Finite Groups 2

List of groups implemented

• Alternating
• Aut, Aut2 WIP
• CentralProduct
• CompleteMonomialGroup
• CompleteWreath
• Cyclic
• Dicyclic
• Dihedral
• Direct
• ElementaryAbelianGroup
• Extraspecial
• FalseWitness
• GL, SL, PGL, PSL, AGL, ASL WIP
• GeneralizedAlternating
• GeneralizedQuaternion
• GeneralizedSymmetric
• Heisenberg
• Holomorph
• HyperOctahedralGroup
• Inn
• KleinGroup
• Out WIP
• Quotient
• Semidirect
• Symmetric
• Units, Units2
• Wreath
• WreathCyclic
• WreathSymmetric

Operations

• Automorphism from generators

• Center

• Centralizer

• Commutator

• Commutator subgroup

• Conjugacy class of element

• Conjugacy classes

• Derived series

• Exponent of group

• Group order

• Identity

• Inverse of an element

• Left and right conjugate

• Left and right cosets

• Lower central series

• Nilpotency class

• Normalizer

• Order of all elements

• Order of an element

• Perfect core

• Power of an element in O(log(n))

• Powers of an element

• Product of subsets

• Subgroup from generators

• Sylow subgroups WIP

• isAbelian

• isCyclic

• isIsomorphic WIP

• isNilpotent

• isNormal

• isPerfect

• isPGroup

• isSimple WIP

• isSolvable

• isSubgroup

• Test associativity testing random elements

Group homomorphisms

• Is end/iso/sur/inj/aut
• Image
• Kernel
• Domain
• Codomain
• Composition