For the ctiSession object, we call GetAllSkillgroups. We get the right number of groups. Then we did GetAllProperties for each group. We get all properties except the SkillGroupName.
We even tried EnableSkillGroupStatistics for each group and enable all messages in SetMessageFilter. We get events like OnNewSkillGroupStatisticsEvent, QueryAgentStateConf, AgentPreCallEvent, etc. However, we never got the OnSkillInfoEvent which is required to get the SkilGroupName.