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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
2
⋊C
4
Direct product G=N×Q with N=
C
7
and Q=
C
2
2
⋊C
4
d
ρ
Label
ID
C
7
×C
2
2
⋊C
4
56
C7xC2^2:C4
112,20
Semidirect products G=N:Q with N=
C
7
and Q=
C
2
2
⋊C
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
2
2
⋊C
4
) =
D
14
⋊C
4
φ:
C
2
2
⋊C
4
/
C
2
×C
4
→
C
2
⊆ Aut
C
7
56
C7:1(C2^2:C4)
112,13
C
7
⋊
2
(C
2
2
⋊C
4
) =
C
2
3
.D
7
φ:
C
2
2
⋊C
4
/
C
2
3
→
C
2
⊆ Aut
C
7
56
C7:2(C2^2:C4)
112,18
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○
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◁