73,80,105,219,37)(31,36,220,104,81,72,99,211)(32,224,100,71,82,103,221,35)(33,34,222,102,83,84,101,223)(39,42,214,110,75,78,107,217)(40,216,108,77,76,109,215,41) );

G=PermutationGroup([(1,192,41,134),(2,161,42,124),(3,194,29,136),(4,163,30,126),(5,196,31,138),(6,165,32,114),(7,184,33,140),(8,167,34,116),(9,186,35,128),(10,155,36,118),(11,188,37,130),(12,157,38,120),(13,190,39,132),(14,159,40,122),(15,103,197,48),(16,69,198,211),(17,105,199,50),(18,57,200,213),(19,107,201,52),(20,59,202,215),(21,109,203,54),(22,61,204,217),(23,111,205,56),(24,63,206,219),(25,99,207,44),(26,65,208,221),(27,101,209,46),(28,67,210,223),(43,143,112,93),(45,145,100,95),(47,147,102,97),(49,149,104,85),(51,151,106,87),(53,153,108,89),(55,141,110,91),(58,88,214,152),(60,90,216,154),(62,92,218,142),(64,94,220,144),(66,96,222,146),(68,98,224,148),(70,86,212,150),(71,168,177,117),(72,187,178,129),(73,156,179,119),(74,189,180,131),(75,158,181,121),(76,191,182,133),(77,160,169,123),(78,193,170,135),(79,162,171,125),(80,195,172,137),(81,164,173,113),(82,183,174,139),(83,166,175,115),(84,185,176,127)], [(1,54,169,60),(2,61,170,55),(3,56,171,62),(4,63,172,43),(5,44,173,64),(6,65,174,45),(7,46,175,66),(8,67,176,47),(9,48,177,68),(10,69,178,49),(11,50,179,70),(12,57,180,51),(13,52,181,58),(14,59,182,53),(15,117,98,186),(16,187,85,118),(17,119,86,188),(18,189,87,120),(19,121,88,190),(20,191,89,122),(21,123,90,192),(22,193,91,124),(23,125,92,194),(24,195,93,126),(25,113,94,196),(26,183,95,114),(27,115,96,184),(28,185,97,116),(29,111,79,218),(30,219,80,112),(31,99,81,220),(32,221,82,100),(33,101,83,222),(34,223,84,102),(35,103,71,224),(36,211,72,104),(37,105,73,212),(38,213,74,106),(39,107,75,214),(40,215,76,108),(41,109,77,216),(42,217,78,110),(127,147,167,210),(128,197,168,148),(129,149,155,198),(130,199,156,150),(131,151,157,200),(132,201,158,152),(133,153,159,202),(134,203,160,154),(135,141,161,204),(136,205,162,142),(137,143,163,206),(138,207,164,144),(139,145,165,208),(140,209,166,146)], [(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)], [(1,14,60,53,169,182,54,59),(2,58,55,181,170,52,61,13),(3,12,62,51,171,180,56,57),(4,70,43,179,172,50,63,11),(5,10,64,49,173,178,44,69),(6,68,45,177,174,48,65,9),(7,8,66,47,175,176,46,67),(15,208,186,165,98,145,117,139),(16,138,118,144,85,164,187,207),(17,206,188,163,86,143,119,137),(18,136,120,142,87,162,189,205),(19,204,190,161,88,141,121,135),(20,134,122,154,89,160,191,203),(21,202,192,159,90,153,123,133),(22,132,124,152,91,158,193,201),(23,200,194,157,92,151,125,131),(24,130,126,150,93,156,195,199),(25,198,196,155,94,149,113,129),(26,128,114,148,95,168,183,197),(27,210,184,167,96,147,115,127),(28,140,116,146,97,166,185,209),(29,38,218,106,79,74,111,213),(30,212,112,73,80,105,219,37),(31,36,220,104,81,72,99,211),(32,224,100,71,82,103,221,35),(33,34,222,102,83,84,101,223),(39,42,214,110,75,78,107,217),(40,216,108,77,76,109,215,41)])

64 conjugacy classes

class 1 2A2B2C2D2E4A···4F4G4H7A7B7C8A···8H14A···14I14J···14O28A···28R28S···28X
order1222224···4447778···814···1414···1428···2828···28
size11118562···285622214···142···28···84···48···8

64 irreducible representations

dim111111112222222244
type+++++++++++++++
imageC1C2C2C2C2C2C2C2D4D4D7D14D14D14C4○D8C7⋊D4D4×D7D4.8D14
kernelC42.214D14C4×C7⋊C8C4.D28C2×D4⋊D7C2×D4.D7C2×Q8⋊D7C2×C7⋊Q16C7×C4.4D4C7⋊C8C2×C28C4.4D4C42C2×D4C2×Q8C14C2×C4C4C2
# reps11111111423333812612

Matrix representation of C42.214D14 in GL6(𝔽113)

11200000
01120000
0015900
00639800
0000980
0000098
,
100000
010000
0019100
007211200
00008491
00002829
,
80800000
3390000
006210900
00855100
0000774
000010036
,
80800000
9330000
000400
00286200
000087109
00007777

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

׿
×
𝔽