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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
8
.
4
Q
8
Direct product G=N×Q with N=
C
7
and Q=
C
8
.
4
Q
8
d
ρ
Label
ID
C
7
×C
8
.
4
Q
8
224
2
C7xC8.4Q8
448,172
Semidirect products G=N:Q with N=
C
7
and Q=
C
8
.
4
Q
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
8
.
4
Q
8
) =
C
8
.
7
Dic
14
φ:
C
8
.
4
Q
8
/
C
8
.C
4
→
C
2
⊆ Aut
C
7
224
4
C7:1(C8.4Q8)
448,50
C
7
⋊
2
(C
8
.
4
Q
8
) =
C
112
.C
4
φ:
C
8
.
4
Q
8
/
C
2
×C
16
→
C
2
⊆ Aut
C
7
224
2
C7:2(C8.4Q8)
448,63
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𝔽
○
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