metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.74D6, C3⋊C8⋊8D4, C4⋊1D4⋊4S3, C3⋊3(C8⋊3D4), C4.15(S3×D4), (C2×D4).57D6, C12.32(C2×D4), (C2×C12).292D4, C42⋊7S3⋊15C2, C6.21(C4⋊1D4), C6.95(C8⋊C22), (C6×D4).73C22, C2.12(C12⋊3D4), C42.S3⋊13C2, (C4×C12).122C22, (C2×C12).392C23, C2.16(D12⋊6C22), (C2×D12).106C22, (C2×Dic6).111C22, (C2×D4⋊S3)⋊15C2, (C3×C4⋊1D4)⋊3C2, (C2×D4.S3)⋊13C2, (C2×C6).523(C2×D4), (C2×C4).70(C3⋊D4), (C2×C3⋊C8).131C22, (C2×C4).490(C22×S3), C22.196(C2×C3⋊D4), SmallGroup(192,633)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.74D6
G = < a,b,c,d | a4=b4=c6=1, d2=cbc-1=b-1, ab=ba, cac-1=a-1, dad-1=ab2, bd=db, dcd-1=b-1c-1 >
Subgroups: 464 in 144 conjugacy classes, 43 normal (17 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, S3, C6, C6, C6, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, Dic3, C12, C12, D6, C2×C6, C2×C6, C42, C22⋊C4, C2×C8, D8, SD16, C2×D4, C2×D4, C2×Q8, C3⋊C8, Dic6, D12, C2×Dic3, C2×C12, C2×C12, C3×D4, C22×S3, C22×C6, C8⋊C4, C4.4D4, C4⋊1D4, C2×D8, C2×SD16, C2×C3⋊C8, D6⋊C4, D4⋊S3, D4.S3, C4×C12, C2×Dic6, C2×D12, C6×D4, C6×D4, C8⋊3D4, C42.S3, C42⋊7S3, C2×D4⋊S3, C2×D4.S3, C3×C4⋊1D4, C42.74D6
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C3⋊D4, C22×S3, C4⋊1D4, C8⋊C22, S3×D4, C2×C3⋊D4, C8⋊3D4, D12⋊6C22, C12⋊3D4, C42.74D6
Character table of C42.74D6
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 3 | 4A | 4B | 4C | 4D | 4E | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 24 | 2 | 2 | 2 | 4 | 4 | 24 | 2 | 2 | 2 | 8 | 8 | 8 | 8 | 12 | 12 | 12 | 12 | 4 | 4 | 4 | 4 | 4 | 4 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ4 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ5 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ6 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ7 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ8 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ9 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 2 | -2 | -2 | -2 | 2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | -2 | 2 | -2 | orthogonal lifted from D4 |
| ρ10 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | -1 | 2 | 2 | 2 | 2 | 0 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ11 | 2 | 2 | 2 | 2 | -2 | 2 | 0 | -1 | 2 | 2 | -2 | -2 | 0 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | 1 | 1 | orthogonal lifted from D6 |
| ρ12 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 2 | 0 | 0 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ14 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | 2 | 2 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ15 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 2 | 0 | 0 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ16 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | orthogonal lifted from D4 |
| ρ17 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 2 | -2 | -2 | 2 | -2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | -2 | -2 | 2 | orthogonal lifted from D4 |
| ρ18 | 2 | 2 | 2 | 2 | 2 | -2 | 0 | -1 | 2 | 2 | -2 | -2 | 0 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | 1 | 1 | orthogonal lifted from D6 |
| ρ19 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | -1 | -2 | -2 | 2 | -2 | 0 | -1 | -1 | -1 | √-3 | -√-3 | √-3 | -√-3 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 1 | 1 | -1 | complex lifted from C3⋊D4 |
| ρ20 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | -1 | -2 | -2 | -2 | 2 | 0 | -1 | -1 | -1 | √-3 | -√-3 | -√-3 | √-3 | 0 | 0 | 0 | 0 | 1 | -1 | 1 | 1 | -1 | 1 | complex lifted from C3⋊D4 |
