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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=
C
8
×A
4
Direct product G=N×Q with N=
C
3
and Q=
C
8
×A
4
d
ρ
Label
ID
A
4
×C
24
72
3
A4xC24
288,637
Semidirect products G=N:Q with N=
C
3
and Q=
C
8
×A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
⋊(C
8
×A
4
) =
A
4
×C
3
⋊C
8
φ:
C
8
×A
4
/
C
4
×A
4
→
C
2
⊆ Aut
C
3
72
6
C3:(C8xA4)
288,408
Non-split extensions G=N.Q with N=
C
3
and Q=
C
8
×A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
.(C
8
×A
4
) =
C
8
×C
3
.A
4
central extension (φ=1)
72
3
C3.(C8xA4)
288,76
×
⋊
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𝔽
○
≀
ℚ
◁