ATLAS: Unitary group U5(2)
Order = 13685760.
Mult = 1.
Out = 2.
Standard generators
Standard generators of U5(2) are
a
and b where
a is in class 2A,
b has order 5,
and ab has order 11.
An automorphism may be obtained by mapping
(a,b) to (a,(abb)^-5b(abb)^5).
Standard generators of U5(2).2 are
c
and d where
c has order 2 (so is in class 2C),
d has order 4 (so is in class 4D),
cd has order 11,
and cdcdd has order 4.
Representations
The representations of U5(2) available are
- Some irreducibles in characteristic 2
- a and
b as
5 x 5 matrices over GF(4) - the natural representation.
- a and
b as
24 x 24 matrices over GF(2).
- a and
b as
74 x 74 matrices over GF(2).
- Some irreducibles in characteristic 3
- a and
b as
10 x 10 matrices over GF(3).
- a and
b as
44 x 44 matrices over GF(3).
- a and
b as
55 x 55 matrices over GF(3).
- a and
b as
100 x 100 matrices over GF(3).
- a and
b as
110 x 110 matrices over GF(3).
- Some irreducibles in characteristic 5.
- a and
b as
11 x 11 matrices over GF(25).
- a and
b as
43 x 43 matrices over GF(5).
- a and
b as
55 x 55 matrices over GF(5).
- a and
b as
120 x 120 matrices over GF(5).
- a and
b as
176 x 176 matrices over GF(5).
- Some irreducibles in characteristic 11.
- a and
b as
11 x 11 matrices over GF(121).
- a and
b as
44 x 44 matrices over GF(11).
- a and
b as
55 x 55 matrices over GF(11).
- a and
b as
119 x 119 matrices over GF(11).
- Some irreducibles in characteristic 7 (not dividing the group order!).
- a and
b as
10 x 10 matrices over GF(7).
- a and
b as
11 x 11 matrices over GF(7).
- All primitive permutation representations
- a and
b as
permutations on 165 points.
- a and
b as
permutations on 176 points.
- a and
b as
permutations on 297 points.
- a and
b as
permutations on 1408 points.
- a and
b as
permutations on 3520 points.
- a and
b as
permutations on 20736 points.
The representations of U5(2):2 available are
- c and
d as
10 x 10 matrices over GF(2).
- c and
d as
10 x 10 matrices over GF(3).
- c and
d as
permutations on 165 points.
- c and
d as
permutations on 176 points.
Maximal subgroups
The maximal subgroups of U5(2) are as follows.
- 2^1+6.3^1+2.2A4
- 3 x U4(2), with generators
here, mapping to standard generators of U4(2).
- 2^4+4:(3 x A5)
- 3^4:S5
- S3 x 3^1+2:2A4
- L2(11), with standard generators
here.
The maximal subgroups of U5(2):2 are as follows.
- U5(2)
- 2^1+6.3^1+2.2S4
- (3 x U4(2)):2
- 2^4+4:(3 x A5):2
- 3^4:(S5 x 2)
- S3 x 3^1+2:2S4
- L2(11):2
Return to main ATLAS page.
Last updated 25.03.99
R.A.Wilson@bham.ac.uk
richard@ukonline.co.uk