Finite Group DatabasebetaFinite Group Databasebeta| order | 7800 |
| isoclinism | isoclinic class of PSL(2,𝔽25) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
| projective special linear | PSL(2,𝔽25) |
| projective symplectic | PSp(2,𝔽25) |
| omega | Ω−(4,𝔽5) |
| projective special unitary | PSU(2,𝔽25) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
37 conjugacy classes of subgroups.
Permutation generators:
(2,3,5,8,4)(6,13,15,7,14)(9,18,10,20,19)(11,12,22,24,21)(16,23,26,25,17);(3,6,12,5,11,10,4,9,17,8,16,7)(13,23,24,22,15,18,19,21,26,25,20,14);(1,2)(3,4)(6,10)(7,9)(11,12)(13,23)(14,24)(15,25)(16,17)(18,26)(19,21)(20,22)15 conjugacy classes — view the full character table.
| maximal subgroup of | PGL(2,𝔽25), PΣL(2,𝔽25), C2×PSL(2,𝔽25), … |
| maximal normal subgroup of | PGL(2,𝔽25), PΣL(2,𝔽25), C2×PSL(2,𝔽25), … |
| maximal quotient of | SL(2,𝔽25), C2×PSL(2,𝔽25) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((2,3,5,8,4)(6,13,15,7,14)(9,18,10,20,19)(11,12,22,24,21)(16,23,26,25,17), (3,6,12,5,11,10,4,9,17,8,16,7)(13,23,24,22,15,18,19,21,26,25,20,14), (1,2)(3,4)(6,10)(7,9)(11,12)(13,23)(14,24)(15,25)(16,17)(18,26)(19,21)(20,22));