The Student Room Group

Number of Groups

Just a quick question:
(up to isomorphism) what is the number of groups of order 2048?

I need to check my answer: does anyone have a link or anything? (i cannot find anything). Even the algebra program GAP is unhelpful.
I think you mean

http://www.wolframalpha.com/input/?i=FiniteGroupCount%5B2048%5D

but Wolfram can't answer it for 2048.

The answer for 1024 is 49487365422.

This paper is from 2008 and says:

The next value, gnu(2048), is still not precisely known, but it strictly exceeds 1774274116992170, which is the exact number of groups of order 2048 that have exponent-2 class 2, and can confidently be expected to agree with that number in its first 3 digits.

I'm forced to feel that someone, somewhere, is trolling...
Original post by DFranklin
I think you mean

http://www.wolframalpha.com/input/?i=FiniteGroupCount%5B2048%5D

but Wolfram can't answer it for 2048.

The answer for 1024 is 49487365422.

This paper is from 2008 and says:

The next value, gnu(2048), is still not precisely known, but it strictly exceeds 1774274116992170, which is the exact number of groups of order 2048 that have exponent-2 class 2, and can confidently be expected to agree with that number in its first 3 digits.

I'm forced to feel that someone, somewhere, is trolling...


I didn't know what I was doing - I was just taking a punt. I've never studied groups.
Original post by Mr M
I didn't know what I was doing - I was just taking a punt. I've never studied groups.

To be clear, I'm not accusing you of trolling...
Original post by DFranklin
To be clear, I'm not accusing you of trolling...


I realised that. I'll keep an eye on the OP to see if he is up to no good.
Original post by DFranklin
I'm forced to feel that someone, somewhere, is trolling...

If OP simply missed out the condition "abelian", then it becomes a reasonable question (being the result of an exercise in the use of the Structure Theorem).
Original post by Smaug123
If OP simply missed out the condition "abelian", then it becomes a reasonable question (being the result of an exercise in the use of the Structure Theorem).


Possible, but:

1) That's a pretty sloppy error to make at this level.
2) It's a bit of a coincidence that 2048 is the smallest number for which the answer is unknown.
Original post by DFranklin
Possible, but:

1) That's a pretty sloppy error to make at this level.
2) It's a bit of a coincidence that 2048 is the smallest number for which the answer is unknown.

Oh wow, didn't realise this was Sloane 1!
(edited 9 years ago)
Reply 9
Original post by DFranklin
To be clear, I'm not accusing you of trolling...


Original post by Mr M
I realised that. I'll keep an eye on the OP to see if he is up to no good.


Original post by Smaug123
Oh wow, didn't realise this was Sloane 1!


i am doing a course at the moment in probabilistic group theory, and I realized one of the questions in the book would be very simple if I knew the number of groups (up to isomorphism obviously) of order 2048 - evidently the author realized that too when asking the question!

for some reason I though that number was known..

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