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Apr
13
comment Is character same as one dimensional irreducible representation?
Yes, the Klein group is abelian so all of its irreducible representations are one-dimensional, and can be identified with their characters. (In fact, this characterises abelian groups.) The row $1111$ is the (character of) the trivial representation which sends every group element to $1$. It's true that it is not very interesting, as every group has this representation, and they all look pretty much the same, so all you can really tell from it is the number of conjugacy classes.
Apr
9
answered Prove metacyclic group is generated by two elements.
Mar
26
comment How to print long strings in MAGMA?
This is a wild guess as I've not used magma, but have you tried either adding a newline, or closing or otherwise flushing your output file? Perhaps there is a way to do that. Adding a newline might be enough if the output is lined buffered. Again, just some speculative ideas.
Mar
21
comment Presentation of $C_p\ :\ C_q$ , where $p,q$ are primes and $q|p-1$
The map $a\mapsto a^k$ must be an automorphism of the cyclic group $\langle a\rangle$, so $k$ just needs to be relatively prime to $p$.
Mar
21
comment Presentation of $C_p\ :\ C_q$ , where $p,q$ are primes and $q|p-1$
What is f? I took a guess that it was defined as a two-generator free group, but your example then seems to work just fine for me.
Mar
9
comment Which kind of product do we have here?
I think this is called a Zappa–Szép product. See Wikipedia, for example.
Feb
8
awarded  Necromancer
Feb
3
comment Which non-abelian finite groups have the property that every subgroup is normal?
Yes, these are called Hamiltonian groups and all have the form $Q_8\times A\times B$, where $A$ is an elementary abelian $2$-group, and $B$ is an abelian group of odd order. Here is a link.
Jan
21
comment Number of groups of order $9261$?
@Peter I agree, but ... RTFM? :-) The first paragraph of documentation for this function fairly clearly describes its behaviour. I'm sure the package authors had their reasons for making this design choice. (See, for example, p. 9 of the manual.)
Jan
21
comment Number of groups of order $9261$?
@Peter Please note that my answer does not suggest any error in the ConstructAllGroups command, but rather with how it is used.
Jan
21
comment Number of groups of order $9261$?
@AlexanderKonovalov Thanks for your comment, and for improving my answer formatting.
Jan
21
answered Number of groups of order $9261$?
Jan
16
comment When is every group of order $n$ nilpotent of class $\leq c$?
@FrancisBegbie Yes, I've added a link to a reference.
Jan
16
revised When is every group of order $n$ nilpotent of class $\leq c$?
Added reference.
Jan
16
answered When is every group of order $n$ nilpotent of class $\leq c$?
Jan
6
comment Groups of order $64$ with abelian group of automorphism
@pGroups Right. I forgot to simplify the other presentation.
Jan
4
comment Is $gnu(2304)$ known?
@AlexanderKonovalov Yes, I checked and that is indeed the source for that particular value.
Jan
4
comment Is $gnu(2304)$ known?
According to Maple, $\operatorname{gnu}( 2304 ) = 15756130$. However, Maple does not know $\operatorname{gnu}( 3072 )$.
Dec
29
revised Groups of order $64$ with abelian group of automorphism
Added requested presentations.
Dec
29
revised Groups of order $64$ with abelian group of automorphism
added 4 characters in body