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

Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C3⋊S3

Direct product G=N×Q with N=C3×C6 and Q=C3⋊S3
dρLabelID
C3⋊S3×C3×C636C3:S3xC3xC6324,173

Semidirect products G=N:Q with N=C3×C6 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1(C3⋊S3) = C2×He3⋊4S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C654(C3xC6):1(C3:S3)324,144
(C3×C6)⋊2(C3⋊S3) = C2×He3⋊5S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6366(C3xC6):2(C3:S3)324,150
(C3×C6)⋊3(C3⋊S3) = C6×C33⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6108(C3xC6):3(C3:S3)324,174
(C3×C6)⋊4(C3⋊S3) = C2×C34⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6162(C3xC6):4(C3:S3)324,175

Non-split extensions G=N.Q with N=C3×C6 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C3⋊S3) = C33⋊Dic3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6366-(C3xC6).1(C3:S3)324,22
(C3×C6).2(C3⋊S3) = He3.3Dic3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C61086-(C3xC6).2(C3:S3)324,23
(C3×C6).3(C3⋊S3) = He3⋊Dic3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C61086-(C3xC6).3(C3:S3)324,24
(C3×C6).4(C3⋊S3) = 3- 1+2.Dic3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C61086-(C3xC6).4(C3:S3)324,25
(C3×C6).5(C3⋊S3) = C2×C33⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6186+(C3xC6).5(C3:S3)324,77
(C3×C6).6(C3⋊S3) = C2×He3.3S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6546+(C3xC6).6(C3:S3)324,78
(C3×C6).7(C3⋊S3) = C2×He3⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6546+(C3xC6).7(C3:S3)324,79
(C3×C6).8(C3⋊S3) = C2×3- 1+2.S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6546+(C3xC6).8(C3:S3)324,80
(C3×C6).9(C3⋊S3) = C33⋊4C12φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6108(C3xC6).9(C3:S3)324,98
(C3×C6).10(C3⋊S3) = C33.Dic3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6108(C3xC6).10(C3:S3)324,100
(C3×C6).11(C3⋊S3) = He3.4Dic3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C61086-(C3xC6).11(C3:S3)324,101
(C3×C6).12(C3⋊S3) = He3⋊6Dic3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6366(C3xC6).12(C3:S3)324,104
(C3×C6).13(C3⋊S3) = C2×C33.S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C654(C3xC6).13(C3:S3)324,146
(C3×C6).14(C3⋊S3) = C2×He3.4S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C6546+(C3xC6).14(C3:S3)324,147
(C3×C6).15(C3⋊S3) = C9⋊Dic9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6324(C3xC6).15(C3:S3)324,19
(C3×C6).16(C3⋊S3) = C32⋊2Dic9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6366(C3xC6).16(C3:S3)324,20
(C3×C6).17(C3⋊S3) = C2×C9⋊D9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6162(C3xC6).17(C3:S3)324,74
(C3×C6).18(C3⋊S3) = C2×C32⋊2D9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6366(C3xC6).18(C3:S3)324,75
(C3×C6).19(C3⋊S3) = C3×C9⋊Dic3φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6108(C3xC6).19(C3:S3)324,96
(C3×C6).20(C3⋊S3) = C32⋊5Dic9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6324(C3xC6).20(C3:S3)324,103
(C3×C6).21(C3⋊S3) = C6×C9⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6108(C3xC6).21(C3:S3)324,142
(C3×C6).22(C3⋊S3) = C2×C32⋊4D9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6162(C3xC6).22(C3:S3)324,149
(C3×C6).23(C3⋊S3) = C3×C33⋊5C4φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6108(C3xC6).23(C3:S3)324,157
(C3×C6).24(C3⋊S3) = C34⋊8C4φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C6324(C3xC6).24(C3:S3)324,158
(C3×C6).25(C3⋊S3) = C3×He3⋊3C4central extension (φ=1)108(C3xC6).25(C3:S3)324,99
(C3×C6).26(C3⋊S3) = C6×He3⋊C2central extension (φ=1)54(C3xC6).26(C3:S3)324,145
(C3×C6).27(C3⋊S3) = C32×C3⋊Dic3central extension (φ=1)36(C3xC6).27(C3:S3)324,156

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