Home
About
Cn
Dn
Sn
An
Degree
Linear
Irr Reps
Characters
x
:
.
o
wr

Extensions 1→N→G→Q→1 with N=2- 1+4 and Q=C4

Direct product G=NxQ with N=2- 1+4 and Q=C4
dρLabelID
C4x2- 1+464C4xES-(2,2)128,2162

Semidirect products G=N:Q with N=2- 1+4 and Q=C4
extensionφ:Q→Out NdρLabelID
2- 1+4:C4 = C42.3D4φ: C4/C1 → C4 ⊆ Out 2- 1+4164ES-(2,2):C4128,136
2- 1+4:2C4 = 2- 1+4:2C4φ: C4/C2 → C2 ⊆ Out 2- 1+432ES-(2,2):2C4128,525
2- 1+4:3C4 = 2+ 1+4:4C4φ: C4/C2 → C2 ⊆ Out 2- 1+4324ES-(2,2):3C4128,526
2- 1+4:4C4 = 2- 1+4:4C4φ: C4/C2 → C2 ⊆ Out 2- 1+464ES-(2,2):4C4128,1630
2- 1+4:5C4 = 2- 1+4:5C4φ: C4/C2 → C2 ⊆ Out 2- 1+4164ES-(2,2):5C4128,1633

Non-split extensions G=N.Q with N=2- 1+4 and Q=C4
extensionφ:Q→Out NdρLabelID
2- 1+4.C4 = C42.4D4φ: C4/C1 → C4 ⊆ Out 2- 1+4164-ES-(2,2).C4128,137
2- 1+4.2C4 = C4.22C25φ: trivial image324ES-(2,2).2C4128,2305

׿
x
:
Z
F
o
wr
Q
<