ATLAS: Linear group L2(49)

Order = 58800 = 24.3.52.72.
Mult = 2.
Out = 22.

Standard generators

Standard generators of L2(49) are a and b where a has order 2, b has order 3, ab has order 25 and ababb has order 24.
Standard generators of the double cover 2.L2(49) = SL2(49) are preimages A and B where A has order 3 and AB has order 25.

Automorphisms

An outer automorphism of type 2a of order 2 may be obtained by mapping (a, b) to (a, bb).

Presentations

Presentations for L2(49) ... in terms of their standard generators are given below.

< a, b | a2 = b3 = (ababab-1)4 = (ab)6(ab-1)2(ab)3(abab-1)2(ab)4(ab-1)2 = 1 >.


Representations

The representations of L2(49) available are: The representations of 2.L2(49) = SL2(49) available are: The representations of L2(49):21 = PGL2(49) available are:

Maximal subgroups

The maximal subgroups of L2(49) include the following:
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Last updated 8th October 1998,
R.A.Wilson, R.A.Parker and J.N.Bray