ATLAS: Unitary group U_{3}(11)
Order = 70915680 = 2^{5}.3^{2}.5.11^{3}.37.
Mult = 3.
Out = S_{3}.
Standard generators
Standard generators of U_{3}(11) are a and b where a has order 2, b has order 3, ab has order 37 and ababb has order 4.
Standard generators of the triple cover 3.U_{3}(11) are preimages A and B where A has order 2 and AB has order 37.
Standard generators of U_{3}(11):2 are
c and d where
c has order 2 (necessarily class 2B), d has order 4
(necessarily class 4D),
cd has order 37 and cdd has order 10.
Standard generators of 3.U_{3}(11):2 are preimages
C and D where
CD has order 37.
Standard generators of U_{3}(11):3 are not defined.
Standard generators of U_{3}(11):S_{3} are not defined.
Representations
The representations of U_{3}(11) available are
- a and
b as
permutations on 1332 points.
- a and
b as
110 × 110 matrices over GF(2).
- a and
b as
370 × 370 matrices over GF(2).
- a and
b as
370 × 370 matrices over GF(2).
- a and
b as
370 × 370 matrices over GF(2).
- a and
b as
8 × 8 matrices over GF(11).
- a and
b as
10 × 10 matrices over GF(121).
The representations of 3.U_{3}(11) available are
- A and
B as
3 × 3 matrices over GF(121) - the natural representation.
The representations of U_{3}(11):2 available are
- c and
d as
permutations on 1332 points.
- c and
d as
110 × 110 matrices over GF(2).
- c and
d as
8 × 8 matrices over GF(11).
The representations of 3.U_{3}(11).2 available are
- C and
D as
6 × 6 matrices over GF(11).
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Last updated 26.05.00
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk