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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
2
×C
4
and Q=
C
3
.A
4
Direct product G=N×Q with N=
C
2
×C
4
and Q=
C
3
.A
4
d
ρ
Label
ID
C
2
×C
4
×C
3
.A
4
72
C2xC4xC3.A4
288,343
Non-split extensions G=N.Q with N=
C
2
×C
4
and Q=
C
3
.A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
(C
2
×C
4
).
1
(C
3
.A
4
) =
C
4
×Q
8
⋊C
9
central extension (φ=1)
288
(C2xC4).1(C3.A4)
288,72
(C
2
×C
4
).
2
(C
3
.A
4
) =
C
2
×Q
8
.C
18
central extension (φ=1)
144
(C2xC4).2(C3.A4)
288,347
×
⋊
ℤ
𝔽
○
≀
ℚ
◁