ATLAS: Exceptional group G_{2}(5)
Order = 5859000000 = 2^{6}.3^{3}.5^{6}.7.31.
Mult = 1.
Out = 1.
Standard generators
Standard generators of G_{2}(5) are
a
and b where
a is in class 2A, b is in class 3B,
ab has order 7 and ababb has order 15.
Representations
The representations of G_{2}(5) available are
- a and
b as
124 × 124 matrices over GF(2).
- a and
b as
124 × 124 matrices over GF(3).
- a and
b as
651 × 651 matrices over GF(3).
- a and
b as
7 × 7 matrices over GF(5) - the natural representation.
- a and
b as
14 × 14 matrices over GF(5) - the Lie algebra.
- a and
b as
27 × 27 matrices over GF(5).
- a and
b as
64 × 64 matrices over GF(5).
- a and
b as
77 × 77 matrices over GF(5).
- a and
b as
77 × 77 matrices over GF(5).
- a and
b as
97 × 97 matrices over GF(5).
- a and
b as
permutations on 3906 points - on the cosets of N(5A^{2}).
- a and
b as
permutations on 7750 points.
- a and
b as
permutations on 7875 points.
Maximal subgroups
The maximal subgroups of G_{2}(5) are
Conjugacy classes
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Last updated 18th March 1998,
R.A.Wilson, R.A.Parker and J.N.Bray