Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| isoclinism | isoclinic class of PSL(2,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C2 |
| direct product | C11×PSL(2,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C11 | PSL(2,𝔽13) |
| commutator, hypocenter | PSL(2,𝔽13) | C11 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽13) | |
| UCS | C1 ◁ C11 | |
32 conjugacy classes of subgroups.
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11×PSL(2,𝔽13) |
| maximal normal subgroup of | C3×C11×PSL(2,𝔽13) |
| maximal quotient of | C3×C11×PSL(2,𝔽13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 189);