> < ^ Date: Thu, 30 Mar 2000 09:14:23 +0100 (BST)
> < ^ From: Derek Holt <dfh@maths.warwick.ac.uk >
> < ^ Subject: Re: Maximal subgroups of SymmetricGroup(9)

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.

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