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

Extensions 1→N→G→Q→1 with N=C3×D4 and Q=C2×C10

Direct product G=N×Q with N=C3×D4 and Q=C2×C10
dρLabelID
D4×C2×C30240D4xC2xC30480,1181

Semidirect products G=N:Q with N=C3×D4 and Q=C2×C10
extensionφ:Q→Out NdρLabelID
(C3×D4)⋊1(C2×C10) = C5×S3×D8φ: C2×C10/C5 → C22 ⊆ Out C3×D41204(C3xD4):1(C2xC10)480,789
(C3×D4)⋊2(C2×C10) = C5×D8⋊S3φ: C2×C10/C5 → C22 ⊆ Out C3×D41204(C3xD4):2(C2xC10)480,790
(C3×D4)⋊3(C2×C10) = C10×D4⋊S3φ: C2×C10/C10 → C2 ⊆ Out C3×D4240(C3xD4):3(C2xC10)480,810
(C3×D4)⋊4(C2×C10) = C5×D4⋊D6φ: C2×C10/C10 → C2 ⊆ Out C3×D41204(C3xD4):4(C2xC10)480,828
(C3×D4)⋊5(C2×C10) = S3×D4×C10φ: C2×C10/C10 → C2 ⊆ Out C3×D4120(C3xD4):5(C2xC10)480,1154
(C3×D4)⋊6(C2×C10) = C10×D4⋊2S3φ: C2×C10/C10 → C2 ⊆ Out C3×D4240(C3xD4):6(C2xC10)480,1155
(C3×D4)⋊7(C2×C10) = C5×D4⋊6D6φ: C2×C10/C10 → C2 ⊆ Out C3×D41204(C3xD4):7(C2xC10)480,1156
(C3×D4)⋊8(C2×C10) = C5×S3×C4○D4φ: C2×C10/C10 → C2 ⊆ Out C3×D41204(C3xD4):8(C2xC10)480,1160
(C3×D4)⋊9(C2×C10) = C5×D4○D12φ: C2×C10/C10 → C2 ⊆ Out C3×D41204(C3xD4):9(C2xC10)480,1161
(C3×D4)⋊10(C2×C10) = D8×C30φ: C2×C10/C10 → C2 ⊆ Out C3×D4240(C3xD4):10(C2xC10)480,937
(C3×D4)⋊11(C2×C10) = C15×C8⋊C22φ: C2×C10/C10 → C2 ⊆ Out C3×D41204(C3xD4):11(C2xC10)480,941
(C3×D4)⋊12(C2×C10) = C4○D4×C30φ: trivial image240(C3xD4):12(C2xC10)480,1183
(C3×D4)⋊13(C2×C10) = C15×2+ 1+4φ: trivial image1204(C3xD4):13(C2xC10)480,1184

Non-split extensions G=N.Q with N=C3×D4 and Q=C2×C10
extensionφ:Q→Out NdρLabelID
(C3×D4).1(C2×C10) = C5×D8⋊3S3φ: C2×C10/C5 → C22 ⊆ Out C3×D42404(C3xD4).1(C2xC10)480,791
(C3×D4).2(C2×C10) = C5×S3×SD16φ: C2×C10/C5 → C22 ⊆ Out C3×D41204(C3xD4).2(C2xC10)480,792
(C3×D4).3(C2×C10) = C5×Q8⋊3D6φ: C2×C10/C5 → C22 ⊆ Out C3×D41204(C3xD4).3(C2xC10)480,793
(C3×D4).4(C2×C10) = C5×D4.D6φ: C2×C10/C5 → C22 ⊆ Out C3×D42404(C3xD4).4(C2xC10)480,794
(C3×D4).5(C2×C10) = C5×Q8.7D6φ: C2×C10/C5 → C22 ⊆ Out C3×D42404(C3xD4).5(C2xC10)480,795
(C3×D4).6(C2×C10) = C5×D12⋊6C22φ: C2×C10/C10 → C2 ⊆ Out C3×D41204(C3xD4).6(C2xC10)480,811
(C3×D4).7(C2×C10) = C10×D4.S3φ: C2×C10/C10 → C2 ⊆ Out C3×D4240(C3xD4).7(C2xC10)480,812
(C3×D4).8(C2×C10) = C5×Q8.13D6φ: C2×C10/C10 → C2 ⊆ Out C3×D42404(C3xD4).8(C2xC10)480,829
(C3×D4).9(C2×C10) = C5×Q8.14D6φ: C2×C10/C10 → C2 ⊆ Out C3×D42404(C3xD4).9(C2xC10)480,830
(C3×D4).10(C2×C10) = C5×Q8○D12φ: C2×C10/C10 → C2 ⊆ Out C3×D42404(C3xD4).10(C2xC10)480,1162
(C3×D4).11(C2×C10) = SD16×C30φ: C2×C10/C10 → C2 ⊆ Out C3×D4240(C3xD4).11(C2xC10)480,938
(C3×D4).12(C2×C10) = C15×C4○D8φ: C2×C10/C10 → C2 ⊆ Out C3×D42402(C3xD4).12(C2xC10)480,940
(C3×D4).13(C2×C10) = C15×C8.C22φ: C2×C10/C10 → C2 ⊆ Out C3×D42404(C3xD4).13(C2xC10)480,942
(C3×D4).14(C2×C10) = C15×2- 1+4φ: trivial image2404(C3xD4).14(C2xC10)480,1185

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