In the 2nd edition AtB rule book, rule 9.2 "Group Action Details", under "New Example: Figure 17" it shows two German units under group activation group firing at a target. One unit is a LMG, 2 activation cost for firing with an AV of 4. The second unit is a rifle group, 3 activation cost for an AV of 2.
The example notes "they group fire for 3 AP's and miss".
In Fig. 18 preceding this, the two units group fire using CAP's to pay for the action. It notes "both German units command group fire...with LMG as fire leader for 2 CAP's"
Why was the more expensive to fire/less powerful rifle group used as the "group fire leader" in the "New Example" example rather than the more economical to fire, more deadly LMG as in Fig. 18?
Brain fart on the part of the rules author?
Some rule specific to how grouped units using "group activation" have to chose their Fire Leader?
Looks like they fixed this oversight in the latest rules (v25) that you can download from www.academygames.com.