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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=
Q
8
and Q=
C
3
×C
9
Direct product G=N×Q with N=
Q
8
and Q=
C
3
×C
9
d
ρ
Label
ID
Q
8
×C
3
×C
9
216
Q8xC3xC9
216,79
Semidirect products G=N:Q with N=
Q
8
and Q=
C
3
×C
9
extension
φ:Q→Out N
d
ρ
Label
ID
Q
8
⋊
1
(C
3
×C
9
) =
C
9
×SL
2
(𝔽
3
)
φ:
C
3
×C
9
/
C
9
→
C
3
⊆ Out
Q
8
72
2
Q8:1(C3xC9)
216,38
Q
8
⋊
2
(C
3
×C
9
) =
C
3
×Q
8
⋊C
9
φ:
C
3
×C
9
/
C
3
2
→
C
3
⊆ Out
Q
8
216
Q8:2(C3xC9)
216,40
×
⋊
ℤ
𝔽
○
≀
ℚ
◁