metacyclic, supersoluble, monomial, A-group
Aliases: C9⋊5F7, C63⋊2C6, D63⋊2C3, C7⋊C3⋊D9, C7⋊(C3×D9), C21.3(C3×S3), C3.3(C3⋊F7), (C9×C7⋊C3)⋊1C2, (C3×C7⋊C3).5S3, SmallGroup(378,20)
Series: Derived ►Chief ►Lower central ►Upper central
| C63 — C9⋊5F7 |
Generators and relations for C9⋊5F7
G = < a,b,c | a9=b7=c6=1, ab=ba, cac-1=a-1, cbc-1=b5 >
Character table of C9⋊5F7
| class | 1 | 2 | 3A | 3B | 3C | 3D | 3E | 6A | 6B | 7 | 9A | 9B | 9C | 9D | 9E | 9F | 9G | 9H | 9I | 21A | 21B | 63A | 63B | 63C | 63D | 63E | 63F | |
| size | 1 | 63 | 2 | 7 | 7 | 14 | 14 | 63 | 63 | 6 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 14 | 14 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | |
| 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 | 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 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ4 | 1 | -1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ6 | ζ65 | 1 | 1 | 1 | 1 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ5 | 1 | -1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ65 | ζ6 | 1 | 1 | 1 | 1 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ6 | 1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ7 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ8 | 2 | 0 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 2 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | -1 | -1 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | orthogonal lifted from D9 |
| ρ9 | 2 | 0 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 2 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | -1 | -1 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | orthogonal lifted from D9 |
| ρ10 | 2 | 0 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 2 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | -1 | -1 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | orthogonal lifted from D9 |
| ρ11 | 2 | 0 | 2 | -1-√-3 | -1+√-3 | -1-√-3 | -1+√-3 | 0 | 0 | 2 | -1 | -1 | -1 | ζ65 | ζ65 | ζ6 | ζ6 | ζ6 | ζ65 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | complex lifted from C3×S3 |
| ρ12 | 2 | 0 | 2 | -1+√-3 | -1-√-3 | -1+√-3 | -1-√-3 | 0 | 0 | 2 | -1 | -1 | -1 | ζ6 | ζ6 | ζ65 | ζ65 | ζ65 | ζ6 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | complex lifted from C3×S3 |
| ρ13 | 2 | 0 | -1 | -1-√-3 | -1+√-3 | ζ6 | ζ65 | 0 | 0 | 2 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ97 | ζ94+ζ92 | ζ98+ζ94 | ζ92+ζ9 | ζ97+ζ95 | ζ95+ζ9 | -1 | -1 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | complex lifted from C3×D9 |
