?
G = C14.422+ (1+4) order 448 = 26·7
42nd non-split extension by C14 of 2+ (1+4) acting via 2+ (1+4)/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.422+ (1+4), C4⋊C4⋊7D14, (C2×D4)⋊9D14, C4⋊D4⋊16D7, C28⋊2D4⋊22C2, C22⋊C4⋊29D14, (C22×C4)⋊20D14, C23⋊D14⋊12C2, D14⋊Q8⋊15C2, D14.4(C4○D4), (D4×C14)⋊15C22, (C2×C28).42C23, C4⋊Dic7⋊33C22, Dic7⋊D4⋊14C2, Dic7⋊4D4⋊10C2, C28.17D4⋊18C2, (C2×C14).157C24, Dic7⋊C4⋊29C22, D14⋊C4.70C22, (C22×C28)⋊41C22, C7⋊4(C22.32C24), (C4×Dic7)⋊24C22, C2.44(D4⋊6D14), C23.D7⋊25C22, C23.17(C22×D7), Dic7.D4⋊20C2, (C2×Dic14)⋊26C22, C23.D14⋊18C2, (C22×C14).24C23, (C2×Dic7).76C23, (C22×D7).65C23, (C23×D7).49C22, C22.178(C23×D7), C23.18D14⋊22C2, C23.23D14⋊22C2, (C22×Dic7)⋊21C22, (C4×C7⋊D4)⋊55C2, (D7×C22⋊C4)⋊7C2, C2.41(D7×C4○D4), C4⋊C4⋊D7⋊13C2, (C7×C4⋊D4)⋊19C2, (C7×C4⋊C4)⋊14C22, (C2×C4×D7).85C22, C14.154(C2×C4○D4), (C7×C22⋊C4)⋊16C22, (C2×C4).178(C22×D7), (C2×C7⋊D4).30C22, SmallGroup(448,1066)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1292 in 250 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×6], C4 [×10], C22, C22 [×20], C7, C2×C4 [×4], C2×C4 [×10], D4 [×9], Q8, C23 [×3], C23 [×6], D7 [×3], C14 [×3], C14 [×3], C42 [×2], C22⋊C4 [×2], C22⋊C4 [×12], C4⋊C4, C4⋊C4 [×5], C22×C4, C22×C4 [×3], C2×D4 [×3], C2×D4 [×4], C2×Q8, C24, Dic7 [×6], C28 [×4], D14 [×2], D14 [×9], C2×C14, C2×C14 [×9], C2×C22⋊C4, C4×D4 [×2], C22≀C2 [×2], C4⋊D4, C4⋊D4 [×2], C22⋊Q8, C22.D4 [×2], C4.4D4 [×2], C42⋊2C2 [×2], Dic14, C4×D7 [×2], C2×Dic7 [×6], C2×Dic7, C7⋊D4 [×6], C2×C28 [×4], C2×C28, C7×D4 [×3], C22×D7 [×2], C22×D7 [×4], C22×C14 [×3], C22.32C24, C4×Dic7 [×2], Dic7⋊C4 [×4], C4⋊Dic7, D14⋊C4 [×6], C23.D7 [×6], C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14, C2×C4×D7 [×2], C22×Dic7, C2×C7⋊D4 [×4], C22×C28, D4×C14 [×3], C23×D7, C23.D14, D7×C22⋊C4, Dic7⋊4D4, Dic7.D4, D14⋊Q8, C4⋊C4⋊D7, C4×C7⋊D4, C23.23D14, C23.18D14, C28.17D4, C23⋊D14 [×2], C28⋊2D4, Dic7⋊D4, C7×C4⋊D4, C14.422+ (1+4)
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2+ (1+4) [×2], C22×D7 [×7], C22.32C24, C23×D7, D4⋊6D14 [×2], D7×C4○D4, C14.422+ (1+4)
Generators and relations
G = < a,b,c,d,e | a14=b4=c2=e2=1, d2=a7b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc=a7b-1, bd=db, be=eb, dcd-1=ece=a7c, ede=a7b2d >
►On 112 points
Generators in S112
(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)
(1 67 23 83)(2 68 24 84)(3 69 25 71)(4 70 26 72)(5 57 27 73)(6 58 28 74)(7 59 15 75)(8 60 16 76)(9 61 17 77)(10 62 18 78)(11 63 19 79)(12 64 20 80)(13 65 21 81)(14 66 22 82)(29 93 56 103)(30 94 43 104)(31 95 44 105)(32 96 45 106)(33 97 46 107)(34 98 47 108)(35 85 48 109)(36 86 49 110)(37 87 50 111)(38 88 51 112)(39 89 52 99)(40 90 53 100)(41 91 54 101)(42 92 55 102)
(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(43 50)(44 51)(45 52)(46 53)(47 54)(48 55)(49 56)(57 80)(58 81)(59 82)(60 83)(61 84)(62 71)(63 72)(64 73)(65 74)(66 75)(67 76)(68 77)(69 78)(70 79)(85 109)(86 110)(87 111)(88 112)(89 99)(90 100)(91 101)(92 102)(93 103)(94 104)(95 105)(96 106)(97 107)(98 108)
(1 51 16 31)(2 50 17 30)(3 49 18 29)(4 48 19 42)(5 47 20 41)(6 46 21 40)(7 45 22 39)(8 44 23 38)(9 43 24 37)(10 56 25 36)(11 55 26 35)(12 54 27 34)(13 53 28 33)(14 52 15 32)(57 108 80 91)(58 107 81 90)(59 106 82 89)(60 105 83 88)(61 104 84 87)(62 103 71 86)(63 102 72 85)(64 101 73 98)(65 100 74 97)(66 99 75 96)(67 112 76 95)(68 111 77 94)(69 110 78 93)(70 109 79 92)
