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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
5
and Q=
C
3
×Q
16
Direct product G=N×Q with N=
C
5
and Q=
C
3
×Q
16
d
ρ
Label
ID
C
15
×Q
16
240
2
C15xQ16
240,88
Semidirect products G=N:Q with N=
C
5
and Q=
C
3
×Q
16
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊
1
(C
3
×Q
16
) =
C
3
×Dic
20
φ:
C
3
×Q
16
/
C
24
→
C
2
⊆ Aut
C
5
240
2
C5:1(C3xQ16)
240,37
C
5
⋊
2
(C
3
×Q
16
) =
C
3
×C
5
⋊Q
16
φ:
C
3
×Q
16
/
C
3
×Q
8
→
C
2
⊆ Aut
C
5
240
4
C5:2(C3xQ16)
240,47
×
⋊
ℤ
𝔽
○
≀
ℚ
◁