| ρ14 | 2 | 0 | -1 | -1+√-3 | -1-√-3 | ζ65 | ζ6 | 0 | 0 | 2 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ95 | ζ98+ζ94 | ζ98+ζ97 | ζ94+ζ92 | ζ95+ζ9 | ζ92+ζ9 | -1 | -1 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | complex lifted from C3×D9 |
| ρ15 | 2 | 0 | -1 | -1-√-3 | -1+√-3 | ζ6 | ζ65 | 0 | 0 | 2 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ94+ζ92 | ζ95+ζ9 | ζ92+ζ9 | ζ97+ζ95 | ζ98+ζ94 | ζ98+ζ97 | -1 | -1 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | complex lifted from C3×D9 |
| ρ16 | 2 | 0 | -1 | -1+√-3 | -1-√-3 | ζ65 | ζ6 | 0 | 0 | 2 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ92+ζ9 | ζ97+ζ95 | ζ95+ζ9 | ζ98+ζ97 | ζ94+ζ92 | ζ98+ζ94 | -1 | -1 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | complex lifted from C3×D9 |
| ρ17 | 2 | 0 | -1 | -1-√-3 | -1+√-3 | ζ6 | ζ65 | 0 | 0 | 2 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ9 | ζ98+ζ97 | ζ97+ζ95 | ζ98+ζ94 | ζ92+ζ9 | ζ94+ζ92 | -1 | -1 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | complex lifted from C3×D9 |
| ρ18 | 2 | 0 | -1 | -1+√-3 | -1-√-3 | ζ65 | ζ6 | 0 | 0 | 2 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ94 | ζ92+ζ9 | ζ94+ζ92 | ζ95+ζ9 | ζ98+ζ97 | ζ97+ζ95 | -1 | -1 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | complex lifted from C3×D9 |
| ρ19 | 6 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 6 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from F7 |
| ρ20 | 6 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -3 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | 1+√21/2 | 1+√21/2 | 1-√21/2 | 1-√21/2 | 1-√21/2 | 1+√21/2 | orthogonal lifted from C3⋊F7 |
| ρ21 | 6 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -3 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | 1-√21/2 | 1-√21/2 | 1+√21/2 | 1+√21/2 | 1+√21/2 | 1-√21/2 | orthogonal lifted from C3⋊F7 |
| ρ22 | 6 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 3ζ98+3ζ9 | 3ζ97+3ζ92 | 3ζ95+3ζ94 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√21/2 | 1-√21/2 | ζ95ζ74+ζ95ζ72+ζ95ζ7-ζ94ζ74-ζ94ζ72-ζ94ζ7-ζ94 | ζ98ζ74+ζ98ζ72+ζ98ζ7-ζ9ζ74-ζ9ζ72-ζ9ζ7-ζ9 | -ζ97ζ76-ζ97ζ75-ζ97ζ73-ζ97+ζ92ζ76+ζ92ζ75+ζ92ζ73 | -ζ95ζ74-ζ95ζ72-ζ95ζ7-ζ95+ζ94ζ74+ζ94ζ72+ζ94ζ7 | -ζ98ζ74-ζ98ζ72-ζ98ζ7-ζ98+ζ9ζ74+ζ9ζ72+ζ9ζ7 | -ζ97ζ74-ζ97ζ72-ζ97ζ7-ζ97+ζ92ζ74+ζ92ζ72+ζ92ζ7 | orthogonal faithful |
| ρ23 | 6 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 3ζ95+3ζ94 | 3ζ98+3ζ9 | 3ζ97+3ζ92 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√21/2 | 1-√21/2 | -ζ97ζ74-ζ97ζ72-ζ97ζ7-ζ97+ζ92ζ74+ζ92ζ72+ζ92ζ7 | ζ95ζ74+ζ95ζ72+ζ95ζ7-ζ94ζ74-ζ94ζ72-ζ94ζ7-ζ94 | -ζ98ζ74-ζ98ζ72-ζ98ζ7-ζ98+ζ9ζ74+ζ9ζ72+ζ9ζ7 | -ζ97ζ76-ζ97ζ75-ζ97ζ73-ζ97+ζ92ζ76+ζ92ζ75+ζ92ζ73 | -ζ95ζ74-ζ95ζ72-ζ95ζ7-ζ95+ζ94ζ74+ζ94ζ72+ζ94ζ7 | ζ98ζ74+ζ98ζ72+ζ98ζ7-ζ9ζ74-ζ9ζ72-ζ9ζ7-ζ9 | orthogonal faithful |
