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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=
S
4
Direct product G=N×Q with N=
D
5
and Q=
S
4
d
ρ
Label
ID
D
5
×S
4
20
6+
D5xS4
240,194
Non-split extensions G=N.Q with N=
D
5
and Q=
S
4
extension
φ:Q→Out N
d
ρ
Label
ID
D
5
.S
4
=
A
4
⋊F
5
φ:
S
4
/
A
4
→
C
2
⊆ Out
D
5
20
12+
D5.S4
240,192
×
⋊
ℤ
𝔽
○
≀
ℚ
◁