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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=
3
-
1+2
Direct product G=N×Q with N=
Q
8
and Q=
3
-
1+2
d
ρ
Label
ID
Q
8
×3
-
1+2
72
6
Q8xES-(3,1)
216,81
Semidirect products G=N:Q with N=
Q
8
and Q=
3
-
1+2
extension
φ:Q→Out N
d
ρ
Label
ID
Q
8
⋊
1
3
-
1+2
=
C
18
.A
4
φ:
3
-
1+2
/
C
9
→
C
3
⊆ Out
Q
8
72
6
Q8:1ES-(3,1)
216,39
Q
8
⋊
2
3
-
1+2
=
Q
8
⋊3
-
1+2
φ:
3
-
1+2
/
C
3
2
→
C
3
⊆ Out
Q
8
72
6
Q8:2ES-(3,1)
216,41
×
⋊
ℤ
𝔽
○
≀
ℚ
◁