**Thomas Breuer
**

Email: sam@math.rwth-aachen.de

Homepage: http://www.math.rwth-aachen.de/~Thomas.Breuer

© 2013–2015 by Thomas Breuer

This manuscript may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see http://www.gnu.org/licenses.

1 Maintenance Issues for the **GAP** Character Table Library

1.2 Some finite factor groups of perfect space groups (February 2014)

1.2-1 Constructing the space groups in question

1.2-2 Constructing the factor groups in question

1.2-3 Examples with point group A_5

1.2-4 Examples with point group L_3(2)

1.2-5 Example with point group SL_2(7)

1.2-6 Example with point group 2^3.L_3(2)

1.2-7 Examples with point group A_6

1.2-8 Examples with point group L_2(8)

1.2-9 Example with point group M_11

1.2-10 Example with point group U_3(3)

1.2-11 Examples with point group U_4(2)

1.2-12 A remark on one of the example groups

1.2-1 Constructing the space groups in question

1.2-2 Constructing the factor groups in question

1.2-3 Examples with point group A_5

1.2-4 Examples with point group L_3(2)

1.2-5 Example with point group SL_2(7)

1.2-6 Example with point group 2^3.L_3(2)

1.2-7 Examples with point group A_6

1.2-8 Examples with point group L_2(8)

1.2-9 Example with point group M_11

1.2-10 Example with point group U_3(3)

1.2-11 Examples with point group U_4(2)

1.2-12 A remark on one of the example groups

2 Using Table Automorphisms for Constructing Character Tables in **GAP**

2.3 The Constructions

2.3-1 Character Tables of Groups of the Structure M.G.A

2.3-2 Character Tables of Groups of the Structure G.S_3

2.3-3 Character Tables of Groups of the Structure G.2^2

2.3-4 Character Tables of Groups of the Structure 2^2.G (August 2005)

2.3-5 p-Modular Tables of Extensions by p-singular Automorphisms

2.3-6 Character Tables of Subdirect Products of Index Two (July 2007)

2.3-1 Character Tables of Groups of the Structure M.G.A

2.3-2 Character Tables of Groups of the Structure G.S_3

2.3-3 Character Tables of Groups of the Structure G.2^2

2.3-4 Character Tables of Groups of the Structure 2^2.G (August 2005)

2.3-5 p-Modular Tables of Extensions by p-singular Automorphisms

2.3-6 Character Tables of Subdirect Products of Index Two (July 2007)

2.4 Examples for the Type M.G.A

2.4-1 Character Tables of Dihedral Groups

2.4-2 An M.G.A Type Example with M noncentral in M.G (May 2004)

2.4-3**Atlas** Tables of the Type M.G.A

2.4-4 More**Atlas** Tables of the Type M.G.A

2.4-5 The Character Tables of 4_2.L_3(4).2_3 and 12_2.L_3(4).2_3

2.4-6 The Character Tables of 12_1.U_4(3).2_2' and 12_2.U_4(3).2_3' (December 2015)

2.4-7 The Character Table of (2^2 × F_4(2)):2 < B (March 2003)

2.4-8 The Character Table of 2.(S_3 × Fi_22.2) < 2.B (March 2003)

2.4-9 The Character Table of (2 × 2.Fi_22):2 < Fi_24 (November 2008)

2.4-10 The Character Table of S_3 × 2.U_4(3).2_2 ≤ 2.Fi_22 (September 2002)

2.4-11 The Character Table of 4.HS.2 ≤ HN.2 (May 2002)

2.4-12 The Character Tables of 4.A_6.2_3, 12.A_6.2_3, and 4.L_2(25).2_3

2.4-13 Pseudo Character Tables of the Type M.G.A (May 2004)

2.4-14 Some Extra-ordinary p-Modular Tables of the Type M.G.A (September 2005)

2.4-1 Character Tables of Dihedral Groups

2.4-2 An M.G.A Type Example with M noncentral in M.G (May 2004)

2.4-3

2.4-4 More

2.4-5 The Character Tables of 4_2.L_3(4).2_3 and 12_2.L_3(4).2_3

2.4-6 The Character Tables of 12_1.U_4(3).2_2' and 12_2.U_4(3).2_3' (December 2015)

2.4-7 The Character Table of (2^2 × F_4(2)):2 < B (March 2003)

2.4-8 The Character Table of 2.(S_3 × Fi_22.2) < 2.B (March 2003)

2.4-9 The Character Table of (2 × 2.Fi_22):2 < Fi_24 (November 2008)

