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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
21
Direct product G=N×Q with N=
Q
8
and Q=
C
21
d
ρ
Label
ID
Q
8
×C
21
168
2
Q8xC21
168,41
Semidirect products G=N:Q with N=
Q
8
and Q=
C
21
extension
φ:Q→Out N
d
ρ
Label
ID
Q
8
⋊C
21
=
C
7
×SL
2
(𝔽
3
)
φ:
C
21
/
C
7
→
C
3
⊆ Out
Q
8
56
2
Q8:C21
168,22
×
⋊
ℤ
𝔽
○
≀
ℚ
◁