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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
2
3
and Q=
C
7
⋊C
3
Direct product G=N×Q with N=
C
2
3
and Q=
C
7
⋊C
3
d
ρ
Label
ID
C
2
3
×C
7
⋊C
3
56
C2^3xC7:C3
168,51
Semidirect products G=N:Q with N=
C
2
3
and Q=
C
7
⋊C
3
extension
φ:Q→Aut N
d
ρ
Label
ID
C
2
3
⋊(C
7
⋊C
3
) =
AΓL
1
(𝔽
8
)
φ:
C
7
⋊C
3
/
C
1
→
C
7
⋊C
3
⊆ Aut
C
2
3
8
7+
C2^3:(C7:C3)
168,43
C
2
3
⋊
2
(C
7
⋊C
3
) =
C
2
×C
7
⋊A
4
φ:
C
7
⋊C
3
/
C
7
→
C
3
⊆ Aut
C
2
3
42
3
C2^3:2(C7:C3)
168,53
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