ATLAS: Unitary group U_{3}(11)
Order = 70915680 = 2^{5}.3^{2}.5.11^{3}.37.
Mult = 3.
Out = S_{3}.
The following information is available for U_{3}(11):
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.
To find standard generators for U_{3}(11):

Find any element of even order. This powers up to x of order 2.
[The probability of success at each attempt is 19 in 32 (about 1 in 2).]

Find any element of order divisible by 3. This powers up to y of order 3.
[The probability of success at each attempt is 1 in 9.]

Find conjugates a of x and b of y such that ab has order 37 and ababb has order 4.
[The probability of success at each attempt is 288 in 4477 (about 1 in 16).]

Now a and b are standard generators for U_{3}(11).
The representations of U_{3}(11) available are:

Permutations on 1332 points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 110 over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 370[a] over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 370[b] over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 370[c] over GF(2):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 8 over GF(11):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).

Dimension 10 over GF(121):
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP).
The representations of 3.U_{3}(11) available are:

Dimension 3 over GF(121):
A and
B (Meataxe),
A and
B (Meataxe binary),
A and
B (GAP).
The representations of U_{3}(11):2 available are:

Permutations on 1332 points:
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 110 over GF(2):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).

Dimension 8 over GF(11):
c and
d (Meataxe),
c and
d (Meataxe binary),
c and
d (GAP).
The representations of 3.U_{3}(11):2 available are:

Dimension 6 over GF(11):
C and
D (Meataxe),
C and
D (Meataxe binary),
C and
D (GAP).
The maximal subgroups of U_{3}(11) are:
The maximal subgroups of U_{3}(11):2 are:
The maximal subgroups of U_{3}(11):3 are:

U_{3}(11).

11^{1+2}:120.

3 × 2.(L_{2}(11) × 2).2.

12^{2}:S_{3}.

111:3 = F_{111} × 3.

3^{2}:2A_{4}.
The maximal subgroups of U_{3}(11):S_{3} are:

U_{3}(11):3.

U_{3}(11):2.

11^{1+2}:(5 × 24:2).

(3 × 2.(L_{2}(11) × 2).2).2.

12^{2}:D_{12}.

111:6 = F_{222} × 3.

3^{2}:2S_{4}.
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Version 2.0 created on 24th February 2001.
Last updated 17.12.01 by RAW.
Information checked to
Level 0 on 24.02.01 by JNB.
R.A.Wilson, R.A.Parker and J.N.Bray.