Finite Group DatabasebetaFinite Group Databasebeta| order | 11220 |
| isoclinism | isoclinic class of PSL(2,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C17 · Schur multiplier (H2) = C2 |
| direct product | C17×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C17 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C17 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C17 | |
32 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C17×PSL(2,𝔽11) |
| maximal normal subgroup of | C3×C17×PSL(2,𝔽11) |
| maximal quotient of | C3×C17×PSL(2,𝔽11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11220, 122);