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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
6
×Q
8
Direct product G=N×Q with N=
C
5
and Q=
C
6
×Q
8
d
ρ
Label
ID
Q
8
×C
30
240
Q8xC30
240,187
Semidirect products G=N:Q with N=
C
5
and Q=
C
6
×Q
8
extension
φ:Q→Aut N
d
ρ
Label
ID
C
5
⋊
1
(C
6
×Q
8
) =
C
6
×Dic
10
φ:
C
6
×Q
8
/
C
2
×C
12
→
C
2
⊆ Aut
C
5
240
C5:1(C6xQ8)
240,155
C
5
⋊
2
(C
6
×Q
8
) =
C
3
×Q
8
×D
5
φ:
C
6
×Q
8
/
C
3
×Q
8
→
C
2
⊆ Aut
C
5
120
4
C5:2(C6xQ8)
240,161
×
⋊
ℤ
𝔽
○
≀
ℚ
◁