ATLAS: Linear group L2(16)

Order = 4080 = 24.3.5.17.
Mult = 1.
Out = 4.

Standard generators

Standard generators of L2(16) are a and b where a has order 2, b has order 3 and ab has order 15.

Standard generators of L2(16):2 are c and d where c is in class 2B, d has order 4 and cd has order 15.

Standard generators of L2(16):4 are e and f where e is in class 2A, f is in class 4B/B', ef has order 8, eff has order 6 and efeffefff has order 4. .


Presentations

Presentations for L2(16), L2(16):2 and L2(16):4 in terms of their standard generators are given below.

< a, b | a2 = b3 = (ab)15 = ((ab)5(ab-1)3)2 = 1 >.

< c, d | c2 = d4 = [c, dcd]2 = cd(cdcd2)2(cd2cd)2cdcd-1 = 1 >.

< e, f | e2 = f4 = (ef)8 = (ef2)6 = (ef)3(ef-1)3(ef)2(ef-1)2(ef)2ef2 = 1 >.


Representations

The representations of L2(16) available are

Maximal subgroups

The maximal subgroups of L2(16) are as follows. The maximal subgroups of L2(16):2 are as follows. The maximal subgroups of L2(16):4 are as follows.
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Last updated 8th October 1998,
R.A.Wilson, R.A.Parker and J.N.Bray