2.4-10 The Character Table of S_3 × 2.U_4(3).2_2 ≤ 2.Fi_22 (September 2002)

2.4-11 The Character Table of 4.HS.2 ≤ HN.2 (May 2002)

2.4-12 The Character Tables of 4.A_6.2_3, 12.A_6.2_3, and 4.L_2(25).2_3

2.4-13 Pseudo Character Tables of the Type M.G.A (May 2004)

2.4-14 Some Extra-ordinary p-Modular Tables of the Type M.G.A (September 2005)

2.6 Examples for the Type G.2^2

2.6-1 The Character Table of A_6.2^2

2.6-2**Atlas** Tables of the Type G.2^2 – Easy Cases

2.6-3 The Character Table of S_4(9).2^2 (September 2011)

2.6-4 The Character Tables of Groups of the Type 2.L_3(4).2^2 (June 2010)

2.6-5 The Character Tables of Groups of the Type 6.L_3(4).2^2 (October 2011)

2.6-6 The Character Tables of Groups of the Type 2.U_4(3).2^2 (February 2012)

2.6-7 The Character Tables of Groups of the Type 4_1.L_3(4).2^2 (October 2011)

2.6-8 The Character Tables of Groups of the Type 4_2.L_3(4).2^2 (October 2011)

2.6-9 The Character Table of Aut(L_2(81))

2.6-10 The Character Table of O_8^+(3).2^2_111

2.6-1 The Character Table of A_6.2^2

2.6-2

2.6-3 The Character Table of S_4(9).2^2 (September 2011)

2.6-4 The Character Tables of Groups of the Type 2.L_3(4).2^2 (June 2010)

2.6-5 The Character Tables of Groups of the Type 6.L_3(4).2^2 (October 2011)

2.6-6 The Character Tables of Groups of the Type 2.U_4(3).2^2 (February 2012)

2.6-7 The Character Tables of Groups of the Type 4_1.L_3(4).2^2 (October 2011)

2.6-8 The Character Tables of Groups of the Type 4_2.L_3(4).2^2 (October 2011)

2.6-9 The Character Table of Aut(L_2(81))

2.6-10 The Character Table of O_8^+(3).2^2_111

4 **GAP** Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups

5 **GAP** Computations with O_8^+(5).S_3 and O_8^+(2).S_3

8 Ambiguous Class Fusions in the **GAP** Character Table Library

8.7 Fusions Determined by Information about the Groups

8.7-1 U_3(3).2 → Fi_24^' (November 2002)

8.7-2 L_2(13).2 → Fi_24^' (September 2002)

8.7-3 M_11 → B (April 2009)

8.7-4 L_2(11):2 → B (April 2009)

8.7-5 L_3(3) → B (April 2009)

8.7-6 L_2(17).2 → B (March 2004)

8.7-7 L_2(49).2_3 → B (June 2006)

8.7-8 2^3.L_3(2) → G_2(5) (January 2004)

8.7-9 5^{1+4}.2^{1+4}.A_5.4 → B (April 2009)

8.7-10 The fusion from the character table of 7^2:2L_2(7).2 into the table of marks (January 2004)

8.7-11 3 × U_4(2) → 3_1.U_4(3) (March 2010)

8.7-12 2.3^4.2^3.S_4 → 2.A12 (September 2011)

8.7-13 127:7 → L_7(2) (January 2012)

8.7-14 L_2(59) → M (May 2009)

8.7-15 L_2(71) → M (May 2009)

8.7-16 L_2(41) → M (April 2012)

8.7-1 U_3(3).2 → Fi_24^' (November 2002)

8.7-2 L_2(13).2 → Fi_24^' (September 2002)

8.7-3 M_11 → B (April 2009)

8.7-4 L_2(11):2 → B (April 2009)

8.7-5 L_3(3) → B (April 2009)

8.7-6 L_2(17).2 → B (March 2004)

8.7-7 L_2(49).2_3 → B (June 2006)

8.7-8 2^3.L_3(2) → G_2(5) (January 2004)

8.7-9 5^{1+4}.2^{1+4}.A_5.4 → B (April 2009)

8.7-10 The fusion from the character table of 7^2:2L_2(7).2 into the table of marks (January 2004)

8.7-11 3 × U_4(2) → 3_1.U_4(3) (March 2010)

8.7-12 2.3^4.2^3.S_4 → 2.A12 (September 2011)

8.7-13 127:7 → L_7(2) (January 2012)

8.7-14 L_2(59) → M (May 2009)

8.7-15 L_2(71) → M (May 2009)

8.7-16 L_2(41) → M (April 2012)

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