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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
2
and Q=
C
27
Direct product G=N×Q with N=
C
3
2
and Q=
C
27
d
ρ
Label
ID
C
3
2
×C
27
243
C3^2xC27
243,48
Semidirect products G=N:Q with N=
C
3
2
and Q=
C
27
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
2
⋊C
27
=
C
3
2
⋊C
27
φ:
C
27
/
C
9
→
C
3
⊆ Aut
C
3
2
81
C3^2:C27
243,12
Non-split extensions G=N.Q with N=
C
3
2
and Q=
C
27
extension
φ:Q→Aut N
d
ρ
Label
ID
C
3
2
.C
27
=
C
81
⋊C
3
φ:
C
27
/
C
9
→
C
3
⊆ Aut
C
3
2
81
3
C3^2.C27
243,24
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𝔽
○
≀
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◁