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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
×S
3
and Q=
D
7
Direct product G=N×Q with N=
C
5
×S
3
and Q=
D
7
d
ρ
Label
ID
C
5
×S
3
×D
7
105
4
C5xS3xD7
420,25
Semidirect products G=N:Q with N=
C
5
×S
3
and Q=
D
7
extension
φ:Q→Out N
d
ρ
Label
ID
(C
5
×S
3
)⋊D
7
=
S
3
×D
35
φ:
D
7
/
C
7
→
C
2
⊆ Out
C
5
×S
3
105
4+
(C5xS3):D7
420,29
×
⋊
ℤ
𝔽
○
≀
ℚ
◁