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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
.
10
C
4
2
Direct product G=N×Q with N=
C
7
and Q=
C
4
.
10
C
4
2
d
ρ
Label
ID
C
7
×C
4
.
10
C
4
2
112
4
C7xC4.10C4^2
448,142
Semidirect products G=N:Q with N=
C
7
and Q=
C
4
.
10
C
4
2
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊(C
4
.
10
C
4
2
) =
C
28
.
21
C
4
2
φ:
C
4
.
10
C
4
2
/
C
2
×M
4
(2)
→
C
2
⊆ Aut
C
7
112
4
C7:(C4.10C4^2)
448,117
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⋊
ℤ
𝔽
○
≀
ℚ
◁