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

Extensions 1→N→G→Q→1 with N=M4(2) and Q=C2×C4

Direct product G=N×Q with N=M4(2) and Q=C2×C4
dρLabelID
C2×C4×M4(2)64C2xC4xM4(2)128,1603

Semidirect products G=N:Q with N=M4(2) and Q=C2×C4
extensionφ:Q→Out NdρLabelID
M4(2)⋊1(C2×C4) = C24.21D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2):1(C2xC4)128,588
M4(2)⋊2(C2×C4) = C4≀C2⋊C4φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2):2(C2xC4)128,591
M4(2)⋊3(C2×C4) = C42⋊9(C2×C4)φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2):3(C2xC4)128,592
M4(2)⋊4(C2×C4) = C8.C22⋊C4φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2):4(C2xC4)128,614
M4(2)⋊5(C2×C4) = C8⋊C22⋊C4φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2):5(C2xC4)128,615
M4(2)⋊6(C2×C4) = C42.426D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)164M4(2):6(C2xC4)128,638
M4(2)⋊7(C2×C4) = C4×C8⋊C22φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2):7(C2xC4)128,1676
M4(2)⋊8(C2×C4) = C4×C8.C22φ: C2×C4/C4 → C2 ⊆ Out M4(2)64M4(2):8(C2xC4)128,1677
M4(2)⋊9(C2×C4) = C42.275C23φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2):9(C2xC4)128,1678
M4(2)⋊10(C2×C4) = C42.276C23φ: C2×C4/C4 → C2 ⊆ Out M4(2)64M4(2):10(C2xC4)128,1679
M4(2)⋊11(C2×C4) = C4×C4.D4φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2):11(C2xC4)128,487
M4(2)⋊12(C2×C4) = C4×C4≀C2φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2):12(C2xC4)128,490
M4(2)⋊13(C2×C4) = D4.C42φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2):13(C2xC4)128,491
M4(2)⋊14(C2×C4) = C2×M4(2)⋊C4φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2):14(C2xC4)128,1642
M4(2)⋊15(C2×C4) = C24.100D4φ: C2×C4/C22 → C2 ⊆ Out M4(2)32M4(2):15(C2xC4)128,1643
M4(2)⋊16(C2×C4) = C4○D4.7Q8φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2):16(C2xC4)128,1644
M4(2)⋊17(C2×C4) = C4○D4.8Q8φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2):17(C2xC4)128,1645
M4(2)⋊18(C2×C4) = C2×C42⋊6C4φ: C2×C4/C22 → C2 ⊆ Out M4(2)32M4(2):18(C2xC4)128,464
M4(2)⋊19(C2×C4) = C24.63D4φ: C2×C4/C22 → C2 ⊆ Out M4(2)32M4(2):19(C2xC4)128,465
M4(2)⋊20(C2×C4) = C2×C22.C42φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2):20(C2xC4)128,473
M4(2)⋊21(C2×C4) = C2×M4(2)⋊4C4φ: C2×C4/C22 → C2 ⊆ Out M4(2)32M4(2):21(C2xC4)128,475
M4(2)⋊22(C2×C4) = C2×C8○2M4(2)φ: trivial image64M4(2):22(C2xC4)128,1604
M4(2)⋊23(C2×C4) = M4(2)○2M4(2)φ: trivial image32M4(2):23(C2xC4)128,1605
M4(2)⋊24(C2×C4) = C4×C8○D4φ: trivial image64M4(2):24(C2xC4)128,1606
M4(2)⋊25(C2×C4) = D4.5C42φ: trivial image64M4(2):25(C2xC4)128,1607

