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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
16
Direct product G=N×Q with N=
C
7
and Q=
C
4
×C
16
d
ρ
Label
ID
C
4
×C
112
448
C4xC112
448,149
Semidirect products G=N:Q with N=
C
7
and Q=
C
4
×C
16
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
4
×C
16
) =
C
4
×C
7
⋊C
16
φ:
C
4
×C
16
/
C
4
×C
8
→
C
2
⊆ Aut
C
7
448
C7:1(C4xC16)
448,17
C
7
⋊
2
(C
4
×C
16
) =
C
16
×Dic
7
φ:
C
4
×C
16
/
C
2
×C
16
→
C
2
⊆ Aut
C
7
448
C7:2(C4xC16)
448,57
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⋊
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𝔽
○
≀
ℚ
◁