| ρ24 | 6 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 3ζ97+3ζ92 | 3ζ95+3ζ94 | 3ζ98+3ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√21/2 | 1-√21/2 | ζ98ζ74+ζ98ζ72+ζ98ζ7-ζ9ζ74-ζ9ζ72-ζ9ζ7-ζ9 | -ζ97ζ74-ζ97ζ72-ζ97ζ7-ζ97+ζ92ζ74+ζ92ζ72+ζ92ζ7 | -ζ95ζ74-ζ95ζ72-ζ95ζ7-ζ95+ζ94ζ74+ζ94ζ72+ζ94ζ7 | -ζ98ζ74-ζ98ζ72-ζ98ζ7-ζ98+ζ9ζ74+ζ9ζ72+ζ9ζ7 | -ζ97ζ76-ζ97ζ75-ζ97ζ73-ζ97+ζ92ζ76+ζ92ζ75+ζ92ζ73 | ζ95ζ74+ζ95ζ72+ζ95ζ7-ζ94ζ74-ζ94ζ72-ζ94ζ7-ζ94 | orthogonal faithful |
| ρ25 | 6 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 3ζ95+3ζ94 | 3ζ98+3ζ9 | 3ζ97+3ζ92 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√21/2 | 1+√21/2 | -ζ97ζ76-ζ97ζ75-ζ97ζ73-ζ97+ζ92ζ76+ζ92ζ75+ζ92ζ73 | -ζ95ζ74-ζ95ζ72-ζ95ζ7-ζ95+ζ94ζ74+ζ94ζ72+ζ94ζ7 | ζ98ζ74+ζ98ζ72+ζ98ζ7-ζ9ζ74-ζ9ζ72-ζ9ζ7-ζ9 | -ζ97ζ74-ζ97ζ72-ζ97ζ7-ζ97+ζ92ζ74+ζ92ζ72+ζ92ζ7 | ζ95ζ74+ζ95ζ72+ζ95ζ7-ζ94ζ74-ζ94ζ72-ζ94ζ7-ζ94 | -ζ98ζ74-ζ98ζ72-ζ98ζ7-ζ98+ζ9ζ74+ζ9ζ72+ζ9ζ7 | orthogonal faithful |
| ρ26 | 6 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 3ζ97+3ζ92 | 3ζ95+3ζ94 | 3ζ98+3ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√21/2 | 1+√21/2 | -ζ98ζ74-ζ98ζ72-ζ98ζ7-ζ98+ζ9ζ74+ζ9ζ72+ζ9ζ7 | -ζ97ζ76-ζ97ζ75-ζ97ζ73-ζ97+ζ92ζ76+ζ92ζ75+ζ92ζ73 | ζ95ζ74+ζ95ζ72+ζ95ζ7-ζ94ζ74-ζ94ζ72-ζ94ζ7-ζ94 | ζ98ζ74+ζ98ζ72+ζ98ζ7-ζ9ζ74-ζ9ζ72-ζ9ζ7-ζ9 | -ζ97ζ74-ζ97ζ72-ζ97ζ7-ζ97+ζ92ζ74+ζ92ζ72+ζ92ζ7 | -ζ95ζ74-ζ95ζ72-ζ95ζ7-ζ95+ζ94ζ74+ζ94ζ72+ζ94ζ7 | orthogonal faithful |
| ρ27 | 6 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 3ζ98+3ζ9 | 3ζ97+3ζ92 | 3ζ95+3ζ94 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√21/2 | 1+√21/2 | -ζ95ζ74-ζ95ζ72-ζ95ζ7-ζ95+ζ94ζ74+ζ94ζ72+ζ94ζ7 | -ζ98ζ74-ζ98ζ72-ζ98ζ7-ζ98+ζ9ζ74+ζ9ζ72+ζ9ζ7 | -ζ97ζ74-ζ97ζ72-ζ97ζ7-ζ97+ζ92ζ74+ζ92ζ72+ζ92ζ7 | ζ95ζ74+ζ95ζ72+ζ95ζ7-ζ94ζ74-ζ94ζ72-ζ94ζ7-ζ94 | ζ98ζ74+ζ98ζ72+ζ98ζ7-ζ9ζ74-ζ9ζ72-ζ9ζ7-ζ9 | -ζ97ζ76-ζ97ζ75-ζ97ζ73-ζ97+ζ92ζ76+ζ92ζ75+ζ92ζ73 | orthogonal faithful |
►On 63 points
Generators in S63
(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)
(1 30 46 24 59 14 45)(2 31 47 25 60 15 37)(3 32 48 26 61 16 38)(4 33 49 27 62 17 39)(5 34 50 19 63 18 40)(6 35 51 20 55 10 41)(7 36 52 21 56 11 42)(8 28 53 22 57 12 43)(9 29 54 23 58 13 44)
(2 9)(3 8)(4 7)(5 6)(10 34 20 50 41 63)(11 33 21 49 42 62)(12 32 22 48 43 61)(13 31 23 47 44 60)(14 30 24 46 45 59)(15 29 25 54 37 58)(16 28 26 53 38 57)(17 36 27 52 39 56)(18 35 19 51 40 55)
