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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=
S
3
×C
9
Direct product G=N×Q with N=
C
5
and Q=
S
3
×C
9
d
ρ
Label
ID
S
3
×C
45
90
2
S3xC45
270,9
Semidirect products G=N:Q with N=
C
5
and Q=
S
3
×C
9
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(S
3
×C
9
) =
C
9
×D
15
φ:
S
3
×C
9
/
C
3
×C
9
→
C
2
⊆ Aut
C
5
90
2
C5:(S3xC9)
270,13
×
⋊
ℤ
𝔽
○
≀
ℚ
◁