metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.70D6, C4⋊C4.76D6, (C2×C12).85D4, C42.C2⋊2S3, C4⋊D12.7C2, C6.D8⋊41C2, C12.71(C4○D4), C2.22(D4⋊D6), C6.123(C8⋊C22), (C2×C12).385C23, C42.S3⋊11C2, (C4×C12).115C22, C4.13(Q8⋊3S3), C6.55(C4.4D4), C2.8(C12.23D4), (C2×D12).103C22, C3⋊3(C42.29C22), (C2×C6).516(C2×D4), (C3×C42.C2)⋊2C2, (C2×C4).67(C3⋊D4), (C2×C3⋊C8).127C22, (C3×C4⋊C4).123C22, (C2×C4).483(C22×S3), C22.189(C2×C3⋊D4), SmallGroup(192,626)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.70D6
G = < a,b,c,d | a4=b4=1, c6=a2, d2=a2b-1, ab=ba, cac-1=a-1b2, dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c5 >
Subgroups: 416 in 110 conjugacy classes, 39 normal (15 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, S3, C6, C6, C8, C2×C4, C2×C4, C2×C4, D4, C23, C12, C12, D6, C2×C6, C42, C4⋊C4, C4⋊C4, C2×C8, C2×D4, C3⋊C8, D12, C2×C12, C2×C12, C2×C12, C22×S3, C8⋊C4, D4⋊C4, C42.C2, C4⋊1D4, C2×C3⋊C8, C4×C12, C3×C4⋊C4, C3×C4⋊C4, C2×D12, C2×D12, C42.29C22, C42.S3, C6.D8, C4⋊D12, C3×C42.C2, C42.70D6
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C4○D4, C3⋊D4, C22×S3, C4.4D4, C8⋊C22, Q8⋊3S3, C2×C3⋊D4, C42.29C22, C12.23D4, D4⋊D6, C42.70D6
Character table of C42.70D6
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | 12I | 12J | |
| size | 1 | 1 | 1 | 1 | 24 | 24 | 2 | 2 | 2 | 4 | 4 | 8 | 8 | 2 | 2 | 2 | 12 | 12 | 12 | 12 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | |
| 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 | -1 | 2 | 2 | -2 | -2 | -2 | 2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | orthogonal lifted from D6 |
| ρ10 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | -2 | -2 | 2 | -2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | -2 | -2 | 2 | -2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | orthogonal lifted from D6 |
| ρ12 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | -2 | -2 | -2 | 2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ14 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | 2 | 2 | -2 | -2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ15 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -2 | -2 | -2 | 2 | 0 | 0 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | 1 | -1 | 1 | 1 | 1 | -√-3 | √-3 | -√-3 | √-3 | complex lifted from C3⋊D4 |
| ρ16 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -2 | -2 | 2 | -2 | 0 | 0 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | -1 | 1 | 1 | -1 | 1 | -√-3 | √-3 | √-3 | -√-3 | complex lifted from C3⋊D4 |
| ρ17 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -2 | -2 | -2 | 2 | 0 | 0 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | 1 | -1 | 1 | 1 | 1 | √-3 | -√-3 | √-3 | -√-3 | complex lifted from C3⋊D4 |
| ρ18 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -2 | -2 | 2 | -2 | 0 | 0 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | -1 | 1 | 1 | -1 | 1 | √-3 | -√-3 | -√-3 | √-3 | complex lifted from C3⋊D4 |
| ρ19 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | -2i | 0 | 0 | 2i | 0 | 0 | 0 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ20 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 2i | 0 | 0 | -2i | 0 | 0 | 0 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ21 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 2i | -2i | 0 | 0 | 0 | 0 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | -2i | 2i | 0 | 0 | 0 | 0 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 4 | 4 | -4 | -4 | 0 | 0 | -2 | 4 | -4 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | orthogonal lifted from Q8⋊3S3, Schur index 2 |
