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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
3
and Q=
C
2
2
.F
5
Direct product G=N×Q with N=
C
3
and Q=
C
2
2
.F
5
d
ρ
Label
ID
C
3
×C
2
2
.F
5
120
4
C3xC2^2.F5
240,116
Semidirect products G=N:Q with N=
C
3
and Q=
C
2
2
.F
5
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
⋊
1
(C
2
2
.F
5
) =
D
6
.F
5
φ:
C
2
2
.F
5
/
C
5
⋊C
8
→
C
2
⊆ Aut
C
3
120
8-
C3:1(C2^2.F5)
240,100
C
3
⋊
2
(C
2
2
.F
5
) =
C
15
⋊
8
M
4
(2)
φ:
C
2
2
.F
5
/
C
2
×Dic
5
→
C
2
⊆ Aut
C
3
120
4
C3:2(C2^2.F5)
240,123
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○
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