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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
2
and Q=
C
5
Direct product G=N×Q with N=
C
10
2
and Q=
C
5
d
ρ
Label
ID
C
5
×C
10
2
500
C5xC10^2
500,56
Semidirect products G=N:Q with N=
C
10
2
and Q=
C
5
extension
φ:Q→Aut N
d
ρ
Label
ID
C
10
2
⋊C
5
=
C
2
2
×He
5
φ:
C
5
/
C
1
→
C
5
⊆ Aut
C
10
2
100
C10^2:C5
500,35
Non-split extensions G=N.Q with N=
C
10
2
and Q=
C
5
extension
φ:Q→Aut N
d
ρ
Label
ID
C
10
2
.C
5
=
C
2
2
×5
-
1+2
φ:
C
5
/
C
1
→
C
5
⊆ Aut
C
10
2
100
C10^2.C5
500,36
×
⋊
ℤ
𝔽
○
≀
ℚ
◁