| ρ21 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | -1 | -2 | -2 | 2 | -2 | 0 | -1 | -1 | -1 | -√-3 | √-3 | -√-3 | √-3 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 1 | 1 | -1 | complex lifted from C3⋊D4 |
| ρ22 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | -1 | -2 | -2 | -2 | 2 | 0 | -1 | -1 | -1 | -√-3 | √-3 | √-3 | -√-3 | 0 | 0 | 0 | 0 | 1 | -1 | 1 | 1 | -1 | 1 | complex lifted from C3⋊D4 |
| ρ23 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | -2 | 4 | -4 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ24 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | -4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C8⋊C22 |
| ρ25 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | -2 | -4 | 4 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ26 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C8⋊C22 |
| ρ27 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√-3 | 0 | 0 | 2√-3 | complex lifted from D12⋊6C22 |
| ρ28 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√-3 | 0 | 0 | -2√-3 | complex lifted from D12⋊6C22 |
| ρ29 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√-3 | 0 | 0 | 2√-3 | 0 | complex lifted from D12⋊6C22 |
| ρ30 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√-3 | 0 | 0 | -2√-3 | 0 | complex lifted from D12⋊6C22 |
►On 96 points
Generators in S96
(1 32 59 90)(2 29 60 95)(3 26 61 92)(4 31 62 89)(5 28 63 94)(6 25 64 91)(7 30 57 96)(8 27 58 93)(9 88 40 73)(10 85 33 78)(11 82 34 75)(12 87 35 80)(13 84 36 77)(14 81 37 74)(15 86 38 79)(16 83 39 76)(17 47 68 55)(18 44 69 52)(19 41 70 49)(20 46 71 54)(21 43 72 51)(22 48 65 56)(23 45 66 53)(24 42 67 50)
(1 7 5 3)(2 8 6 4)(9 15 13 11)(10 16 14 12)(17 23 21 19)(18 24 22 20)(25 31 29 27)(26 32 30 28)(33 39 37 35)(34 40 38 36)(41 47 45 43)(42 48 46 44)(49 55 53 51)(50 56 54 52)(57 63 61 59)(58 64 62 60)(65 71 69 67)(66 72 70 68)(73 79 77 75)(74 80 78 76)(81 87 85 83)(82 88 86 84)(89 95 93 91)(90 96 94 92)
(1 20 81 82 19 2)(3 18 83 88 21 8)(4 7 22 87 84 17)(5 24 85 86 23 6)(9 43 93 26 52 39)(10 38 53 25 94 42)(11 41 95 32 54 37)(12 36 55 31 96 48)(13 47 89 30 56 35)(14 34 49 29 90 46)(15 45 91 28 50 33)(16 40 51 27 92 44)(57 65 80 77 68 62)(58 61 69 76 73 72)(59 71 74 75 70 60)(63 67 78 79 66 64)
(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)
G:=sub<Sym(96)| (1,32,59,90)(2,29,60,95)(3,26,61,92)(4,31,62,89)(5,28,63,94)(6,25,64,91)(7,30,57,96)(8,27,58,93)(9,88,40,73)(10,85,33,78)(11,82,34,75)(12,87,35,80)(13,84,36,77)(14,81,37,74)(15,86,38,79)(16,83,39,76)(17,47,68,55)(18,44,69,52)(19,41,70,49)(20,46,71,54)(21,43,72,51)(22,48,65,56)(23,45,66,53)(24,42,67,50), (1,7,5,3)(2,8,6,4)(9,15,13,11)(10,16,14,12)(17,23,21,19)(18,24,22,20)(25,31,29,27)(26,32,30,28)(33,39,37,35)(34,40,38,36)(41,47,45,43)(42,48,46,44)(49,55,53,51)(50,56,54,52)(57,63,61,59)(58,64,62,60)(65,71,69,67)(66,72,70,68)(73,79,77,75)(74,80,78,76)(81,87,85,83)(82,88,86,84)(89,95,93,91)(90,96,94,92), (1,20,81,82,19,2)(3,18,83,88,21,8)(4,7,22,87,84,17)(5,24,85,86,23,6)(9,43,93,26,52,39)(10,38,53,25,94,42)(11,41,95,32,54,37)(12,36,55,31,96,48)(13,47,89,30,56,35)(14,34,49,29,90,46)(15,45,91,28,50,33)(16,40,51,27,92,44)(57,65,80,77,68,62)(58,61,69,76,73,72)(59,71,74,75,70,60)(63,67,78,79,66,64), (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)>;
