ATLAS: Linear group L2(27)

Order = 9828 = 22.33.7.13.
Mult = 2.
Out = 6.

Standard generators

Standard generators of L2(27) are a and b where a has order 2, b has order 3 and ab has order 7.
Standard generators of the double cover 2.L2(27) = SL2(27) are preimages A and B where B has order 3 and AB has order 7.

Standard generators of L2(27).2 are c and d where c has order 2 (necessarily 2B), d has order 4, and cd has order 7.

Standard generators of the double cover 2.L2(27).2 are preimages C and D where CD has order 7.

Standard generators of L2(27).3 are e and f where e has order 2, f has order 3, ef has order 9, efeff has order 7, efefefeffefeffeff has order 9 .

Standard generators of the double cover 2.L2(27).3 are preimages E and F where F has order 3 and EF has order 9.

Standard generators of L2(27).6 are g and h where g has order 2 (necessarily 2B), h has order 3 (necessarily 3C), gh has order 24, and ghghh has order 13.

Standard generators of the double cover 2.L2(27).6 are preimages G and H where H has order 3.


Representations

The representations of L2(27) available are The representations of 2.L2(27) available are

Conjugacy classes

A set of generators for the maximal cyclic subgroups of L2(27) can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.


Main ATLAS page Go to main ATLAS (version 2.0) page.
Linear groups page Go to linear groups page.
Old L2(27) page Go to old L2(27) page - ATLAS version 1.
ftp access Anonymous ftp access is also available on for.mat.bham.ac.uk.

Version 2.0 file created on 24th January 2002, from Version 1 file last updated on 06.12.97.
Last updated 27.08.04 by RAW.
Information checked to Level 0 on 24.01.02 by RAW.
R.A.Wilson, R.A.Parker and J.N.Bray.