ATLAS: Exceptional group G2(4)

Order = 251596800.
Mult = 2.
Out = 2.

Standard generators

Standard generators of G2(4) are a and b where a is in class 2A, b is in class 5C/D, and ab has order 13.
Standard generators of the double cover 2G2(4) are pre-images A and B where B has order 5 and AB has order 13.

Standard generators of G2(4):2 are c and d where c is in class 2C, d is in class 4D, cd has order 13, and cdcddd has order 6.
Standard generators of the double cover 2.G2(4):2 are pre-images C and D where CD has order 13.

Automorphisms

The outer automorphism of G2(4) can be realised by the map taking (a,b) to (a,b2).

Black box algorithms


Representations

The representations of G2(4) available are The representations of G2(4):2 available are The representations of 2.G2(4) available are The representations of 2.G2(4):2 available are

Maximal subgroups

The maximal subgroups of G2(4) are The maximal subgroups of G2(4):2 are
- Return to main ATLAS page. - Last updated 24.03.99

- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk