scholarly journals The Projective Character Tables of a Solvable Group 26:6×2

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Abraham Love Prins
Keyword(s):  
Simple Group ◽  
Soluble Group ◽  
Galois Field ◽  
Maximal Subgroups ◽  
Finite Soluble Group ◽  
Character Tables ◽  
Extension Group ◽  
Projective Character ◽  
Ordinary Character ◽  
Clifford Theory

The Chevalley–Dickson simple group G24 of Lie type G2 over the Galois field GF4 and of order 251596800=212.33.52.7.13 has a class of maximal subgroups of the form 24+6:A5×3, where 24+6 is a special 2-group with center Z24+6=24. Since 24 is normal in 24+6:A5×3, the group 24+6:A5×3 can be constructed as a nonsplit extension group of the form G¯=24·26:A5×3. Two inertia factor groups, H1=26:A5×3 and H2=26:6×2, are obtained if G¯ acts on 24. In this paper, the author presents a method to compute all projective character tables of H2. These tables become very useful if one wants to construct the ordinary character table of G¯ by means of Fischer–Clifford theory. The method presented here is very effective to compute the irreducible projective character tables of a finite soluble group of manageable size.

Brauer pairs with the same projective character tables

1990 ◽  
Vol 18 (10) ◽  
pp. 3437-3446
Author(s):  
Surinder K. Sehgal ◽  
Ron Solomon
Keyword(s):  
Character Tables ◽  
Projective Character ◽  
Brauer Pairs

Projective character tables and Opechowski's theorem

Physica ◽  
1973 ◽  
Vol 70 (3) ◽  
pp. 505-519 ◽  
Author(s):  
N.B. Backhouse
Keyword(s):  
Character Tables ◽  
Projective Character

THE BAD BEHAVIOR OF REPRESENTATION GROUPS

2005 ◽  
Vol 04 (02) ◽  
pp. 139-151
Author(s):  
R. J. HIGGS
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Central Extension ◽  
Full Automorphism Group ◽  
Character Tables ◽  
Projective Character ◽  
Inner Automorphisms ◽  
A Finite Group ◽  
Representation Group

Let (H, A) be a primitive central extension of a finite group G. We show that A is not characteristic in H in general, and further demonstrate in a series of examples that results, which hold about inner automorphisms of H, do not extend to the full automorphism group of H. We also give some new results about isoclinism and representation groups of G in the case that H is capable. Finally we give an example of two non-isomorphic groups of the same order, which not only have a representation group in common, but also have identical projective character tables.

Fusions of character tables III: Fusions of cyclic groups and a generalisation of a condition of Camina

2010 ◽  
Vol 178 (1) ◽  
pp. 325-348 ◽  
Author(s):  
Stephen P. Humphries ◽  
Brent L. Kerby ◽  
Kenneth W. Johnson
Keyword(s):  
Cyclic Groups ◽  
Character Tables

NATURAL EXISTENCE PROOF FOR LYONS SIMPLE GROUP

2003 ◽  
Vol 02 (03) ◽  
pp. 277-315
Author(s):  
GERHARD O. MICHLER ◽  
MICHAEL WELLER ◽  
KATSUSHI WAKI
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Conjugacy Classes ◽  
Existence Proof ◽  
Sporadic Simple Group ◽  
Character Tables ◽  
The Given ◽  
Fold Cover

In this article we give a self-contained existence proof for Lyons' sporadic simple group G by application of the first author's algorithm [18] to the given centralizer H ≅ 2A11 of a 2-central involution of G. It also yields four matrix generators of G inside GL 111 (5) which are given in Appendix A. From the subgroup U ≅ (3 × 2A8) : 2 of H ≅ 2A11, we construct a subgroup E of G which is isomorphic to the 3-fold cover 3McL: 2 of the automorphism group of the McLaughlin group McL. Furthermore, the character tables of E ≅ 3McL : 2 and G are determined and representatives of their conjugacy classes are given as short words in their generating matrices.

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