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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=
D
5
and Q=
2
+
1+4
Direct product G=N×Q with N=
D
5
and Q=
2
+
1+4
d
ρ
Label
ID
D
5
×2
+
1+4
40
8+
D5xES+(2,2)
320,1622
Non-split extensions G=N.Q with N=
D
5
and Q=
2
+
1+4
extension
φ:Q→Out N
d
ρ
Label
ID
D
5
.
1
2
+
1+4
=
D
10
.C
2
4
φ:
2
+
1+4
/
C
2
×D
4
→
C
2
⊆ Out
D
5
40
8+
D5.1ES+(2,2)
320,1596
D
5
.
2
2
+
1+4
=
D
5
.2
+
1+4
φ:
2
+
1+4
/
C
4
○D
4
→
C
2
⊆ Out
D
5
40
8
D5.2ES+(2,2)
320,1604
×
⋊
ℤ
𝔽
○
≀
ℚ
◁