G:=sub<Sym(63)| (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), (1,30,46,24,59,14,45)(2,31,47,25,60,15,37)(3,32,48,26,61,16,38)(4,33,49,27,62,17,39)(5,34,50,19,63,18,40)(6,35,51,20,55,10,41)(7,36,52,21,56,11,42)(8,28,53,22,57,12,43)(9,29,54,23,58,13,44), (2,9)(3,8)(4,7)(5,6)(10,34,20,50,41,63)(11,33,21,49,42,62)(12,32,22,48,43,61)(13,31,23,47,44,60)(14,30,24,46,45,59)(15,29,25,54,37,58)(16,28,26,53,38,57)(17,36,27,52,39,56)(18,35,19,51,40,55)>;
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), (1,30,46,24,59,14,45)(2,31,47,25,60,15,37)(3,32,48,26,61,16,38)(4,33,49,27,62,17,39)(5,34,50,19,63,18,40)(6,35,51,20,55,10,41)(7,36,52,21,56,11,42)(8,28,53,22,57,12,43)(9,29,54,23,58,13,44), (2,9)(3,8)(4,7)(5,6)(10,34,20,50,41,63)(11,33,21,49,42,62)(12,32,22,48,43,61)(13,31,23,47,44,60)(14,30,24,46,45,59)(15,29,25,54,37,58)(16,28,26,53,38,57)(17,36,27,52,39,56)(18,35,19,51,40,55) );
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)], [(1,30,46,24,59,14,45),(2,31,47,25,60,15,37),(3,32,48,26,61,16,38),(4,33,49,27,62,17,39),(5,34,50,19,63,18,40),(6,35,51,20,55,10,41),(7,36,52,21,56,11,42),(8,28,53,22,57,12,43),(9,29,54,23,58,13,44)], [(2,9),(3,8),(4,7),(5,6),(10,34,20,50,41,63),(11,33,21,49,42,62),(12,32,22,48,43,61),(13,31,23,47,44,60),(14,30,24,46,45,59),(15,29,25,54,37,58),(16,28,26,53,38,57),(17,36,27,52,39,56),(18,35,19,51,40,55)]])
Matrix representation of C9⋊5F7 ►in GL8(𝔽127)
| 9 | 22 | 0 | 0 | 0 | 0 | 0 | 0 |
| 105 | 31 | 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 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 126 | 126 | 126 | 126 | 126 | 126 |
| 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 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 126 | 126 | 126 | 126 | 126 | 126 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(8,GF(127))| [9,105,0,0,0,0,0,0,22,31,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,126,1,0,0,0,0,0,0,126,0,1,0,0,0,0,0,126,0,0,1,0,0,0,0,126,0,0,0,1,0,0,0,126,0,0,0,0,1,0,0,126,0,0,0,0,0],[0,19,0,0,0,0,0,0,19,0,0,0,0,0,0,0,0,0,1,0,0,0,126,0,0,0,0,0,0,1,126,0,0,0,0,0,0,0,126,0,0,0,0,0,1,0,126,0,0,0,0,0,0,0,126,1,0,0,0,1,0,0,126,0] >;
C9⋊5F7 in GAP, Magma, Sage, TeX
C_9\rtimes_5F_7
% in TeX
G:=Group("C9:5F7"); // GroupNames label
G:=SmallGroup(378,20);
// by ID
G=gap.SmallGroup(378,20);
# by ID
G:=PCGroup([5,-2,-3,-3,-7,-3,2072,642,2163,368,6304]);
// Polycyclic
G:=Group<a,b,c|a^9=b^7=c^6=1,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^5>;
// generators/relations
Export
Subgroup lattice of C9⋊5F7 in TeX
Character table of C9⋊5F7 in TeX