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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
×He
3
Direct product G=N×Q with N=
C
5
and Q=
C
2
×He
3
d
ρ
Label
ID
C
10
×He
3
90
3
C10xHe3
270,21
Semidirect products G=N:Q with N=
C
5
and Q=
C
2
×He
3
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
2
×He
3
) =
D
5
×He
3
φ:
C
2
×He
3
/
He
3
→
C
2
⊆ Aut
C
5
45
6
C5:(C2xHe3)
270,6
×
⋊
ℤ
𝔽
○
≀
ℚ
◁