ATLAS:
Unitary group U_{3}(8)
Order = 5515776.
Mult = 3.
Out = 3 x S3.
Standard generators
Standard generators of U3(8) are
a
and b where
a has order 2,
b has order 3 (necessarily in class 3C),
ab has order 19.
Standard generators of U3(8):6 are
g
and h where
g is in class 2,
h is in class 3,
and gh is in class 18.
Standard generators for U3(8) may be obtained from those of U3(8):6 as
(ghghghhgh)^{6},
(gh)^{6}.
Representations
The representations of U3(8) available are
- a and
b as
8 x 8 matrices over GF(8).
- a and
b as
27 x 27 matrices over GF(4).
- a and
b as
56 x 56 matrices over GF(3).
- a and
b as
133 x 133 matrices over GF(3).
- a and
b as
133 x 133 matrices over GF(3).
- a and
b as
133 x 133 matrices over GF(3).
The representations of U3(8):6 available are
- g and
h as
24 x 24 matrices over GF(2).
- g and
h as
54 x 54 matrices over GF(2).
- g and
h as
56 x 56 matrices over GF(3).
- g and
h as
133 x 133 matrices over GF(3).
- g and
h as
permutations on 3648 points.
Maximal subgroups
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Last updated 25.05.00
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk