Finite Group DatabasebetaFinite Group Databasebeta| order | 14880 |
| isoclinism | isoclinic class of PSL(2,𝔽31) |
| automorphism | Aut(G) = PGL(2,𝔽31) (order 29760) · Inn(G) = G · Out(G) = C2 |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
| projective special linear | PSL(2,𝔽31) |
| projective symplectic | PSp(2,𝔽31) |
| projective special unitary | PSU(2,𝔽31) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
29 conjugacy classes of subgroups.
Permutation generators:
(1,2)(3,4)(5,11)(6,10)(7,9)(8,19)(12,15)(13,25)(14,27)(16,29)(17,21)(18,30)(20,24)(22,31)(23,28)(26,32);(2,3,5,12,28,30,18,7,16,6,15,27,25,21,14,11,19,22,13,17,31,24,9,23,10,26,32,29,20,8,4);(3,6,17,19,31,26,16,15,20,28,30,14,5,13,7)(4,9,25,11,27,18,23,24,12,29,32,22,8,21,10)18 conjugacy classes — view the full character table.
| maximal subgroup of | PGL(2,𝔽31) |
| maximal normal subgroup of | PGL(2,𝔽31) |
| maximal quotient of | Sp(2,𝔽31) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2)(3,4)(5,11)(6,10)(7,9)(8,19)(12,15)(13,25)(14,27)(16,29)(17,21)(18,30)(20,24)(22,31)(23,28)(26,32), (2,3,5,12,28,30,18,7,16,6,15,27,25,21,14,11,19,22,13,17,31,24,9,23,10,26,32,29,20,8,4), (3,6,17,19,31,26,16,15,20,28,30,14,5,13,7)(4,9,25,11,27,18,23,24,12,29,32,22,8,21,10));