Fischer group:Fi23

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Definition

This group, denoted $\operatorname {Fi} _{23}$, is one of the three Fischer groups. Fischer groups are 3-transposition groups that are not the symmetric groups or alternating group. $\operatorname {Fi} _{23}$ is one of the 26 sporadic simple groups that appear in the classification of finite simple groups.

The order of the group is:

$4089470473293004800=2^{18}\cdot 3^{13}\cdot 5^{2}\cdot 7\cdot 11\cdot 13\cdot 17\cdot 23$

Arithmetic functions

Function	Value	Similar groups	Explanation for function value
order (number of elements, equivalently, cardinality or size of underlying set)	4089470473293004800	groups with same order
number of conjugacy classes	98

Linear representation theory

Further information: linear representation theory of Fischer group:Fi23 Linear representation theory of Fischer group:Fi23

External links

• Fi23 on the Atlas of Finite Groups