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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
54
Direct product G=N×Q with N=
C
5
and Q=
C
54
d
ρ
Label
ID
C
270
270
1
C270
270,4
Semidirect products G=N:Q with N=
C
5
and Q=
C
54
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊C
54
=
D
5
×C
27
φ:
C
54
/
C
27
→
C
2
⊆ Aut
C
5
135
2
C5:C54
270,2
×
⋊
ℤ
𝔽
○
≀
ℚ
◁