I would say,"group one-eleven" or "group one hundred-eleven." "Group one one one" is OK but I think would be rare among Americans. "Double one one" - no, sounds strange. If you want to say it that way, it would be "triple one." "Group one hundred and eleven" would also be common, but Americans tend to use as few words as possible to convey the meaning.

You can say one-one-one triple one or one hundred and eleven Double one one would be too confusing. But there is probably a name for this group that everyone uses and is familiar with it, so that would be the best one. How is it called in original language?

The first two options are not used. "Double one one" is nonsense. "One one one" separates the numbers too much and can be confusing, as it doesn't show the relationship between the numbers at all. "One hundred and eleven" is the standard, but how it is spoken can change. "The students of group ONE-ELEVEN have 2 lessons today" is the most common way of saying such a number. In these expressions, the "hundred and" of "one hundred and eleven" is left out, i.e. "423 = four-twenty-three; 830 = eight-thirty; 135 = one-thirty-five." Another example is even higher numbers: 3,450 can be spoken as "thirty-four-fifty, thirty-four hundred and fifty, or the basic three thousand four hundred and fifty." Using large numbers in everyday conversation can tend to create a mouthful of words, so using the "thirty-four-fifty" example can be common, for example, when referring to an address (eighty-two-thirty Washington Street), a phone number, or other everyday terms. When using such numbers for mathematical reasons, one usually speaks them normally (example: The questionnaire was given to eight thousand two hundred and thirty people).

Please say one hundred and eleven (111). I work in a school too!

I'd say 'group one -eleven' . Interesting question, I;ve been in Russia for a while, know there is a more or less set way of reading out your mobile but never bothered to think about it. Много узнаете в этой жизни! I'd say the same for rooms in educational institutes. e.g room 101 = room one 'oh' one, '133' = one - thirty three', maybe coz they're on a certain floor