G:=Group( (1,32,59,90)(2,29,60,95)(3,26,61,92)(4,31,62,89)(5,28,63,94)(6,25,64,91)(7,30,57,96)(8,27,58,93)(9,88,40,73)(10,85,33,78)(11,82,34,75)(12,87,35,80)(13,84,36,77)(14,81,37,74)(15,86,38,79)(16,83,39,76)(17,47,68,55)(18,44,69,52)(19,41,70,49)(20,46,71,54)(21,43,72,51)(22,48,65,56)(23,45,66,53)(24,42,67,50), (1,7,5,3)(2,8,6,4)(9,15,13,11)(10,16,14,12)(17,23,21,19)(18,24,22,20)(25,31,29,27)(26,32,30,28)(33,39,37,35)(34,40,38,36)(41,47,45,43)(42,48,46,44)(49,55,53,51)(50,56,54,52)(57,63,61,59)(58,64,62,60)(65,71,69,67)(66,72,70,68)(73,79,77,75)(74,80,78,76)(81,87,85,83)(82,88,86,84)(89,95,93,91)(90,96,94,92), (1,20,81,82,19,2)(3,18,83,88,21,8)(4,7,22,87,84,17)(5,24,85,86,23,6)(9,43,93,26,52,39)(10,38,53,25,94,42)(11,41,95,32,54,37)(12,36,55,31,96,48)(13,47,89,30,56,35)(14,34,49,29,90,46)(15,45,91,28,50,33)(16,40,51,27,92,44)(57,65,80,77,68,62)(58,61,69,76,73,72)(59,71,74,75,70,60)(63,67,78,79,66,64), (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) );
G=PermutationGroup([[(1,32,59,90),(2,29,60,95),(3,26,61,92),(4,31,62,89),(5,28,63,94),(6,25,64,91),(7,30,57,96),(8,27,58,93),(9,88,40,73),(10,85,33,78),(11,82,34,75),(12,87,35,80),(13,84,36,77),(14,81,37,74),(15,86,38,79),(16,83,39,76),(17,47,68,55),(18,44,69,52),(19,41,70,49),(20,46,71,54),(21,43,72,51),(22,48,65,56),(23,45,66,53),(24,42,67,50)], [(1,7,5,3),(2,8,6,4),(9,15,13,11),(10,16,14,12),(17,23,21,19),(18,24,22,20),(25,31,29,27),(26,32,30,28),(33,39,37,35),(34,40,38,36),(41,47,45,43),(42,48,46,44),(49,55,53,51),(50,56,54,52),(57,63,61,59),(58,64,62,60),(65,71,69,67),(66,72,70,68),(73,79,77,75),(74,80,78,76),(81,87,85,83),(82,88,86,84),(89,95,93,91),(90,96,94,92)], [(1,20,81,82,19,2),(3,18,83,88,21,8),(4,7,22,87,84,17),(5,24,85,86,23,6),(9,43,93,26,52,39),(10,38,53,25,94,42),(11,41,95,32,54,37),(12,36,55,31,96,48),(13,47,89,30,56,35),(14,34,49,29,90,46),(15,45,91,28,50,33),(16,40,51,27,92,44),(57,65,80,77,68,62),(58,61,69,76,73,72),(59,71,74,75,70,60),(63,67,78,79,66,64)], [(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)]])
Matrix representation of C42.74D6 ►in GL6(𝔽73)
| 72 | 71 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 13 | 0 | 0 |
| 0 | 0 | 60 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 43 | 13 |
| 0 | 0 | 0 | 0 | 60 | 30 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 71 | 0 |
| 0 | 0 | 0 | 72 | 0 | 71 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 72 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 46 | 27 | 0 | 54 |
| 0 | 0 | 46 | 19 | 19 | 19 |
| 0 | 0 | 27 | 0 | 27 | 46 |
| 0 | 0 | 0 | 27 | 27 | 54 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 46 | 46 | 19 | 0 |
| 0 | 0 | 0 | 27 | 54 | 54 |
| 0 | 0 | 27 | 0 | 27 | 46 |
| 0 | 0 | 46 | 46 | 19 | 46 |
G:=sub<GL(6,GF(73))| [72,1,0,0,0,0,71,1,0,0,0,0,0,0,43,60,0,0,0,0,13,30,0,0,0,0,0,0,43,60,0,0,0,0,13,30],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,0,1,0,0,0,0,72,0,1,0,0,71,0,1,0,0,0,0,71,0,1],[1,72,0,0,0,0,0,72,0,0,0,0,0,0,46,46,27,0,0,0,27,19,0,27,0,0,0,19,27,27,0,0,54,19,46,54],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,46,0,27,46,0,0,46,27,0,46,0,0,19,54,27,19,0,0,0,54,46,46] >;
C42.74D6 in GAP, Magma, Sage, TeX
C_4^2._{74}D_6 % in TeX
G:=Group("C4^2.74D6"); // GroupNames label
G:=SmallGroup(192,633);
// by ID
G=gap.SmallGroup(192,633);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,253,344,254,555,1123,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^6=1,d^2=c*b*c^-1=b^-1,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a*b^2,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations
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