For general background and history of the Fischer sporadic groups, see Fischer group.
This article may be confusing or unclear to readers. Please help clarify the article. There might be a discussion about this on the talk page.(August 2021) (Learn how and when to remove this message)
Algebraic structure → Group theory Group theory
Basic notions
Subgroup
Normal subgroup
Quotient group
(Semi-)direct product
Group homomorphisms
kernel
image
direct sum
wreath product
simple
finite
infinite
continuous
multiplicative
additive
cyclic
abelian
dihedral
nilpotent
solvable
action
Glossary of group theory
List of group theory topics
Finite groups
Cyclic group Zn
Symmetric group Sn
Alternating group An
Dihedral group Dn
Quaternion group Q
Cauchy's theorem
Lagrange's theorem
Sylow theorems
Hall's theorem
p-group
Elementary abelian group
Frobenius group
Schur multiplier
Classification of finite simple groups
cyclic
alternating
Lie type
sporadic
Discrete groups
Lattices
Integers ()
Free group
Modular groups
PSL(2, )
SL(2, )
Arithmetic group
Lattice
Hyperbolic group
Topological and Lie groups
Solenoid
Circle
General linear GL(n)
Special linear SL(n)
Orthogonal O(n)
Euclidean E(n)
Special orthogonal SO(n)
Unitary U(n)
Special unitary SU(n)
Symplectic Sp(n)
G2
F4
E6
E7
E8
Lorentz
Poincaré
Conformal
Diffeomorphism
Loop
Infinite dimensional Lie group
O(∞)
SU(∞)
Sp(∞)
Algebraic groups
Linear algebraic group
Reductive group
Abelian variety
Elliptic curve
v
t
e
In the area of modern algebra known as group theory, the Fischer groupFi22 is a sporadic simple group of order
as group theory, the Fischergroups are the three sporadic simple groupsFi22, Fi23 and Fi24 introduced by Bernd Fischer (1971, 1976). The Fischer groups...
automorphism group has order 2, with the full automorphism group being the group 2F4(2). The Tits group occurs as a maximal subgroup of the FischergroupFi22. The...
Janko groups J1, J2 or HJ, J3 or HJM, J4 Conway groups Co1, Co2, Co3 FischergroupsFi22, Fi23, Fi24′ or F3+ Higman-Sims group HS McLaughlin group McL Held...
automorphism group: Trivial. Other names: F1, M1, Monster group, Friendly giant, Fischer's monster. Remarks: Contains all but 6 of the other sporadic groups as...
suggested by Bernd Fischer in unpublished work from the early 1970s during his investigation of {3,4}-transposition groups: groups generated by a class...
cover of the FischergroupFi22. It has a second rank-3 action on 137632 points Fi23 is the centralizer of a transposition in the Fischergroup Fi24. When...
the area of modern algebra known as group theory, the Fischergroup Fi24 or F24′ or F3+ is a sporadic simple group of order 1,255,205,709,190,661,721...
permutation group. This gives several "chains" of rank-3 permutation groups, such as the Suzuki chain and the chain ending with the Fischergroups. Some unusual...
Global Information
