Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| isoclinism | isoclinic class of PSL(2,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×PSL(2,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C5 | PSL(2,𝔽13) |
| commutator, hypocenter | PSL(2,𝔽13) | C3×C5 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽13) | |
| UCS | C1 ◁ C3×C5 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 210 |
A minimal faithful permutation representation — 2 generators on 22 points:
(10,11,18)(12,19,22)(13,14,16)(15,20,21);(1,2,3)(4,5,6,7,8)(9,10)(11,13)(12,14)(16,20)(17,21)(19,22)135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 857);