  
  [1X2 [33X[0;0YClassification[133X[101X
  
  [33X[0;0YThe  [13Xclass number[113X [23Xk(G)[123X of a group [23XG[123X is the number of conjugacy classes of [23XG[123X.
  In 1903, Landau proved in [Lan03] that for every [23Xn \in \mathbb{N}[123X, there are
  only  finitely many finite groups with exactly [23Xn[123X conjugacy classes. Thus, it
  is possible to classify finite groups according to their class number.[133X
  
  
  [1X2.1 [33X[0;0YGroups with at most 14 conjugacy classes[133X[101X
  
  [33X[0;0YThe  [5XSmallClassNr[105X  package  provides  access to the finite groups with class
  number at most [23X14[123X. These groups were classified in the following papers:[133X
  
  [30X    [33X[0;6Y[23Xk(G)  \leq  5[123X,  by  Miller in [Mil11] and independently by Burnside in
        [Bur11][133X
  
  [30X    [33X[0;6Y[23Xk(G) = 6,7[123X, by Poland in [Pol68][133X
  
  [30X    [33X[0;6Y[23Xk(G) = 8[123X, by Kosvintsev in [Kos74][133X
  
  [30X    [33X[0;6Y[23Xk(G) = 9[123X, by Odincov and Starostin in [OS76][133X
  
  [30X    [33X[0;6Y[23Xk(G) = 10,11[123X, by Vera López and Vera López in [VV85][133X
  
  [30X    [33X[0;6Y[23Xk(G) = 12[123X, by Vera López and Vera López in [VV86][133X
  
  [30X    [33X[0;6Y[23Xk(G) = 13, 14[123X, by Vera López and Sangroniz in [VS07][133X
  
  [33X[0;0YRemarks:[133X
  
  [31X1[131X   [33X[0;6YIn  [VV85], three distinct groups of the form [23X(C_5 \times C_5) \rtimes
        C_4[123X  with  class  number  [23X10[123X  are given. However, only two such groups
        exist, being the ones with [10XIdClassNr[110X equal to [10X[10,25][110X and [10X[10,26][110X.[133X
  
  [31X2[131X   [33X[0;6YIn  [VV86],  48  groups  with  class  number  12 are listed. There are
        actually  51  such  groups,  the  three  groups  missing in [VV86] are
        provided  in  the  appendix  of  [VS07].  These  are  the  groups with
        [10XIdClassNr[110X equal to [10X[12,13][110X, [10X[12,16][110X and [10X[12,39][110X.[133X
  
  
  [1X2.2 [33X[0;0YGroups with 15 to 20 conjugacy classes[133X[101X
  
  [33X[0;0YThe [5XSmallClassNr[105X package also provides access to many (but probably not all)
  of  the  finite groups with class number 15 to 20. Although quite extensive,
  this should be considered as an [12Xincomplete[112X classification.[133X
  
  [33X[0;0YNote  that [2XIdClassNr[102X ([14X3.1-2[114X) may not work properly for these groups. While a
  [13Xknown[113X  group  of  class  number  15  to  20 will be correctly identified, an
  unknown group will produce an incorrect id or cause an error.[133X
  
  [1X2.2-1 LoadIncompleteSmallClassNrGroups[101X
  
  [33X[1;0Y[29X[2XLoadIncompleteSmallClassNrGroups[102X(  ) [32X function[133X
  
  [33X[0;0YLoads the known groups with class numbers 15 to 20.[133X
  
