Finite groups

direct product of two cyclic groups of order two; smallest group that is non-cyclic

theorem

mathematical group based upon a finite number of elements

symmetry group of a configuration in space

composition table

group of even-parity permutations

group with one element

group whose operation is composition of permutations

finite group with 8 elements, whose elements can be represented by multiplication of unit quaternions {±1, ±i, ±j, ±k}

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3D symmetry group

3D symmetry group

type of cyclic group in group theory

commutative group in which all nonzero elements have the same order

mathematical group consisting of the moves possible in the Rubik's Cube mechanical puzzle

group of units of the ring of integers modulo n

full icosahedral symmetry

transitive permutation group with restrictions on fixed point behavior

Group realized geometrically by reflections across the sides of a triangle

In mathematics, the projective special linear group , isomorphic to , is a finite simple group that has important applications in algebra, geometry, and number theory. It is the automorphism group of the Klein quartic as well as the symmetry group of the Fano plane. With 168 elements, PSL(2, 7) is the smallest nonabelian simple group after the alternating group A5 with 60 elements, isomorphic to .

subgroup whose order is coprime to its index

representations of finite groups, particularly on vector spaces

study of groups and rings of integers of number fields localized at a prime