ATLAS: Linear group L2(17)

Order = 2448 = 24.32.17.
Mult = 2.
Out = 2.

Standard generators

Standard generators of L2(17) are a and b where a has order 2, b has order 3 and ab has order 17.
Standard generators of the double cover 2.L2(17) = SL2(17) are preimages A and B where B has order 3 and AB has order 17.

Standard generators of L2(17):2 = PGL2(17) are c and d where c is in class 2B, d has order 3, cd has order 16 and cdcdd has order 4. These conditions ensure that cd is in class 16B.
Standard generators of either of the double covers 2.L2(17).2 = 2.PGL2(17) are preimages C and D where D has order 3.


Presentations

Presentations for L2(17) and L2(17):2 = PGL2(17) in terms of their standard generators are given below.

< a, b | a2 = b3 = (ab)17 = ((ab)5(ab-1)3)2 = 1 >.

< c, d | c2 = d3 = (cd)16 = [c, d]4 = [a, (ab)5]2 = 1 >.


Representations

The representations of L2(17) available are: The representations of 2.L2(17) = SL2(17) available are: The representations of L2(17):2 = PGL2(17) available are:

Maximal subgroups

The maximal subgroups of L2(17) are as follows. The maximal subgroups of L2(17):2 = PGL2(17) are as follows.

Conjugacy classes

The 11 conjugacy classes of L2(17) are as follows. The 19 conjugacy classes of L2(17):2 = PGL2(17) are as follows.
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Last updated 11th April 2000,
R.A.Wilson, R.A.Parker and J.N.Bray