Learn Arabic (Modern Standard): رقم المجموعة تسعة.

When you are using a number as a label, a digit, or an identifier (like a phone number, a room number, or a group number), you use the default bare counting form. Because we aren't counting a quantity of things (like "nine groups"), we just use the standalone number تسعة.

Why doesn't the word for number (رقم) have "al-" (the) attached to it, since the translation says "The group number"?

The phrase رقم المجموعة is a possessive phrase (called an Idafa), which literally translates to "the number of the group". In Arabic, the first word of this kind of phrase never takes the prefix for "the" (الـ). It automatically becomes specific because the second word has it.

Where is the word for "is" in this sentence?

Arabic does not use a word for "is" or "are" in simple present-tense sentences. You simply put the subject (رقم المجموعة, the group number) right next to the information about it (تسعة, nine).

Why does the word for group (المجموعة) end in the letter ة?

That letter is the Ta' Marbuta (ة). It is a special ending that usually shows a noun is feminine. It makes an "a" sound here because it is at the end of the word.