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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=
2
+
1+4
Direct product G=N×Q with N=
C
7
and Q=
2
+
1+4
d
ρ
Label
ID
C
7
×2
+
1+4
56
4
C7xES+(2,2)
224,193
Semidirect products G=N:Q with N=
C
7
and Q=
2
+
1+4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
2
+
1+4
=
D
4
⋊
6
D
14
φ:
2
+
1+4
/
C
2
×D
4
→
C
2
⊆ Aut
C
7
56
4
C7:1ES+(2,2)
224,180
C
7
⋊
2
2
+
1+4
=
D
4
⋊
8
D
14
φ:
2
+
1+4
/
C
4
○D
4
→
C
2
⊆ Aut
C
7
56
4+
C7:2ES+(2,2)
224,185
×
⋊
ℤ
𝔽
○
≀
ℚ
◁