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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
5
×A
4
Direct product G=N×Q with N=
C
2
×C
4
and Q=
C
5
×A
4
d
ρ
Label
ID
A
4
×C
2
×C
20
120
A4xC2xC20
480,1126
Non-split extensions G=N.Q with N=
C
2
×C
4
and Q=
C
5
×A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
(C
2
×C
4
).
1
(C
5
×A
4
) =
C
20
×SL
2
(𝔽
3
)
central extension (φ=1)
160
(C2xC4).1(C5xA4)
480,655
(C
2
×C
4
).
2
(C
5
×A
4
) =
C
10
×C
4
.A
4
central extension (φ=1)
160
(C2xC4).2(C5xA4)
480,1130
×
⋊
ℤ
𝔽
○
≀
ℚ
◁