| ρ24 | 4 | -4 | -4 | 4 | 0 | 0 | 4 | 0 | 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 | 4 | 0 | 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 |
| ρ26 | 4 | 4 | -4 | -4 | 0 | 0 | -2 | -4 | 4 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from Q8⋊3S3, Schur index 2 |
| ρ27 | 4 | -4 | 4 | -4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 2√3 | 0 | -2√3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4⋊D6 |
| ρ28 | 4 | -4 | 4 | -4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | -2√3 | 0 | 2√3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4⋊D6 |
| ρ29 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 2√3 | 0 | 0 | -2√3 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4⋊D6 |
| ρ30 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | -2√3 | 0 | 0 | 2√3 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4⋊D6 |
►On 96 points
Generators in S96
(1 44 7 38)(2 71 8 65)(3 46 9 40)(4 61 10 67)(5 48 11 42)(6 63 12 69)(13 33 19 27)(14 57 20 51)(15 35 21 29)(16 59 22 53)(17 25 23 31)(18 49 24 55)(26 77 32 83)(28 79 34 73)(30 81 36 75)(37 95 43 89)(39 85 45 91)(41 87 47 93)(50 78 56 84)(52 80 58 74)(54 82 60 76)(62 94 68 88)(64 96 70 90)(66 86 72 92)
(1 83 90 24)(2 13 91 84)(3 73 92 14)(4 15 93 74)(5 75 94 16)(6 17 95 76)(7 77 96 18)(8 19 85 78)(9 79 86 20)(10 21 87 80)(11 81 88 22)(12 23 89 82)(25 43 54 63)(26 64 55 44)(27 45 56 65)(28 66 57 46)(29 47 58 67)(30 68 59 48)(31 37 60 69)(32 70 49 38)(33 39 50 71)(34 72 51 40)(35 41 52 61)(36 62 53 42)
(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)
(1 6 18 82 90 95 77 23)(2 22 78 94 91 81 19 5)(3 4 20 80 92 93 79 21)(7 12 24 76 96 89 83 17)(8 16 84 88 85 75 13 11)(9 10 14 74 86 87 73 15)(25 70 69 26 54 38 37 55)(27 68 71 36 56 48 39 53)(28 52 40 47 57 35 72 67)(29 66 61 34 58 46 41 51)(30 50 42 45 59 33 62 65)(31 64 63 32 60 44 43 49)
G:=sub<Sym(96)| (1,44,7,38)(2,71,8,65)(3,46,9,40)(4,61,10,67)(5,48,11,42)(6,63,12,69)(13,33,19,27)(14,57,20,51)(15,35,21,29)(16,59,22,53)(17,25,23,31)(18,49,24,55)(26,77,32,83)(28,79,34,73)(30,81,36,75)(37,95,43,89)(39,85,45,91)(41,87,47,93)(50,78,56,84)(52,80,58,74)(54,82,60,76)(62,94,68,88)(64,96,70,90)(66,86,72,92), (1,83,90,24)(2,13,91,84)(3,73,92,14)(4,15,93,74)(5,75,94,16)(6,17,95,76)(7,77,96,18)(8,19,85,78)(9,79,86,20)(10,21,87,80)(11,81,88,22)(12,23,89,82)(25,43,54,63)(26,64,55,44)(27,45,56,65)(28,66,57,46)(29,47,58,67)(30,68,59,48)(31,37,60,69)(32,70,49,38)(33,39,50,71)(34,72,51,40)(35,41,52,61)(36,62,53,42), (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), (1,6,18,82,90,95,77,23)(2,22,78,94,91,81,19,5)(3,4,20,80,92,93,79,21)(7,12,24,76,96,89,83,17)(8,16,84,88,85,75,13,11)(9,10,14,74,86,87,73,15)(25,70,69,26,54,38,37,55)(27,68,71,36,56,48,39,53)(28,52,40,47,57,35,72,67)(29,66,61,34,58,46,41,51)(30,50,42,45,59,33,62,65)(31,64,63,32,60,44,43,49)>;
