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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
×C
8
Direct product G=N×Q with N=
C
27
and Q=
C
2
×C
8
d
ρ
Label
ID
C
2
×C
216
432
C2xC216
432,23
Semidirect products G=N:Q with N=
C
27
and Q=
C
2
×C
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
27
⋊
1
(C
2
×C
8
) =
C
8
×D
27
φ:
C
2
×C
8
/
C
8
→
C
2
⊆ Aut
C
27
216
2
C27:1(C2xC8)
432,5
C
27
⋊
2
(C
2
×C
8
) =
C
2
×C
27
⋊C
8
φ:
C
2
×C
8
/
C
2
×C
4
→
C
2
⊆ Aut
C
27
432
C27:2(C2xC8)
432,9
×
⋊
ℤ
𝔽
○
≀
ℚ
◁