⌂
→
Groups
→
Abstract
→
Interesting
Citation
·
Feedback
·
Hide Menu
Some interesting groups
Introduction
Overview
Random
Universe
Knowledge
L-functions
Rational
All
Modular forms
Classical
Maass
Hilbert
Bianchi
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
Learn more
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