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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
3
×A
4
Direct product G=N×Q with N=
C
7
and Q=
C
3
×A
4
d
ρ
Label
ID
A
4
×C
21
84
3
A4xC21
252,39
Semidirect products G=N:Q with N=
C
7
and Q=
C
3
×A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
3
×A
4
) =
A
4
×C
7
⋊C
3
φ:
C
3
×A
4
/
A
4
→
C
3
⊆ Aut
C
7
28
9
C7:1(C3xA4)
252,27
C
7
⋊
2
(C
3
×A
4
) =
C
3
×C
7
⋊A
4
φ:
C
3
×A
4
/
C
2
×C
6
→
C
3
⊆ Aut
C
7
84
3
C7:2(C3xA4)
252,40
×
⋊
ℤ
𝔽
○
≀
ℚ
◁