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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
4
and Q=
C
80
Direct product G=N×Q with N=
C
4
and Q=
C
80
d
ρ
Label
ID
C
4
×C
80
320
C4xC80
320,150
Semidirect products G=N:Q with N=
C
4
and Q=
C
80
extension
φ:Q→Aut N
d
ρ
Label
ID
C
4
⋊C
80
=
C
5
×C
4
⋊C
16
φ:
C
80
/
C
40
→
C
2
⊆ Aut
C
4
320
C4:C80
320,168
Non-split extensions G=N.Q with N=
C
4
and Q=
C
80
extension
φ:Q→Aut N
d
ρ
Label
ID
C
4
.C
80
=
C
5
×M
6
(2)
φ:
C
80
/
C
40
→
C
2
⊆ Aut
C
4
160
2
C4.C80
320,175
×
⋊
ℤ
𝔽
○
≀
ℚ
◁