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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
.A
4
and Q=
C
2
×C
4
Direct product G=N×Q with N=
C
3
.A
4
and Q=
C
2
×C
4
d
ρ
Label
ID
C
2
×C
4
×C
3
.A
4
72
C2xC4xC3.A4
288,343
Semidirect products G=N:Q with N=
C
3
.A
4
and Q=
C
2
×C
4
extension
φ:Q→Out N
d
ρ
Label
ID
C
3
.A
4
⋊
1
(C
2
×C
4
) =
C
4
×C
3
.S
4
φ:
C
2
×C
4
/
C
4
→
C
2
⊆ Out
C
3
.A
4
36
6
C3.A4:1(C2xC4)
288,333
C
3
.A
4
⋊
2
(C
2
×C
4
) =
C
2
×C
6
.S
4
φ:
C
2
×C
4
/
C
2
2
→
C
2
⊆ Out
C
3
.A
4
72
C3.A4:2(C2xC4)
288,341
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⋊
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𝔽
○
≀
ℚ
◁