G:=Group( (1,44,7,38)(2,71,8,65)(3,46,9,40)(4,61,10,67)(5,48,11,42)(6,63,12,69)(13,33,19,27)(14,57,20,51)(15,35,21,29)(16,59,22,53)(17,25,23,31)(18,49,24,55)(26,77,32,83)(28,79,34,73)(30,81,36,75)(37,95,43,89)(39,85,45,91)(41,87,47,93)(50,78,56,84)(52,80,58,74)(54,82,60,76)(62,94,68,88)(64,96,70,90)(66,86,72,92), (1,83,90,24)(2,13,91,84)(3,73,92,14)(4,15,93,74)(5,75,94,16)(6,17,95,76)(7,77,96,18)(8,19,85,78)(9,79,86,20)(10,21,87,80)(11,81,88,22)(12,23,89,82)(25,43,54,63)(26,64,55,44)(27,45,56,65)(28,66,57,46)(29,47,58,67)(30,68,59,48)(31,37,60,69)(32,70,49,38)(33,39,50,71)(34,72,51,40)(35,41,52,61)(36,62,53,42), (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), (1,6,18,82,90,95,77,23)(2,22,78,94,91,81,19,5)(3,4,20,80,92,93,79,21)(7,12,24,76,96,89,83,17)(8,16,84,88,85,75,13,11)(9,10,14,74,86,87,73,15)(25,70,69,26,54,38,37,55)(27,68,71,36,56,48,39,53)(28,52,40,47,57,35,72,67)(29,66,61,34,58,46,41,51)(30,50,42,45,59,33,62,65)(31,64,63,32,60,44,43,49) );
G=PermutationGroup([[(1,44,7,38),(2,71,8,65),(3,46,9,40),(4,61,10,67),(5,48,11,42),(6,63,12,69),(13,33,19,27),(14,57,20,51),(15,35,21,29),(16,59,22,53),(17,25,23,31),(18,49,24,55),(26,77,32,83),(28,79,34,73),(30,81,36,75),(37,95,43,89),(39,85,45,91),(41,87,47,93),(50,78,56,84),(52,80,58,74),(54,82,60,76),(62,94,68,88),(64,96,70,90),(66,86,72,92)], [(1,83,90,24),(2,13,91,84),(3,73,92,14),(4,15,93,74),(5,75,94,16),(6,17,95,76),(7,77,96,18),(8,19,85,78),(9,79,86,20),(10,21,87,80),(11,81,88,22),(12,23,89,82),(25,43,54,63),(26,64,55,44),(27,45,56,65),(28,66,57,46),(29,47,58,67),(30,68,59,48),(31,37,60,69),(32,70,49,38),(33,39,50,71),(34,72,51,40),(35,41,52,61),(36,62,53,42)], [(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)], [(1,6,18,82,90,95,77,23),(2,22,78,94,91,81,19,5),(3,4,20,80,92,93,79,21),(7,12,24,76,96,89,83,17),(8,16,84,88,85,75,13,11),(9,10,14,74,86,87,73,15),(25,70,69,26,54,38,37,55),(27,68,71,36,56,48,39,53),(28,52,40,47,57,35,72,67),(29,66,61,34,58,46,41,51),(30,50,42,45,59,33,62,65),(31,64,63,32,60,44,43,49)]])
Matrix representation of C42.70D6 ►in GL8(𝔽73)
| 47 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 68 | 26 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 26 | 65 | 8 |
| 0 | 0 | 0 | 0 | 47 | 0 | 8 | 8 |
| 0 | 0 | 0 | 0 | 8 | 65 | 0 | 26 |
| 0 | 0 | 0 | 0 | 65 | 65 | 47 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 72 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 59 | 46 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 | 0 | 0 |
| 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 27 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
G:=sub<GL(8,GF(73))| [47,68,0,0,0,0,0,0,4,26,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,47,8,65,0,0,0,0,26,0,65,65,0,0,0,0,65,8,0,47,0,0,0,0,8,8,26,0],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,0],[27,59,0,0,0,0,0,0,0,46,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[27,0,0,0,0,0,0,0,0,27,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0] >;
C42.70D6 in GAP, Magma, Sage, TeX
C_4^2._{70}D_6 % in TeX
G:=Group("C4^2.70D6"); // GroupNames label
G:=SmallGroup(192,626);
// by ID
G=gap.SmallGroup(192,626);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,253,120,254,555,100,1123,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^6=a^2,d^2=a^2*b^-1,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^5>;
// generators/relations
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