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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
4
×C
56
224
C4xC56
224,45
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
4
×C
7
⋊C
8
φ:
C
4
×C
8
/
C
4
2
→
C
2
⊆ Aut
C
7
224
C7:1(C4xC8)
224,8
C
7
⋊
2
(C
4
×C
8
) =
C
8
×Dic
7
φ:
C
4
×C
8
/
C
2
×C
8
→
C
2
⊆ Aut
C
7
224
C7:2(C4xC8)
224,19
×
⋊
ℤ
𝔽
○
≀
ℚ
◁