The lifting group has order 320, and is SmallGroup(320,696) in the GAP Library of small groups. Some miscellaneous facts about the group:
- The group is nonabelian.
- It has 44 conjugacy classes.
- It is solvable, supersolvable, but not nilpotent.
- If two elements are randomly chosen from this group, the probability that they commute is 43/319.
- The maximum order among group elements is 20.
- The Sylow 2-subgroups are nonabelian with exponent 8.
- The Sylow 5-subgroup is normal, so the full group is a semi-direct product.
