Statements (65)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:musical_group
|
| gptkbp:character_traits |
D_4 x Z_2
|
| gptkbp:element |
permutations of 4 elements
identity, transpositions, 3-cycles, double transpositions |
| gptkbp:has |
on 4 points
|
| gptkbp:has_character_table |
5 rows and 5 columns
|
| gptkbp:has_conjugacy_classes |
gptkb:5
|
| gptkbp:has_exhibition |
<a,b | a^2 = b^3 = (ab)^4 = 1>
|
| gptkbp:has_irreducible_representations |
gptkb:5
|
| gptkbp:has_normal_subgroups |
{1}, A_4, S_4
|
| gptkbp:has_produced |
3-cycles
transpositions |
| gptkbp:has_subgroup |
A_4
1, 2, 3, 4, 6, 12 S_4 itself |
| https://www.w3.org/2000/01/rdf-schema#label |
S 4
|
| gptkbp:is_a_center_for |
gptkb:musical_group
|
| gptkbp:is_aligned_with |
gptkb:Polygon
|
| gptkbp:is_finite_group |
gptkb:true
|
| gptkbp:is_group |
gptkb:true
|
| gptkbp:is_non_abelian |
gptkb:true
|
| gptkbp:is_related_to |
gptkb:topology
gptkb:Quantum_Mechanics gptkb:Klein_four-group gptkb:philosophy gptkb:psychology Galois theory mathematical physics information theory representation theory symmetric functions finite fields graph theory complexity theory decision theory combinatorial group theory Cayley's theorem discrete mathematics algebraic structures mathematical economics computational group theory |
| gptkbp:is_represented_in |
group actions
permutation matrices 2x2 matrices over finite fields |
| gptkbp:is_used_in |
gptkb:crypt
gptkb:original_programming gptkb:Physics gptkb:strategy gptkb:sociology gptkb:statistical_mechanics gptkb:musical_group geometry algorithm design combinatorial optimization linguistics mathematical modeling operations research algebraic topology coding theory mathematical logic network theory history of mathematics mathematical puzzles combinatorial designs |
| gptkbp:order |
gptkb:24
|