Mult = 2

Out = D

This group is soluble and has exactly 12 normal subgroups. These subgroups have orders 1, 2 (Z(

Type A standard generators of W(F_{4}) are involutions
**a**, **b**, **c** and
**d** such that **ab**, **ac**,
**ad**, **bc**, **bd** and
**cd** have orders 3, 2, 2, 4, 2 and 3 respectively. These
generators satisfy the standard presentation of W(F_{4}).

Type B standard generators of W(F_{4}) are **x**
and **y** where **x** is in class 2C (see below),
**y** has order 6, **xy** has order 6 and **xyy** has order 4.

We may take **x** = **bd** and **y** = **acd**.

Conversely, we have **a** = **y ^{3}**,

The centre is generated by (

< *x*, *y* | *x*^{2} = *y*^{6} = (*xy*)^{6} = (*xy*^{2})^{4} = (*xyxyxy*^{-2})^{2} = 1 >.

The centre is generated by [*x*, *y*]^{3}.

Return to main ATLAS page.

Last updated 24th April 1998,

R.A.Wilson, R.A.Parker and J.N.Bray