ATLAS: Linear group L2(11)

Order = 660 = 22.3.5.11.
Mult = 2.
Out = 2.

Standard generators

Standard generators of L2(11) are a and b where a has order 2, b has order 3 and ab has order 11.
Standard generators of the double cover 2.L2(11) = SL2(11) are preimages A and B where B has order 3 and AB has order 11.

Standard generators of L2(11):2 = PGL2(11) are c and d where c is in class 2B, d has order 3, cd has order 10 and cdcdd has order 11. These conditions imply that cd is in class 10A.
Standard generators of either double cover 2.L2(11).2 = 2.PGL2(11) are preimages C and D where D has order 3.


Presentations

Presentations for L2(11) and L2(11):2 = PGL2(11) in terms of their standard generators are given below.

< a, b | a2 = b3 = (ab)11 = [a, babab]2 = 1 >.

< c, d | c2 = d3 = (cd)10 = (cdcdcd-1)4 = [c, dcdcd-1cd-1cd-1cdcd] = 1 >.


Representations

The representations L2(11) available are: The representations of 2.L2(11) = SL2(11) available are: The representations of L2(11):2 = PGL2(11) available are:

Maximal subgroups

The maximal subgroups of L2(11) are as follows. The maximal subgroups of L2(11):2 = PGL2(11) are as follows. The programs for the maximal subgroups of L2(11) and PGL2(11) are not yet available.

Conjugacy classes

The 8 conjugacy classes of L2(11) are as follows. The 13 conjugacy classes of L2(11):2 = PGL2(11) are as follows.
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Last updated 29th March 1999,
R.A.Wilson, R.A.Parker and J.N.Bray