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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
5
and Q=
C
4
×A
4
Direct product G=N×Q with N=
C
5
and Q=
C
4
×A
4
d
ρ
Label
ID
A
4
×C
20
60
3
A4xC20
240,152
Semidirect products G=N:Q with N=
C
5
and Q=
C
4
×A
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
4
×A
4
) =
A
4
×F
5
φ:
C
4
×A
4
/
A
4
→
C
4
⊆ Aut
C
5
20
12+
C5:(C4xA4)
240,193
C
5
⋊
2
(C
4
×A
4
) =
A
4
×Dic
5
φ:
C
4
×A
4
/
C
2
×A
4
→
C
2
⊆ Aut
C
5
60
6-
C5:2(C4xA4)
240,110
×
⋊
ℤ
𝔽
○
≀
ℚ
◁