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