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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
2
4
and Q=
C
27
Direct product G=N×Q with N=
C
2
4
and Q=
C
27
d
ρ
Label
ID
C
2
3
×C
54
432
C2^3xC54
432,228
Semidirect products G=N:Q with N=
C
2
4
and Q=
C
27
extension
φ:Q→Aut N
d
ρ
Label
ID
C
2
4
⋊
1
C
27
=
C
2
2
×C
9
.A
4
φ:
C
27
/
C
9
→
C
3
⊆ Aut
C
2
4
108
C2^4:1C27
432,225
C
2
4
⋊
2
C
27
=
C
2
4
⋊C
27
φ:
C
27
/
C
9
→
C
3
⊆ Aut
C
2
4
108
C2^4:2C27
432,226
×
⋊
ℤ
𝔽
○
≀
ℚ
◁