ATLAS: Linear group L3(13)
Order = 270178272 = 25.32.7.133.61.
Mult = 3.
Out = S3.
The following information is available for L3(13):
Standard generators of L3(13) are a and b where
a has order 2, b has order 3, ab has order 61
and ababb has order 4. (Extra condition added 1/11/05.)
Standard generators of the triple cover
3.L3(13) = SL3(13) are not defined.
Standard generators of L3(13):2 are not defined.
Standard generators of L3(13):3 = PGL3(13) are
not defined.
Standard generators of L3(13):S3 are not defined.
To find standard generators of L3(13):
- Find an element of even order. This powers up to a of order 2.
- Find an element of order divisible by 3. This powers up to t of
order 3.
- Find a conjugate b of t such that ab has order 61
and ababb has order 4.
- The elements a and b are standard generators.
The representations of L3(13) available are:
-
Permutations on 183a points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP). (Corrected 1/11/05)
-
Permutations on 183b points:
a and
b (Meataxe),
a and
b (Meataxe binary),
a and
b (GAP). (Corrected 1/11/05)
-
Dimension 182 over Z:
a and b (GAP).
-
Dimension 183 over Z:
a and b (GAP).
-
Dimension 183b over Z[i]:
a and b (GAP).
-
Dimension 183c over Z[i]:
a and b (GAP).
-
Dimension 366 over Z:
a and b (GAP).
— reducible over Q(i).
The representations of 3.L3(13) = SL3(13) available are:
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Version 2.0 file created on 3rd August 2004.
Last updated 13.12.05 by JNB.