Non-split extensions G=N.Q with N=M4(2) and Q=C2×C4
extensionφ:Q→Out NdρLabelID
M4(2).1(C2×C4) = C4.10D4⋊2C4φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2).1(C2xC4)128,589
M4(2).2(C2×C4) = M4(2).40D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)324M4(2).2(C2xC4)128,590
M4(2).3(C2×C4) = M4(2).41D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)164M4(2).3(C2xC4)128,593
M4(2).4(C2×C4) = M4(2).44D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)324M4(2).4(C2xC4)128,613
M4(2).5(C2×C4) = M4(2).48D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2).5(C2xC4)128,639
M4(2).6(C2×C4) = M4(2).49D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)64M4(2).6(C2xC4)128,640
M4(2).7(C2×C4) = C4.10D4⋊3C4φ: C2×C4/C2 → C22 ⊆ Out M4(2)64M4(2).7(C2xC4)128,662
M4(2).8(C2×C4) = C4.D4⋊3C4φ: C2×C4/C2 → C22 ⊆ Out M4(2)32M4(2).8(C2xC4)128,663
M4(2).9(C2×C4) = C42.427D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)164M4(2).9(C2xC4)128,664
M4(2).10(C2×C4) = M4(2).5Q8φ: C2×C4/C2 → C22 ⊆ Out M4(2)64M4(2).10(C2xC4)128,683
M4(2).11(C2×C4) = M4(2).6Q8φ: C2×C4/C2 → C22 ⊆ Out M4(2)64M4(2).11(C2xC4)128,684
M4(2).12(C2×C4) = M4(2).27D4φ: C2×C4/C2 → C22 ⊆ Out M4(2)324M4(2).12(C2xC4)128,685
M4(2).13(C2×C4) = C42.283C23φ: C2×C4/C4 → C2 ⊆ Out M4(2)324M4(2).13(C2xC4)128,1687
M4(2).14(C2×C4) = M4(2).51D4φ: C2×C4/C4 → C2 ⊆ Out M4(2)164M4(2).14(C2xC4)128,1688
M4(2).15(C2×C4) = C4×C4.10D4φ: C2×C4/C4 → C2 ⊆ Out M4(2)64M4(2).15(C2xC4)128,488
M4(2).16(C2×C4) = C23.5C42φ: C2×C4/C4 → C2 ⊆ Out M4(2)324M4(2).16(C2xC4)128,489
M4(2).17(C2×C4) = Q8.C42φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2).17(C2xC4)128,496
M4(2).18(C2×C4) = D4.3C42φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2).18(C2xC4)128,497
M4(2).19(C2×C4) = C8.14C42φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2).19(C2xC4)128,504
M4(2).20(C2×C4) = C8.5C42φ: C2×C4/C4 → C2 ⊆ Out M4(2)32M4(2).20(C2xC4)128,505
M4(2).21(C2×C4) = C4×C8.C4φ: C2×C4/C4 → C2 ⊆ Out M4(2)64M4(2).21(C2xC4)128,509
M4(2).22(C2×C4) = C8.6C42φ: C2×C4/C4 → C2 ⊆ Out M4(2)64M4(2).22(C2xC4)128,510
M4(2).23(C2×C4) = C16○D8φ: C2×C4/C4 → C2 ⊆ Out M4(2)322M4(2).23(C2xC4)128,902
M4(2).24(C2×C4) = D8.C8φ: C2×C4/C4 → C2 ⊆ Out M4(2)324M4(2).24(C2xC4)128,903
M4(2).25(C2×C4) = C2×M4(2).C4φ: C2×C4/C22 → C2 ⊆ Out M4(2)32M4(2).25(C2xC4)128,1647
M4(2).26(C2×C4) = M4(2).29C23φ: C2×C4/C22 → C2 ⊆ Out M4(2)324M4(2).26(C2xC4)128,1648
M4(2).27(C2×C4) = C2×C4.C42φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2).27(C2xC4)128,469
M4(2).28(C2×C4) = C24.7Q8φ: C2×C4/C22 → C2 ⊆ Out M4(2)32M4(2).28(C2xC4)128,470
M4(2).29(C2×C4) = C23.15C42φ: C2×C4/C22 → C2 ⊆ Out M4(2)32M4(2).29(C2xC4)128,474
M4(2).30(C2×C4) = C8○D4⋊C4φ: C2×C4/C22 → C2 ⊆ Out M4(2)324M4(2).30(C2xC4)128,546
M4(2).31(C2×C4) = C4○D4.4Q8φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2).31(C2xC4)128,547
M4(2).32(C2×C4) = C4○D4.5Q8φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2).32(C2xC4)128,548
M4(2).33(C2×C4) = C2×D4.C8φ: C2×C4/C22 → C2 ⊆ Out M4(2)64M4(2).33(C2xC4)128,848
M4(2).34(C2×C4) = M5(2)⋊12C22φ: C2×C4/C22 → C2 ⊆ Out M4(2)324M4(2).34(C2xC4)128,849
M4(2).35(C2×C4) = C2×D4○C16φ: trivial image64M4(2).35(C2xC4)128,2138
M4(2).36(C2×C4) = Q8○M5(2)φ: trivial image324M4(2).36(C2xC4)128,2139

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