Dear GAP Forum,

The list of primitive maximal subgroups of A_n and S_n that I sent a
few days ago contained four errors. Thanks to Joachim Neubueser and
Alexander Hulpke for noticing these!

The corrections are:

#17 should be [ [5], [8], [8] ]  not  [ [5], [4,8], [8] ],
#19 should be [ [6], [5], [] ]   not  [ [6], [5], [1] ],
#31 should be [ [8], [7,9,10], [9,10] ] not [ [8], [9,10], [9,10] ],
#49 should be [ [34,38], [32,37], [] ] not [ [34,38], [32,36], [] ],

The full corrected list follows.

For 1 <= n <= 50, maxprim[n][1] is the list of those r for which
PrimitiveGroup(n,r) is maximal in SymmetricGroup(n), but NOTE THAT THIS DOES
NOT INCLUDE AlternatingGroup(n), so you have to add that in separately.

maxprim[n][2] is the list of r for which PrimitiveGroup(n,r) is maximal in
AlternatingGroup(n) and maxprim[n][3] is the subset of maxprim[n][2]
consisting of those that split into two conjugacy classes in the alternating
group.

 maxprim := [
   [ [], [], [] ], 						# 1
   [ [], [], [] ], 						# 2
   [ [], [], [] ], 						# 3
   [ [], [], [] ], 						# 4
   [ [3], [2], [] ], 						# 5
   [ [2], [1], [] ], 						# 6
   [ [4], [5], [5] ], 						# 7
   [ [4], [5], [5] ], 						# 8
   [ [7], [6,9], [9] ], 					# 9
   [ [7], [6], [] ],	 					# 10
   [ [4], [6], [6] ],	 					# 11
   [ [2], [4], [4] ],	 					# 12
   [ [6], [5,7], [7] ], 					# 13
   [ [2], [1], [] ],	 					# 14
   [ [], [4], [4] ],	 					# 15
   [ [], [20], [20] ],	 					# 16
   [ [5], [8], [8] ],	 					# 17
   [ [2], [1], [] ],	 					# 18
   [ [6], [5], [] ],	 					# 19
   [ [2], [1], [] ],	 					# 20
   [ [1,3,7], [2,6], [] ], 					# 21
   [ [2], [1], [] ],	 					# 22
   [ [4], [5], [5] ],	 					# 23
   [ [2], [3], [3] ],	 					# 24
   [ [23,26], [21,24], [] ],					# 25
   [ [5], [2], [] ],						# 26
   [ [13], [11,12], [11] ],					# 27
   [ [11], [9,12], [12] ],					# 28
   [ [6], [5], [] ],						# 29
   [ [2], [1], [] ],	 					# 30
   [ [8], [7,9,10], [9,10] ],					# 31
   [ [4], [3,5], [5] ],					# 32
   [ [], [2], [2] ],	 					# 33
   [ [], [], [] ],	 					# 34
   [ [], [4], [4] ],	 					# 35
   [ [16,19], [14,20], [20] ],					# 36
   [ [9], [8], [] ],	 					# 37
   [ [2], [1], [] ],	 					# 38
   [ [], [], [] ],	 					# 39
   [ [4,6], [2,5], [] ],					# 40
   [ [8], [7], [] ],	 					# 41
   [ [2], [1], [] ],	 					# 42
   [ [8], [7], [] ],	 					# 43
   [ [2], [1], [] ],	 					# 44
   [ [5], [4,7], [7] ],					# 45
   [ [], [], [] ],	 					# 46
   [ [4], [3], [] ],	 					# 47
   [ [2], [1], [] ],	 					# 48
   [ [34,38], [32,37], [] ],					# 49
   [ [6], [2,7], [7] ]						# 50
];

Derek Holt.