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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
10
and Q=
C
50
Direct product G=N×Q with N=
C
10
and Q=
C
50
d
ρ
Label
ID
C
10
×C
50
500
C10xC50
500,34
Semidirect products G=N:Q with N=
C
10
and Q=
C
50
extension
φ:Q→Aut N
d
ρ
Label
ID
C
10
⋊C
50
=
D
5
×C
50
φ:
C
50
/
C
25
→
C
2
⊆ Aut
C
10
100
2
C10:C50
500,29
Non-split extensions G=N.Q with N=
C
10
and Q=
C
50
extension
φ:Q→Aut N
d
ρ
Label
ID
C
10
.C
50
=
Dic
5
×C
25
φ:
C
50
/
C
25
→
C
2
⊆ Aut
C
10
100
2
C10.C50
500,7
×
⋊
ℤ
𝔽
○
≀
ℚ
◁