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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
27
and Q=
C
2
×Q
8
Direct product G=N×Q with N=
C
27
and Q=
C
2
×Q
8
d
ρ
Label
ID
Q
8
×C
54
432
Q8xC54
432,55
Semidirect products G=N:Q with N=
C
27
and Q=
C
2
×Q
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
27
⋊
1
(C
2
×Q
8
) =
C
2
×Dic
54
φ:
C
2
×Q
8
/
C
2
×C
4
→
C
2
⊆ Aut
C
27
432
C27:1(C2xQ8)
432,43
C
27
⋊
2
(C
2
×Q
8
) =
Q
8
×D
27
φ:
C
2
×Q
8
/
Q
8
→
C
2
⊆ Aut
C
27
216
4-
C27:2(C2xQ8)
432,49
×
⋊
ℤ
𝔽
○
≀
ℚ
◁