zu sechst
in a group of six
Describes a group consisting of six people.
Wir waren zu sechst im Urlaub und haben uns ein großes Ferienhaus geteilt.
There were six of us on vacation, and we shared a large holiday house.

six
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in a group of six
Describes a group consisting of six people.
Wir waren zu sechst im Urlaub und haben uns ein großes Ferienhaus geteilt.
There were six of us on vacation, and we shared a large holiday house.

The word 'sechst' is used almost exclusively in the fixed expression 'zu sechst' (in a group of six / six of us). It describes a group of six people and is not declined like an adjective.
Wir sind zu sechst in den Urlaub gefahren.
There were six of us going on vacation.
'Zu sechst' follows a pattern for group numbers: 'zu' + cardinal number + '-t'. This pattern also works for other numbers, for example 'zu dritt' (three people / in a group of three) or 'zu viert' (four people / in a group of four).
Wir waren zu viert, aber dann kamen noch zwei Freunde dazu, also waren wir zu sechst.
There were four of us, but then two more friends joined, so there were six of us.
The expression 'zu sechst' is often combined with verbs that describe a shared activity. Typical examples are 'sein' (to be), 'reisen' (to travel), 'spielen' (to play), or 'arbeiten' (to work).
Wir haben das Projekt zu sechst im Büro bearbeitet.
The six of us worked on the project in the office.
six
'sechs' and 'zu sechst' both have to do with the number 6, but they are used differently. 'sechs' simply names the number: 'sechs Bücher' (six books), 'sechs Personen' (six people), 'sechs Uhr' (six o'clock). 'zu sechst' describes a group of six people doing something together. Learners may confuse the forms because both sound like the same number. Memory tip: for the quantity, use 'sechs'; for a group of people doing an action, use 'zu sechst'.

Die Familie geht heute zu sechst einkaufen.
The family is going shopping as a group of six today.
Im Bus sitzen sechs Kinder aus der Klasse.
There are six children from the class sitting on the bus.