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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
5
and Q=
C
7
⋊C
12
Direct product G=N×Q with N=
C
5
and Q=
C
7
⋊C
12
d
ρ
Label
ID
C
5
×C
7
⋊C
12
140
6
C5xC7:C12
420,1
Semidirect products G=N:Q with N=
C
5
and Q=
C
7
⋊C
12
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
7
⋊C
12
) =
C
35
⋊C
12
φ:
C
7
⋊C
12
/
C
7
⋊C
3
→
C
4
⊆ Aut
C
5
35
12
C5:(C7:C12)
420,15
C
5
⋊
2
(C
7
⋊C
12
) =
C
35
⋊
3
C
12
φ:
C
7
⋊C
12
/
C
2
×C
7
⋊C
3
→
C
2
⊆ Aut
C
5
140
6-
C5:2(C7:C12)
420,3
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