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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
4
and Q=
C
5
×C
10
Direct product G=N×Q with N=
C
4
and Q=
C
5
×C
10
d
ρ
Label
ID
C
10
×C
20
200
C10xC20
200,37
Semidirect products G=N:Q with N=
C
4
and Q=
C
5
×C
10
extension
φ:Q→Aut N
d
ρ
Label
ID
C
4
⋊(C
5
×C
10
) =
D
4
×C
5
2
φ:
C
5
×C
10
/
C
5
2
→
C
2
⊆ Aut
C
4
100
C4:(C5xC10)
200,38
Non-split extensions G=N.Q with N=
C
4
and Q=
C
5
×C
10
extension
φ:Q→Aut N
d
ρ
Label
ID
C
4
.(C
5
×C
10
) =
Q
8
×C
5
2
φ:
C
5
×C
10
/
C
5
2
→
C
2
⊆ Aut
C
4
200
C4.(C5xC10)
200,39
×
⋊
ℤ
𝔽
○
≀
ℚ
◁