ATLAS: Orthogonal group O7(3)

Order = 4585351680 = 29.39.5.7.13.
Mult = 6.
Out = 2.

Standard generators

Standard generators of O7(3) are a and b where a is in class 2A, b has order 7, ab has order 13 and abb has order 20.
Standard generators of the double cover 2.O7(3) are preimages A and B where B has order 7 and AB has order 13.
Standard generators of the triple cover 3.O7(3) are preimages A and B where A has order 2 and B has order 7.
Standard generators of the sextuple cover 6.O7(3) are preimages A and B where A has order and AB has order .

Standard generators of O7(3):2 are c and d where c is in class 2D, d has order 7, and cd has order 26, and cdcdd has order 14.
Standard generators of the double cover 2.O7(3):2 are preimages C and D where C has order and CD has order .
Standard generators of the triple cover 3O7(3):2 are preimages C and D where D has order 7.
Standard generators of the sixfold cover 6.O7(3):2 are preimages C and D where C has order and CD has order .


Automorphisms

The outer automorphism of O7(3) may be realised by mapping (a, b) to (a, b-1). This automorphism resides in Class 2F.

Representations

The representations of O7(3) available are The representations of O7(3):2 available are The representations of 2.O7(3) available are The representation of 2.O7(3).2 available is The representation of 3.O7(3) available is The representation of 3.O7(3):2 available is
Main ATLAS page Return to main ATLAS page.

Last updated 2nd December 1998,
R.A.Wilson, R.A.Parker and J.N.Bray