Number of Groups Watch

tombayes
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#1
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#1
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.
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Mr M
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(Original post by tombayes)
does anyone have a link
http://www.wolframalpha.com/input/?i...+of+order+2048
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DFranklin
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I think you mean

http://www.wolframalpha.com/input/?i...ount%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...
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Mr M
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(Original post by DFranklin)
I think you mean

http://www.wolframalpha.com/input/?i...ount%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.
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DFranklin
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(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...
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Mr M
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(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.
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Smaug123
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(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).
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DFranklin
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(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.
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Smaug123
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(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!
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tombayes
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(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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