Home
About
Cn
Dn
Sn
An
Degree
Linear
Irr Reps
Characters
×
⋊
.
○
≀

Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C3×D5

Direct product G=N×Q with N=C2×C4 and Q=C3×D5
dρLabelID
D5×C2×C12120D5xC2xC12240,156

Semidirect products G=N:Q with N=C2×C4 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C3×D5) = C3×D10⋊C4φ: C3×D5/C15 → C2 ⊆ Aut C2×C4120(C2xC4):1(C3xD5)240,43
(C2×C4)⋊2(C3×D5) = C6×D20φ: C3×D5/C15 → C2 ⊆ Aut C2×C4120(C2xC4):2(C3xD5)240,157
(C2×C4)⋊3(C3×D5) = C3×C4○D20φ: C3×D5/C15 → C2 ⊆ Aut C2×C41202(C2xC4):3(C3xD5)240,158

Non-split extensions G=N.Q with N=C2×C4 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C3×D5) = C3×C10.D4φ: C3×D5/C15 → C2 ⊆ Aut C2×C4240(C2xC4).1(C3xD5)240,41
(C2×C4).2(C3×D5) = C3×C4.Dic5φ: C3×D5/C15 → C2 ⊆ Aut C2×C41202(C2xC4).2(C3xD5)240,39
(C2×C4).3(C3×D5) = C3×C4⋊Dic5φ: C3×D5/C15 → C2 ⊆ Aut C2×C4240(C2xC4).3(C3xD5)240,42
(C2×C4).4(C3×D5) = C6×Dic10φ: C3×D5/C15 → C2 ⊆ Aut C2×C4240(C2xC4).4(C3xD5)240,155
(C2×C4).5(C3×D5) = C6×C5⋊2C8central extension (φ=1)240(C2xC4).5(C3xD5)240,38
(C2×C4).6(C3×D5) = C12×Dic5central extension (φ=1)240(C2xC4).6(C3xD5)240,40

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