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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
3
and Q=
F
7
Direct product G=N×Q with N=
C
3
and Q=
F
7
d
ρ
Label
ID
C
3
×F
7
21
6
C3xF7
126,7
Semidirect products G=N:Q with N=
C
3
and Q=
F
7
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
⋊F
7
=
C
3
⋊F
7
φ:
F
7
/
C
7
⋊C
3
→
C
2
⊆ Aut
C
3
21
6+
C3:F7
126,9
Non-split extensions G=N.Q with N=
C
3
and Q=
F
7
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
.F
7
=
C
7
⋊C
18
central extension (φ=1)
63
6
C3.F7
126,1
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⋊
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𝔽
○
≀
ℚ
◁