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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=
C
2
×S
4
Direct product G=N×Q with N=
C
7
and Q=
C
2
×S
4
d
ρ
Label
ID
C
14
×S
4
42
3
C14xS4
336,214
Semidirect products G=N:Q with N=
C
7
and Q=
C
2
×S
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
2
×S
4
) =
D
7
×S
4
φ:
C
2
×S
4
/
S
4
→
C
2
⊆ Aut
C
7
28
6+
C7:1(C2xS4)
336,212
C
7
⋊
2
(C
2
×S
4
) =
C
2
×C
7
⋊S
4
φ:
C
2
×S
4
/
C
2
×A
4
→
C
2
⊆ Aut
C
7
42
6+
C7:2(C2xS4)
336,215
×
⋊
ℤ
𝔽
○
≀
ℚ
◁