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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
7
and Q=
GL
2
(𝔽
3
)
Direct product G=N×Q with N=
C
7
and Q=
GL
2
(𝔽
3
)
d
ρ
Label
ID
C
7
×GL
2
(𝔽
3
)
56
2
C7xGL(2,3)
336,116
Semidirect products G=N:Q with N=
C
7
and Q=
GL
2
(𝔽
3
)
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊GL
2
(𝔽
3
) =
Q
8
⋊D
21
φ:
GL
2
(𝔽
3
)
/
SL
2
(𝔽
3
)
→
C
2
⊆ Aut
C
7
56
4+
C7:GL(2,3)
336,119
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𝔽
○
≀
ℚ
◁