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C
n
D
n
S
n
A
n
Degree
Linear
Irr Reps
Characters
×
⋊
.
○
≀
Extensions
1→N→G→Q→1 with N=
C
5
and Q=
C
2
×S
4
Direct product G=N×Q with N=
C
5
and Q=
C
2
×S
4
d
ρ
Label
ID
C
10
×S
4
30
3
C10xS4
240,196
Semidirect products G=N:Q with N=
C
5
and Q=
C
2
×S
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊
1
(C
2
×S
4
) =
D
5
×S
4
φ:
C
2
×S
4
/
S
4
→
C
2
⊆ Aut
C
5
20
6+
C5:1(C2xS4)
240,194
C
5
⋊
2
(C
2
×S
4
) =
C
2
×C
5
⋊S
4
φ:
C
2
×S
4
/
C
2
×A
4
→
C
2
⊆ Aut
C
5
30
6+
C5:2(C2xS4)
240,197
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⋊
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𝔽
○
≀
ℚ
◁