Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| isoclinism | isoclinic class of PSL(2,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C3×C11×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C11 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C3×C11 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C3×C11 | |
76 conjugacy classes of subgroups.
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 743);