(1 38)(2 39)(3 40)(4 41)(5 42)(6 29)(7 30)(8 31)(9 32)(10 33)(11 34)(12 35)(13 36)(14 37)(15 43)(16 44)(17 45)(18 46)(19 47)(20 48)(21 49)(22 50)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(57 92)(58 93)(59 94)(60 95)(61 96)(62 97)(63 98)(64 85)(65 86)(66 87)(67 88)(68 89)(69 90)(70 91)(71 100)(72 101)(73 102)(74 103)(75 104)(76 105)(77 106)(78 107)(79 108)(80 109)(81 110)(82 111)(83 112)(84 99)
G:=sub<Sym(112)| (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), (1,67,23,83)(2,68,24,84)(3,69,25,71)(4,70,26,72)(5,57,27,73)(6,58,28,74)(7,59,15,75)(8,60,16,76)(9,61,17,77)(10,62,18,78)(11,63,19,79)(12,64,20,80)(13,65,21,81)(14,66,22,82)(29,93,56,103)(30,94,43,104)(31,95,44,105)(32,96,45,106)(33,97,46,107)(34,98,47,108)(35,85,48,109)(36,86,49,110)(37,87,50,111)(38,88,51,112)(39,89,52,99)(40,90,53,100)(41,91,54,101)(42,92,55,102), (29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(57,80)(58,81)(59,82)(60,83)(61,84)(62,71)(63,72)(64,73)(65,74)(66,75)(67,76)(68,77)(69,78)(70,79)(85,109)(86,110)(87,111)(88,112)(89,99)(90,100)(91,101)(92,102)(93,103)(94,104)(95,105)(96,106)(97,107)(98,108), (1,51,16,31)(2,50,17,30)(3,49,18,29)(4,48,19,42)(5,47,20,41)(6,46,21,40)(7,45,22,39)(8,44,23,38)(9,43,24,37)(10,56,25,36)(11,55,26,35)(12,54,27,34)(13,53,28,33)(14,52,15,32)(57,108,80,91)(58,107,81,90)(59,106,82,89)(60,105,83,88)(61,104,84,87)(62,103,71,86)(63,102,72,85)(64,101,73,98)(65,100,74,97)(66,99,75,96)(67,112,76,95)(68,111,77,94)(69,110,78,93)(70,109,79,92), (1,38)(2,39)(3,40)(4,41)(5,42)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(57,92)(58,93)(59,94)(60,95)(61,96)(62,97)(63,98)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,100)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109)(81,110)(82,111)(83,112)(84,99)>;
G:=Group( (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), (1,67,23,83)(2,68,24,84)(3,69,25,71)(4,70,26,72)(5,57,27,73)(6,58,28,74)(7,59,15,75)(8,60,16,76)(9,61,17,77)(10,62,18,78)(11,63,19,79)(12,64,20,80)(13,65,21,81)(14,66,22,82)(29,93,56,103)(30,94,43,104)(31,95,44,105)(32,96,45,106)(33,97,46,107)(34,98,47,108)(35,85,48,109)(36,86,49,110)(37,87,50,111)(38,88,51,112)(39,89,52,99)(40,90,53,100)(41,91,54,101)(42,92,55,102), (29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(57,80)(58,81)(59,82)(60,83)(61,84)(62,71)(63,72)(64,73)(65,74)(66,75)(67,76)(68,77)(69,78)(70,79)(85,109)(86,110)(87,111)(88,112)(89,99)(90,100)(91,101)(92,102)(93,103)(94,104)(95,105)(96,106)(97,107)(98,108), (1,51,16,31)(2,50,17,30)(3,49,18,29)(4,48,19,42)(5,47,20,41)(6,46,21,40)(7,45,22,39)(8,44,23,38)(9,43,24,37)(10,56,25,36)(11,55,26,35)(12,54,27,34)(13,53,28,33)(14,52,15,32)(57,108,80,91)(58,107,81,90)(59,106,82,89)(60,105,83,88)(61,104,84,87)(62,103,71,86)(63,102,72,85)(64,101,73,98)(65,100,74,97)(66,99,75,96)(67,112,76,95)(68,111,77,94)(69,110,78,93)(70,109,79,92), (1,38)(2,39)(3,40)(4,41)(5,42)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(57,92)(58,93)(59,94)(60,95)(61,96)(62,97)(63,98)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,100)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109)(81,110)(82,111)(83,112)(84,99) );
