ATLAS: Unitary group U4(3)
Order = 3265920.
Mult = 3 x 3 x 4.
Out = D8.
Standard generators
U4(3) and covers

Standard generators of U4(3) are
a
and b where
a has order 2,
b is in class 6A,
ab has order 7,
and abababbababb has order 5.

Standard generators of the double cover 2U4(3) are preimages
A
and B where
B has order
and AB has order .
The following are images of the standard generators under certain outer automorphisms:
U4(3).2_1 and covers

Standard generators of U4(3).2_1 are
c
and d where
c is in class 2B,
d has order 9,
cd has order 14,
and cdcdd has order 9.
U4(3).4 and covers

Standard generators of U4(3).4 are
e
and f where
e is in class 4E,
f has order 9,
ef has order 28,
and efeff has order 6.
The full envelope of U4(3) is 4.3^2.U4(3).D8.
The bicyclic extensions are as follows:
together with some others that I forgot,
such as 3_2.U4(3).2_3' and the like.
Other extensions for which representations
are available are:
Representations
U4(3) and covers

The representations of U4(3) available are
 a and
b as
permutations on 112 points.
 a and
b as
permutations on 162 points.
 a and
b as
permutations on 567 points.
 a and
b as
permutations on 1296 points.
 a and
b as
20 x 20 matrices over GF(2).
 a and
b as
19 x 19 matrices over GF(3).
 a and
b as
35 x 35 matrices over GF(5).
 a and
b as
90 x 90 matrices over GF(5).
The representations of 2.U4(3) available are
 A and
B as
120 x 120 matrices over GF(5).
The representations of 3_1.U4(3) available are
 A and
B as
6 x 6 matrices over GF(4).
 A and
B as
21 x 21 matrices over GF(25).
The representations of 3_2.U4(3) available are
 A and
B as
36 x 36 matrices over GF(4).
 A and
B as
36 x 36 matrices over GF(25).
The representations of 3^2.U4(3) available are
 A and
B as
12 x 12 matrices over GF(4)  reducible.
The representations of 6_1.U4(3) available are
 A and
B as
6 x 6 matrices over GF(25).
The representations of 12_1.U4(3) available are
 A and
B as
84 x 84 matrices over GF(25).
 A and
B as
132 x 132 matrices over GF(25).
The representations of 12_2.U4(3) available are
 A and
B as
36 x 36 matrices over GF(25).
The representations of 4.U4(3) available are
 A and
B as
4 x 4 matrices over GF(9)  the natural representation.
 A and
B as
120 x 120 matrices over GF(5).
U4(3).2_1 and covers

The representations of U4(3).2_1 available are
 c and
d as
20 x 20 matrices over GF(2).
 c and
d as
140 x 140 matrices over GF(2).

The representations of 12_2.U4(3).2_1 available are
 C and
D as
72 x 72 matrices over GF(5).
U4(3).4 and covers

The representations of U4(3).4 available are
 e and
f as
20 x 20 matrices over GF(2).
U4(3).2_3 and covers
Maximal subgroups
Return to main ATLAS page.
Last updated 29.10.99
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk