Finite Group DatabasebetaFinite Group Databasebeta| order | 4080 |
| isoclinism | isoclinic class of SL(2,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C1 |
| projective general linear | PGL(2,𝔽16) |
| projective special linear | PSL(2,𝔽16) |
| special linear | SL(2,𝔽16) |
| symplectic | Sp(2,𝔽16) |
| projective symplectic | PSp(2,𝔽16) |
| omega | Ω−(4,𝔽4) |
| special unitary | SU(2,𝔽16) |
| projective special unitary | PSU(2,𝔽16) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
21 conjugacy classes of subgroups.
Permutation generators:
(1,2)(4,5)(6,10)(7,9)(8,13)(11,15)(12,16)(14,17);(2,3)(4,6)(5,8)(7,12)(9,14)(10,13)(11,15)(16,17);(3,4,7,8,6,11,14,16,12,17,15,10,13,9,5)17 conjugacy classes — view the full character table.
| maximal subgroup of | C5×SL(2,𝔽16), C3×SL(2,𝔽16), GO−(4,𝔽4) |
| maximal normal subgroup of | C5×SL(2,𝔽16), C3×SL(2,𝔽16), GO−(4,𝔽4) |
| maximal quotient of | C5×SL(2,𝔽16), C3×SL(2,𝔽16) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2)(4,5)(6,10)(7,9)(8,13)(11,15)(12,16)(14,17), (2,3)(4,6)(5,8)(7,12)(9,14)(10,13)(11,15)(16,17), (3,4,7,8,6,11,14,16,12,17,15,10,13,9,5));