The character tables of a maximal subgroup of the Monster and some related groups

Paper submitted to LMS J. Comput. Math.

The groups are:

1. 3¹⁺¹²:6.Suz:2 with GAP character table name "3^1+12:6.Suz.2". This is the ‘main’ table in the sense that the others were produced from it.
2. 3¹⁺¹².2.Suz:2 with GAP character table name "3^1+12.2.Suz.2". This is the maximal subgroup N(3B) of the Monster.
3. 3¹²:6.Suz:2 with GAP character table name "3^12.6.Suz.2". (Another quotient.)

The tables should eventually be included in the GAP character table library, CTblLib.

In the mean time, they are available to download here, together with some quotient maps that might not make it into GAP, e.g., (1) to (2) and to (3), (1) to 6.Suz.2.

• N3BetcTables.tar.gz (A folder of 3 GAP library files, 142k).
  New tables. Use the command NotifyCharacterTable to read them into GAP.
• N3BetcQuotientMaps.gap (GAP source file, 9k).
  Quotient maps. They are lists of class indices, each has an explanation of what it is.
• N3BetcFusionMaps.gap (GAP source file, 2k).
  Some fusion maps that I didn’t know where to put. They are lists of class indices, each has an explanation of what it is.

If you need to know anything else then please ask, and I will add it.

Notes on 3¹⁺¹²:6.Suz:2

This is the ‘main’ table in the sense that the others were produced from it.

The classes are ordered as follows: All of the classes lying above a given class X of 6.Suz:2 appear contiguously. You can think of them being labelled (X,v,l) where X is a conjugacy class of 6.Suz:2, v is in the sub-quotient 3¹², and l is in the centre of the extra-special 3-group. More details in the paper...