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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
4
○D
4
and Q=
C
27
Direct product G=N×Q with N=
C
4
○D
4
and Q=
C
27
d
ρ
Label
ID
C
4
○D
4
×C
27
216
2
C4oD4xC27
432,56
Semidirect products G=N:Q with N=
C
4
○D
4
and Q=
C
27
extension
φ:Q→Out N
d
ρ
Label
ID
C
4
○D
4
⋊C
27
=
Q
8
.C
54
φ:
C
27
/
C
9
→
C
3
⊆ Out
C
4
○D
4
216
2
C4oD4:C27
432,42
×
⋊
ℤ
𝔽
○
≀
ℚ
◁