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Some interesting groups

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L-functions

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Modular forms

ClassicalMaass
HilbertBianchi

Varieties

Elliptic curves
over $\Q$
over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Fields

Number fields
$p$-adic fields

Representations

Dirichlet characters
Artin representations

Groups

Galois groups
Sato-Tate groups
Abstract groups
groups
subgroups
characters
conjugacy classes

Database

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  • Source and acknowledgments
  • Completeness of the data
  • Reliability of the data
  • Abstract group labeling
Label Description
4.2 Smallest non-cyclic group
6.1 Smallest nonabelian group
10.1 Proper subgroup of automorphism group
12.1 Central cover of $S_3$
12.3 Rotations of a tetrahedron
18.3 Smaller automorphism group
18.4 Cyclic center, no faithful irrep
24.12 Octahedral group
60.5 First nonsolvable group
64.116 Miller group
96.3 One of the smallest groups with commutator length bigger than 1
96.203 One of the smallest groups with commutator length bigger than 1
120.35 Full icosahedral group
128.1820 Every automorphism central
168.42 Automorphism group of Klein quartic
336.210 No outer automorphisms, not complete
360.118 Alternating group with extra outer automorphisms
432.734 Solvable length 5

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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