ATLAS: Alternating group A8, Linear group L4(2)

Order = 20160 = 26.32.5.7.
Mult = 2.
Out = 2.

Standard generators

Standard generators of A8 are a and b where a is in class 3A, b has order 7, ab has order 6 and abb has order 15.
In the natural representation we may take a = (1, 2, 3) and b = (2, 3, 4, 5, 6, 7, 8).
Standard generators of the double cover 2.A8 are preimages A and B where A has order 3 and B has order 7.

Standard generators of S8 = A8:2 are c and d where c is in class 2C, d has order 7 and cd has order 8.
In the natural representation, we may take c = (1, 2) and d = (2, 3, 4, 5, 6, 7, 8).
Standard generators of either of the double covers 2.S8 are preimages C and D where D has order 7.


Representations

The representations of A8 = L4(2) available are: The representations of 2.A8 available are: The representations of S8 = A8:2 available are:
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Last updated 14th April 1999,
R.A.Wilson, R.A.Parker and J.N.Bray