Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of PSL(2,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | C2×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C2 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C2 | |
41 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22 |
16 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×PSL(2,𝔽11), #72223872, C22×PSL(2,𝔽11), … |
| maximal normal subgroup of | C2×C3×PSL(2,𝔽11), #72223872, C22×PSL(2,𝔽11) |
| maximal quotient of | #72223869, C2×C3×PSL(2,𝔽11), C22×PSL(2,𝔽11), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 134);