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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=
2
+
1+4
and Q=
C
15
Direct product G=N×Q with N=
2
+
1+4
and Q=
C
15
d
ρ
Label
ID
C
15
×2
+
1+4
120
4
C15xES+(2,2)
480,1184
Semidirect products G=N:Q with N=
2
+
1+4
and Q=
C
15
extension
φ:Q→Out N
d
ρ
Label
ID
2
+
1+4
⋊
1
C
15
=
C
5
×Q
8
.A
4
φ:
C
15
/
C
5
→
C
3
⊆ Out
2
+
1+4
120
4
ES+(2,2):1C15
480,1131
2
+
1+4
⋊
2
C
15
=
C
5
×C
2
3
⋊A
4
φ:
C
15
/
C
5
→
C
3
⊆ Out
2
+
1+4
40
4
ES+(2,2):2C15
480,1134
×
⋊
ℤ
𝔽
○
≀
ℚ
◁