I'm afraid I can't provide much motivation other than personal interest. I have found David Burrell's very recent Ph.D. thesis, which identified a transcription error that resulted in an incorrect published count for the number of groups of order $1024$. Burrell's thesis cites a 2017 survey of Eick, Horn, and Hulpke which lists all the orders (up to $20000$) whose number-of-groups was unknown, and $5832$ is not on this list. However, I haven't found a (non-paywalled) source for the actual count. Does anyone happen to have it?
2026-03-25 09:50:08.1774432208
How many non-isomorphic groups of order $5832 = 2^3 \cdot 3^6$ are there?
92 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in FINITE-GROUPS
- List Conjugacy Classes in GAP?
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- Assuming unitarity of arbitrary representations in proof of Schur's lemma
- existence of subgroups of finite abelian groups
- Online reference about semi-direct products in finite group theory?
- classify groups of order $p^2$ simple or not
- Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.
- The number of conjugacy classes of a finite group
- Properties of symmetric and alternating characters
- Finite group, How can I construct solution step-by-step.
Related Questions in COMPUTATIONAL-ALGEBRA
- How to create a group action on some group with GAP
- How to use a stabilizer chain (Schreier-Sims) to prune a centralizer search?
- Is this specific group finite?
- The most efficient way to solve $2^{2017} \mod 9$
- How can I use GAP to collect words into a normal form?
- computer program-software for galois
- Basis for the vector space over $\mathbb{Q}$
- Efficient way to calculate solution to the Von Neumann equation for time evolution
- Grobner basis: Basis for K-vector space.
- How to build a simple Mathematical formula with matching condition
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It seems that the known numbers of groups for a given order ≤20,000 can now be found at:
groups.quendi.de
a website maintained by Max Horn at Kaiserslautern.
According to that site, $2^3.3^6$ appears now to be manageable: there are 29,876 non-isomorphic groups of order $2^3.3^6$.