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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
4
⋊C
8
Direct product G=N×Q with N=
C
7
and Q=
C
4
⋊C
8
d
ρ
Label
ID
C
7
×C
4
⋊C
8
224
C7xC4:C8
224,54
Semidirect products G=N:Q with N=
C
7
and Q=
C
4
⋊C
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
4
⋊C
8
) =
C
28
⋊C
8
φ:
C
4
⋊C
8
/
C
4
2
→
C
2
⊆ Aut
C
7
224
C7:1(C4:C8)
224,10
C
7
⋊
2
(C
4
⋊C
8
) =
Dic
7
⋊C
8
φ:
C
4
⋊C
8
/
C
2
×C
8
→
C
2
⊆ Aut
C
7
224
C7:2(C4:C8)
224,20
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⋊
ℤ
𝔽
○
≀
ℚ
◁