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

Extensions 1→N→G→Q→1 with N=C3×C9 and Q=C3⋊S3

Direct product G=N×Q with N=C3×C9 and Q=C3⋊S3
dρLabelID
C3⋊S3×C3×C954C3:S3xC3xC9486,228

Semidirect products G=N:Q with N=C3×C9 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C3×C9)⋊1(C3⋊S3) = C33⋊C18φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C954(C3xC9):1(C3:S3)486,136
(C3×C9)⋊2(C3⋊S3) = He3.C3⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9):2(C3:S3)486,169
(C3×C9)⋊3(C3⋊S3) = He3⋊C3⋊2S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9):3(C3:S3)486,172
(C3×C9)⋊4(C3⋊S3) = C33⋊6D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C954(C3xC9):4(C3:S3)486,181
(C3×C9)⋊5(C3⋊S3) = He3.(C3⋊S3)φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C981(C3xC9):5(C3:S3)486,186
(C3×C9)⋊6(C3⋊S3) = C3⋊(He3⋊S3)φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C981(C3xC9):6(C3:S3)486,187
(C3×C9)⋊7(C3⋊S3) = C9○He3⋊3S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C981(C3xC9):7(C3:S3)486,245
(C3×C9)⋊8(C3⋊S3) = C9○He3⋊4S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9):8(C3:S3)486,246
(C3×C9)⋊9(C3⋊S3) = C9×C33⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9):9(C3:S3)486,241
(C3×C9)⋊10(C3⋊S3) = C3×C32⋊4D9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9):10(C3:S3)486,240
(C3×C9)⋊11(C3⋊S3) = C33⋊9D9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9243(C3xC9):11(C3:S3)486,247

Non-split extensions G=N.Q with N=C3×C9 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C3×C9).1(C3⋊S3) = C92⋊2S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9273(C3xC9).1(C3:S3)486,61
(C3×C9).2(C3⋊S3) = C9⋊(S3×C9)φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C954(C3xC9).2(C3:S3)486,138
(C3×C9).3(C3⋊S3) = C92⋊3S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).3(C3:S3)486,139
(C3×C9).4(C3⋊S3) = (C32×C9)⋊8S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).4(C3:S3)486,150
(C3×C9).5(C3⋊S3) = C9⋊C9⋊2S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).5(C3:S3)486,152
(C3×C9).6(C3⋊S3) = C92⋊6S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9186(C3xC9).6(C3:S3)486,153
(C3×C9).7(C3⋊S3) = C92⋊5S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9546(C3xC9).7(C3:S3)486,156
(C3×C9).8(C3⋊S3) = (C32×C9).S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C981(C3xC9).8(C3:S3)486,188
(C3×C9).9(C3⋊S3) = C33.D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9276+(C3xC9).9(C3:S3)486,55
(C3×C9).10(C3⋊S3) = He3.3D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9816+(C3xC9).10(C3:S3)486,58
(C3×C9).11(C3⋊S3) = He3.4D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9816+(C3xC9).11(C3:S3)486,59
(C3×C9).12(C3⋊S3) = C33.5D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C981(C3xC9).12(C3:S3)486,162
(C3×C9).13(C3⋊S3) = He3.5D9φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9816+(C3xC9).13(C3:S3)486,163
(C3×C9).14(C3⋊S3) = C3≀C3⋊S3φ: C3⋊S3/C3 → S3 ⊆ Aut C3×C9276+(C3xC9).14(C3:S3)486,189
(C3×C9).15(C3⋊S3) = C9×C9⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C954(C3xC9).15(C3:S3)486,133
(C3×C9).16(C3⋊S3) = C92⋊4S3φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9546(C3xC9).16(C3:S3)486,140
(C3×C9).17(C3⋊S3) = C9⋊D27φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9243(C3xC9).17(C3:S3)486,50
(C3×C9).18(C3⋊S3) = C32⋊2D27φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9546(C3xC9).18(C3:S3)486,51
(C3×C9).19(C3⋊S3) = C3×C27⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9162(C3xC9).19(C3:S3)486,160
(C3×C9).20(C3⋊S3) = C92⋊8S3φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9243(C3xC9).20(C3:S3)486,180
(C3×C9).21(C3⋊S3) = He3⋊4D9φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9546(C3xC9).21(C3:S3)486,182
(C3×C9).22(C3⋊S3) = C32⋊4D27φ: C3⋊S3/C32 → C2 ⊆ Aut C3×C9243(C3xC9).22(C3:S3)486,184
(C3×C9).23(C3⋊S3) = C9×He3⋊C2central extension (φ=1)81(C3xC9).23(C3:S3)486,143
(C3×C9).24(C3⋊S3) = C3×He3.4C6central extension (φ=1)81(C3xC9).24(C3:S3)486,235

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