ATLAS: Alternating group A17
Order = 177843714048000
Mult = 2.
Out = 2.
The following information is available for A17:
Standard generators of A17 are a in class 3A,
b of order 15 such that ab has order 17 (so we must
have b in class 15G).
In the natural
representation we may take
a = (1, 2, 3) and
b = (3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17).
Standard generators of S17 are c in class 2E,
d of order 16 such that cd has order 17 (so we must
have b in class 16A).
In the natural
representation we may take
c = (1, 2) and
d = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17).
To find standard generators of A17:
- Find an element of order 39 or 105 (probability about 1/16) and
power up to give an element s in class 3A.
- Find an element t of order 17 (probability about 1/9).
- Find a conjugate u of t such that su has
order 15 (probability about 1/40). Then u is in class 15G.
- Let a be the inverse of s and b be
su. Then a and b are standard generators
for A17.
To find standard generators of S17:
- Find an element of order 90 or 210 (probability 1/63) and
power up to give an element c in class 2E. Alternatively,
if you look among outer elements only, then elements of order
26 and 70 also work, and the probability rises to about 1/13.
- Find an element t of order 16 (probability 1/16).
- Find an conjugate d of t such that
cd has order 17 (probability about 1/9).
- The elements c and d are standard generators
for S17.
The representations of A17 available are:
- Some primitive permutation representations
-
Permutations on 17 points - the natural representation above:
a and
b (GAP).
-
Permutations on 136 points:
a and
b (GAP).
-
Permutations on 680 points:
a and
b (GAP).
-
Permutations on 2380 points:
a and
b (GAP).
- Some integer matrix representations
-
Dimension 16 (partition [2, 115]):
a and b (GAP).
-
Dimension 119 (partition [22, 113]):
a and b (GAP).
-
Dimension 120 (partition [3, 114]):
a and b (GAP).
-
Dimension 544 (partition [22, 111]):
a and b (GAP).
-
Dimension 560 (partition [4, 113]):
a and b (GAP).
The representations of S17 available are:
- Some primitive permutation representations
-
Permutations on 17 points - the natural representation above:
c and
d (GAP).
-
Permutations on 136 points:
c and
d (GAP).
-
Permutations on 680 points:
c and
d (GAP).
-
Permutations on 2380 points:
c and
d (GAP).
- Some integer matrix representations
-
Dimension 16 (partition [2, 115]):
c and d (GAP).
-
Dimension 119 (partition [22, 113]):
c and d (GAP).
-
Dimension 120 (partition [3, 114]):
c and d (GAP).
-
Dimension 544 (partition [22, 111]):
c and d (GAP).
-
Dimension 560 (partition [4, 113]):
c and d (GAP).
Go to main ATLAS (version 2.0) page.
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Anonymous ftp access is also available on
sylow.mat.bham.ac.uk.
Version 2.0 created on 17th February 2004.
Last updated 27.02.04 by SN.