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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=
He
5
and Q=
C
2
Direct product G=N×Q with N=
He
5
and Q=
C
2
d
ρ
Label
ID
C
2
×He
5
50
5
C2xHe5
250,10
Semidirect products G=N:Q with N=
He
5
and Q=
C
2
extension
φ:Q→Out N
d
ρ
Label
ID
He
5
⋊
1
C
2
=
C
5
2
⋊C
10
φ:
C
2
/
C
1
→
C
2
⊆ Out
He
5
25
10+
He5:1C2
250,5
He
5
⋊
2
C
2
=
He
5
⋊C
2
φ:
C
2
/
C
1
→
C
2
⊆ Out
He
5
25
5
He5:2C2
250,8
×
⋊
ℤ
𝔽
○
≀
ℚ
◁