Properties

Label 91.2.3.c1365551833591188331079076717170973803010984973309425196926272794151202560897218063473701477050781250000000000000000000000000000000000000000000000000
  
Name \(\mathrm{SU}(2)[C_{1365551833591188331079076717170973803010984973309425196926272794151202560897218063473701477050781250000000000000000000000000000000000000000000000000}]\)
Weight $91$
Degree $2$
Real dimension $3$
Components $1.366\times 10^{147}$
Contained in \(\mathrm{USp}(2)\)
Identity component \(\mathrm{SU}(2)\)
Component group \(C_{1365551833591188331079076717170973803010984973309425196926272794151202560897218063473701477050781250000000000000000000000000000000000000000000000000}\)

Learn more

Invariants

Weight:$91$
Degree:$2$
$\mathbb{R}$-dimension:$3$
Components:$1365551833591188331079076717170973803010984973309425196926272794151202560897218063473701477050781250000000000000000000000000000000000000000000000000$
Contained in:$\mathrm{USp}(2)$
Rational:yes

Identity component

Name:$\mathrm{SU}(2)$
$\mathbb{R}$-dimension:$3$
Description:$\left\{\begin{bmatrix}\alpha&\beta\\-\bar\beta&\bar\alpha\end{bmatrix}:\alpha\bar\alpha+\beta\bar\beta = 1,\ \alpha,\beta\in\mathbb{C}\right\}$ Symplectic form:$\begin{bmatrix}0&1\\-1&0\end{bmatrix}$
Hodge circle:$u\mapsto\mathrm{diag}(u,\bar u)$

Component group

Name:$C_{1365551833591188331079076717170973803010984973309425196926272794151202560897218063473701477050781250000000000000000000000000000000000000000000000000}$
Order:$1365551833591188331079076717170973803010984973309425196926272794151202560897218063473701477050781250000000000000000000000000000000000000000000000000$
Abelian:yes
Generators:$\begin{bmatrix}1&0\\0&\zeta_{1365551833591188331079076717170973803010984973309425196926272794151202560897218063473701477050781250000000000000000000000000000000000000000000000000}\end{bmatrix}$

Subgroups and supergroups

Maximal subgroups:$\mathrm{SU}(2)[C_{682775916795594165539538358585486901505492486654712598463136397075601280448609031736850738525390625000000000000000000000000000000000000000000000000}]$, $\mathrm{SU}(2)[C_{455183944530396110359692239056991267670328324436475065642090931383734186965739354491233825683593750000000000000000000000000000000000000000000000000}]$, $\mathrm{SU}(2)[C_{273110366718237666215815343434194760602196994661885039385254558830240512179443612694740295410156250000000000000000000000000000000000000000000000000}]$
Minimal supergroups:$\mathrm{SU}(2)[C_{2731103667182376662158153434341947606021969946618850393852545588302405121794436126947402954101562500000000000000000000000000000000000000000000000000}]$, $\mathrm{SU}(2)[C_{4096655500773564993237230151512921409032954919928275590778818382453607682691654190421104431152343750000000000000000000000000000000000000000000000000}]$, $\mathrm{SU}(2)[C_{6827759167955941655395383585854869015054924866547125984631363970756012804486090317368507385253906250000000000000000000000000000000000000000000000000}]$, $\cdots$

Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$