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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
×C
3
.A
4
Direct product G=N×Q with N=
C
5
and Q=
C
2
×C
3
.A
4
d
ρ
Label
ID
C
10
×C
3
.A
4
90
3
C10xC3.A4
360,46
Semidirect products G=N:Q with N=
C
5
and Q=
C
2
×C
3
.A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
2
×C
3
.A
4
) =
D
5
×C
3
.A
4
φ:
C
2
×C
3
.A
4
/
C
3
.A
4
→
C
2
⊆ Aut
C
5
90
6
C5:(C2xC3.A4)
360,42
×
⋊
ℤ
𝔽
○
≀
ℚ
◁