Suppose for a group $G$, of which we completely understand its conjugacy class structure and character table, is there a simple algorithm to deduce the character table of $G/Z(G)$? Or more generally, $G/N$ for $N \trianglelefteq G$?
2026-03-27 10:31:22.1774607482
The character table of $G/Z(G)$ and $G/N$ given knowledge of the character table of $G$
173 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
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 REPRESENTATION-THEORY
- How does $\operatorname{Ind}^G_H$ behave with respect to $\bigoplus$?
- Minimal dimension needed for linearization of group action
- How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?
- Assuming unitarity of arbitrary representations in proof of Schur's lemma
- Are representation isomorphisms of permutation representations necessarily permutation matrices?
- idempotent in quiver theory
- Help with a definition in Serre's Linear Representations of Finite Groups
- Are there special advantages in this representation of sl2?
- Properties of symmetric and alternating characters
- Representation theory of $S_3$
Related Questions in CHARACTERS
- Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.
- Properties of symmetric and alternating characters
- Counting characters of bounded conductors
- The condition between $\chi(1)$ and $[G:H]$ which gives us a normal subgroup.
- How to realize the character group as a Lie/algebraic/topological group?
- Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$
- Confusion about the conductor for Dirichlet characters
- Relation between characters of symmetric group and general linear group
- Information on semilinear groups.
- Let $ f $ be an irreducible polynomial in $ \mathbb{F }_q [x] $, why $ f ^\frac{s}{deg (f)} $ has degree term $ s-1 $?
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?
The answer is "yes". You can identify the columns of the character table of $G$, which correspond to elements in $N$. Then you take only those characters $\chi$, which have $\chi(1)=\chi(g)$ for every $g\in N$. This gives you some rectangle matrix with some duplicate columns. Just delete duplicate columns until you end up with a square matrix. This is the character table of $G/N$.