ATLAS: Ree group R(27)

Order = 10073444472 = 23.39.7.13.19.37.
Mult = 1.
Out = 3.

Standard generators

Standard generators of R(27) are a and b where a has order 2, b is in class 3A and ab has order 19.

Standard generators of R(27):3 are c and d where c has order 2, d is in class 3D (or 3D'), cd has order 21, cdcdd has order 14 and cdcdcdcddcdcddcdd has order 9. These conditions distinguish classes 3D and 3D'.


Black box algorithms

To find standard generators of R(27): To find standard generators of R(27).3:

Representations

The representations of R(27) available are The representations of R(27):3 available are

Maximal subgroups

The maximal subgroups of R(27) are The maximal subgroups of R(27):3 are

Conjugacy classes

The 35 conjugacy classes of R(27) are roughly as follows:
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Last updated 17th October 1998,
R.A.Wilson, R.A.Parker and J.N.Bray