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C
n
D
n
S
n
A
n
Degree
Linear
Irr Reps
Characters
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⋊
.
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≀
Alternating groups A
n
Group of
even
permutations {1,2,...,n}→{1,2,...,n}, of order ½·n!, index 2 in
S
n
.
Soluble
for n≤4 and
simple
for n≥5.
C
1
=A
1
=A
2
C
3
=A
3
A
4
A
5
A
6
×
⋊
ℤ
𝔽
○
≀
ℚ
◁