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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
2
×SL
2
(𝔽
3
)
Direct product G=N×Q with N=
C
5
and Q=
C
2
×SL
2
(𝔽
3
)
d
ρ
Label
ID
C
10
×SL
2
(𝔽
3
)
80
C10xSL(2,3)
240,153
Semidirect products G=N:Q with N=
C
5
and Q=
C
2
×SL
2
(𝔽
3
)
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
2
×SL
2
(𝔽
3
)) =
D
5
×SL
2
(𝔽
3
)
φ:
C
2
×SL
2
(𝔽
3
)
/
SL
2
(𝔽
3
)
→
C
2
⊆ Aut
C
5
40
4-
C5:(C2xSL(2,3))
240,109
×
⋊
ℤ
𝔽
○
≀
ℚ
◁