G=PermutationGroup([(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)], [(1,67,23,83),(2,68,24,84),(3,69,25,71),(4,70,26,72),(5,57,27,73),(6,58,28,74),(7,59,15,75),(8,60,16,76),(9,61,17,77),(10,62,18,78),(11,63,19,79),(12,64,20,80),(13,65,21,81),(14,66,22,82),(29,93,56,103),(30,94,43,104),(31,95,44,105),(32,96,45,106),(33,97,46,107),(34,98,47,108),(35,85,48,109),(36,86,49,110),(37,87,50,111),(38,88,51,112),(39,89,52,99),(40,90,53,100),(41,91,54,101),(42,92,55,102)], [(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(43,50),(44,51),(45,52),(46,53),(47,54),(48,55),(49,56),(57,80),(58,81),(59,82),(60,83),(61,84),(62,71),(63,72),(64,73),(65,74),(66,75),(67,76),(68,77),(69,78),(70,79),(85,109),(86,110),(87,111),(88,112),(89,99),(90,100),(91,101),(92,102),(93,103),(94,104),(95,105),(96,106),(97,107),(98,108)], [(1,51,16,31),(2,50,17,30),(3,49,18,29),(4,48,19,42),(5,47,20,41),(6,46,21,40),(7,45,22,39),(8,44,23,38),(9,43,24,37),(10,56,25,36),(11,55,26,35),(12,54,27,34),(13,53,28,33),(14,52,15,32),(57,108,80,91),(58,107,81,90),(59,106,82,89),(60,105,83,88),(61,104,84,87),(62,103,71,86),(63,102,72,85),(64,101,73,98),(65,100,74,97),(66,99,75,96),(67,112,76,95),(68,111,77,94),(69,110,78,93),(70,109,79,92)], [(1,38),(2,39),(3,40),(4,41),(5,42),(6,29),(7,30),(8,31),(9,32),(10,33),(11,34),(12,35),(13,36),(14,37),(15,43),(16,44),(17,45),(18,46),(19,47),(20,48),(21,49),(22,50),(23,51),(24,52),(25,53),(26,54),(27,55),(28,56),(57,92),(58,93),(59,94),(60,95),(61,96),(62,97),(63,98),(64,85),(65,86),(66,87),(67,88),(68,89),(69,90),(70,91),(71,100),(72,101),(73,102),(74,103),(75,104),(76,105),(77,106),(78,107),(79,108),(80,109),(81,110),(82,111),(83,112),(84,99)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 19 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 21 | 21 |
| 0 | 0 | 0 | 0 | 0 | 0 | 8 | 26 |
| 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 | 0 | 4 |
| 0 | 0 | 0 | 0 | 0 | 17 | 25 | 11 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 23 | 28 | 0 |
| 0 | 0 | 0 | 0 | 6 | 0 | 0 | 28 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 22 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 24 | 13 |
| 0 | 0 | 0 | 0 | 0 | 0 | 27 | 5 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 24 | 13 |
| 0 | 0 | 0 | 0 | 0 | 0 | 16 | 5 |
G:=sub<GL(8,GF(29))| [19,10,0,0,0,0,0,0,19,7,0,0,0,0,0,0,0,0,19,10,0,0,0,0,0,0,19,7,0,0,0,0,0,0,0,0,19,17,0,0,0,0,0,0,21,28,0,0,0,0,0,0,0,0,21,8,0,0,0,0,0,0,21,26],[12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,25,12,0,0,0,0,0,4,11,0,12],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,2,6,0,0,0,0,0,1,23,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[0,0,28,22,0,0,0,0,0,0,0,1,0,0,0,0,28,22,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,14,3,0,0,0,0,0,0,2,15,0,0,0,0,0,0,0,0,24,27,0,0,0,0,0,0,13,5],[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,20,5,0,0,0,0,0,0,13,9,0,0,0,0,0,0,0,0,24,16,0,0,0,0,0,0,13,5] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4L | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 14 | 14 | 28 | 2 | 2 | 4 | 4 | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ (1+4) | D4⋊6D14 | D7×C4○D4 |
| kernel | C14.422+ (1+4) | C23.D14 | D7×C22⋊C4 | Dic7⋊4D4 | Dic7.D4 | D14⋊Q8 | C4⋊C4⋊D7 | C4×C7⋊D4 | C23.23D14 | C23.18D14 | C28.17D4 | C23⋊D14 | C28⋊2D4 | Dic7⋊D4 | C7×C4⋊D4 | C4⋊D4 | D14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 6 | 3 | 3 | 9 | 2 | 12 | 6 |
In GAP, Magma, Sage, TeX
C_{14}._{42}2_+^{(1+4)} % in TeX
G:=Group("C14.42ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1066);
// by ID
G=gap.SmallGroup(448,1066);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,219,184,675,570,297,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=e^2=1,d^2=a^7*b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,a*e=e*a,c*b*c=a^7*b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=e*c*e=a^7*c,e*d*e=a^7*b^2*d>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