Aliases: CSU2(𝔽5), C2.2S5, SL2(𝔽5).C2, SmallGroup(240,89)
Series: Chief►Derived ►Lower central ►Upper central
| SL2(𝔽5) — CSU2(𝔽5) |
| SL2(𝔽5) — CSU2(𝔽5) |
Character table of CSU2(𝔽5)
| class | 1 | 2 | 3 | 4A | 4B | 5 | 6 | 8A | 8B | 10 | 12A | 12B | |
| size | 1 | 1 | 20 | 20 | 30 | 24 | 20 | 30 | 30 | 24 | 20 | 20 | |
| ρ1 | 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 | linear of order 2 |
| ρ3 | 4 | 4 | 1 | -2 | 0 | -1 | 1 | 0 | 0 | -1 | 1 | 1 | orthogonal lifted from S5 |
| ρ4 | 4 | 4 | 1 | 2 | 0 | -1 | 1 | 0 | 0 | -1 | -1 | -1 | orthogonal lifted from S5 |
| ρ5 | 4 | -4 | -2 | 0 | 0 | -1 | 2 | 0 | 0 | 1 | 0 | 0 | symplectic faithful, Schur index 2 |
| ρ6 | 4 | -4 | 1 | 0 | 0 | -1 | -1 | 0 | 0 | 1 | √3 | -√3 | symplectic faithful, Schur index 2 |
| ρ7 | 4 | -4 | 1 | 0 | 0 | -1 | -1 | 0 | 0 | 1 | -√3 | √3 | symplectic faithful, Schur index 2 |
| ρ8 | 5 | 5 | -1 | -1 | 1 | 0 | -1 | 1 | 1 | 0 | -1 | -1 | orthogonal lifted from S5 |
| ρ9 | 5 | 5 | -1 | 1 | 1 | 0 | -1 | -1 | -1 | 0 | 1 | 1 | orthogonal lifted from S5 |
| ρ10 | 6 | 6 | 0 | 0 | -2 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | orthogonal lifted from S5 |
| ρ11 | 6 | -6 | 0 | 0 | 0 | 1 | 0 | -√2 | √2 | -1 | 0 | 0 | symplectic faithful, Schur index 2 |
| ρ12 | 6 | -6 | 0 | 0 | 0 | 1 | 0 | √2 | -√2 | -1 | 0 | 0 | symplectic faithful, Schur index 2 |
►On 48 points
Generators in S48
(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)
(1 22 5 18)(2 31 6 27)(3 8 7 4)(9 21 13 17)(10 32 14 28)(11 16 15 12)(19 35 23 39)(20 48 24 44)(25 41 29 45)(26 36 30 40)(33 38 37 34)(42 47 46 43)
G:=sub<Sym(48)| (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), (1,22,5,18)(2,31,6,27)(3,8,7,4)(9,21,13,17)(10,32,14,28)(11,16,15,12)(19,35,23,39)(20,48,24,44)(25,41,29,45)(26,36,30,40)(33,38,37,34)(42,47,46,43)>;
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), (1,22,5,18)(2,31,6,27)(3,8,7,4)(9,21,13,17)(10,32,14,28)(11,16,15,12)(19,35,23,39)(20,48,24,44)(25,41,29,45)(26,36,30,40)(33,38,37,34)(42,47,46,43) );
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)], [(1,22,5,18),(2,31,6,27),(3,8,7,4),(9,21,13,17),(10,32,14,28),(11,16,15,12),(19,35,23,39),(20,48,24,44),(25,41,29,45),(26,36,30,40),(33,38,37,34),(42,47,46,43)]])
CSU2(𝔽5) is a maximal subgroup of
C4.6S5 C4.S5 C22.S5
CSU2(𝔽5) is a maximal quotient of C22.2S5
Matrix representation of CSU2(𝔽5) ►in GL4(𝔽3) generated by
| 1 | 2 | 0 | 1 |
| 0 | 0 | 1 | 2 |
| 2 | 0 | 2 | 2 |
| 2 | 2 | 1 | 0 |
| 2 | 0 | 2 | 1 |
| 1 | 2 | 0 | 2 |
| 0 | 2 | 0 | 1 |
| 1 | 2 | 2 | 2 |
G:=sub<GL(4,GF(3))| [1,0,2,2,2,0,0,2,0,1,2,1,1,2,2,0],[2,1,0,1,0,2,2,2,2,0,0,2,1,2,1,2] >;
CSU2(𝔽5) in GAP, Magma, Sage, TeX
{\rm CSU}_2({\mathbb F}_5) % in TeX
G:=Group("CSU(2,5)"); // GroupNames label
G:=SmallGroup(240,89);
// by ID
G=gap.SmallGroup(240,89);
# by ID
Export
Subgroup lattice of CSU2(𝔽5) in TeX
Character table of CSU2(𝔽5) in TeX