die Gruppe
group
A number of people or things that are together, belong together, or form a unit.
Eine Gruppe von Touristen wartete vor dem Museum.
A group of tourists was waiting in front of the museum.

group
Loading your saved state.
group
A number of people or things that are together, belong together, or form a unit.
Eine Gruppe von Touristen wartete vor dem Museum.
A group of tourists was waiting in front of the museum.

The exact meaning of 'Gruppe' (group) is usually clear from the context. Words like 'Touristen' (tourists) or 'Freunde' (friends) point to the general meaning, while terms like 'Elemente' (elements) or 'Soldaten' (soldiers) indicate specialized language.
Eine Gruppe von Wissenschaftlern diskutierte die Ergebnisse.
A group of scientists discussed the results.
The noun 'Gruppe' (group) is the basis for other useful words. These include the verb 'gruppieren' (to arrange in groups) and the compound noun 'die Gruppenarbeit' (group work).
Der Lehrer gruppierte die Schüler für das Projekt neu.
The teacher regrouped the students for the project.
The meanings in chemistry, the military, or mathematics are specific technical terms. In normal everyday life, you will almost exclusively encounter the general meaning 'Ansammlung von Personen oder Dingen' (collection of people or things).
In der Chemie werden die Elemente im Periodensystem in Gruppen eingeteilt.
In chemistry, the elements in the periodic table are divided into groups.
In the general meaning, 'Gruppe' (group) is often combined with certain verbs. Common phrases are 'eine Gruppe bilden' (to form a group), 'in einer Gruppe arbeiten' (to work in a group), or 'zu einer Gruppe gehören' (to belong to a group).
Er möchte gern zu unserer Lerngruppe gehören.
He would like to belong to our study group.
Pay attention to the prepositions. 'In einer Gruppe' describes membership or activity. 'Eine Gruppe von ...' describes what the group consists of.
In dieser Gruppe fühlen sich alle sehr wohl.
Everyone feels very comfortable in this group.
people
'die Leute' and 'die Gruppe' can both refer to several people. 'die Leute' is used more generally or casually when you are not saying exactly who the people are. It can also refer to a specific set of people, for example the people on the bus or the people from the office. 'die Gruppe' sounds more precise: the people belong together or are seen as a unit, for example in a course, on a trip, or while working on a task. Learners may confuse the words because both talk about several people. As a practical rule: when you are just talking about people in general, 'Leute' often fits. When the people belong together or are doing something together, 'Gruppe' is usually a better fit.

Wegen des Wetters ist die Gruppe früher von der Wanderung zurückgekommen.
Because of the weather, the group came back from the hike earlier.
Im Bus sprechen die Leute heute viel über die hohen Preise.
On the bus today, people are talking a lot about the high prices.