Final answer:
A group that splits away from one of the major political parties due to disagreement is called a splinter party.
Step-by-step explanation:
When a group splits away from one of the major political parties due to some disagreement, this action is called a splinter party. Splinter parties are offshoots of a major party and can form when members have different beliefs or agendas. These parties attract supporters from one or both of the existing parties during an election but often fail to attract enough votes to win.