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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
3
2
⋊C
6
Direct product G=N×Q with N=
C
5
and Q=
C
3
2
⋊C
6
d
ρ
Label
ID
C
5
×C
3
2
⋊C
6
45
6
C5xC3^2:C6
270,10
Semidirect products G=N:Q with N=
C
5
and Q=
C
3
2
⋊C
6
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
3
2
⋊C
6
) =
He
3
⋊D
5
φ:
C
3
2
⋊C
6
/
He
3
→
C
2
⊆ Aut
C
5
45
6+
C5:(C3^2:C6)
270,14
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⋊
ℤ
𝔽
○
≀
ℚ
◁