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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
3
.
84
C
2
3
Direct product G=N×Q with N=
C
5
and Q=
C
2
3
.
84
C
2
3
d
ρ
Label
ID
C
5
×C
2
3
.
84
C
2
3
320
C5xC2^3.84C2^3
320,902
Semidirect products G=N:Q with N=
C
5
and Q=
C
2
3
.
84
C
2
3
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(C
2
3
.
84
C
2
3
) =
(C
2
2
×C
4
).D
10
φ:
C
2
3
.
84
C
2
3
/
C
2
.C
4
2
→
C
2
⊆ Aut
C
5
320
C5:(C2^3.84C2^3)
320,289
×
⋊
ℤ
𝔽
○
≀
ℚ
◁