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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=
He
3
⋊C
2
Direct product G=N×Q with N=
C
5
and Q=
He
3
⋊C
2
d
ρ
Label
ID
C
5
×He
3
⋊C
2
45
3
C5xHe3:C2
270,17
Semidirect products G=N:Q with N=
C
5
and Q=
He
3
⋊C
2
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊(He
3
⋊C
2
) =
C
3
2
⋊D
15
φ:
He
3
⋊C
2
/
He
3
→
C
2
⊆ Aut
C
5
45
6
C5:(He3:C2)
270,19
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𝔽
○
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ℚ
◁