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

Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C5×Q8

Direct product G=N×Q with N=C2×C4 and Q=C5×Q8
dρLabelID
Q8×C2×C20320Q8xC2xC20320,1518

Semidirect products G=N:Q with N=C2×C4 and Q=C5×Q8
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C5×Q8) = C5×C23.78C23φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4320(C2xC4):1(C5xQ8)320,896
(C2×C4)⋊2(C5×Q8) = C5×C23.41C23φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4160(C2xC4):2(C5xQ8)320,1546
(C2×C4)⋊3(C5×Q8) = C5×C23.67C23φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4):3(C5xQ8)320,892
(C2×C4)⋊4(C5×Q8) = C10×C4⋊Q8φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4):4(C5xQ8)320,1533
(C2×C4)⋊5(C5×Q8) = C5×C23.37C23φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4160(C2xC4):5(C5xQ8)320,1535

Non-split extensions G=N.Q with N=C2×C4 and Q=C5×Q8
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C5×Q8) = C5×C4.9C42φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4804(C2xC4).1(C5xQ8)320,142
(C2×C4).2(C5×Q8) = C5×C22.C42φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4160(C2xC4).2(C5xQ8)320,148
(C2×C4).3(C5×Q8) = C5×M4(2)⋊4C4φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4804(C2xC4).3(C5xQ8)320,149
(C2×C4).4(C5×Q8) = C5×C23.81C23φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4320(C2xC4).4(C5xQ8)320,899
(C2×C4).5(C5×Q8) = C5×C23.83C23φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4320(C2xC4).5(C5xQ8)320,901
(C2×C4).6(C5×Q8) = C5×M4(2)⋊C4φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4160(C2xC4).6(C5xQ8)320,929
(C2×C4).7(C5×Q8) = C5×M4(2).C4φ: C5×Q8/C10 → C22 ⊆ Aut C2×C4804(C2xC4).7(C5xQ8)320,931
(C2×C4).8(C5×Q8) = C5×C8⋊2C8φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).8(C5xQ8)320,139
(C2×C4).9(C5×Q8) = C5×C8⋊1C8φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).9(C5xQ8)320,140
(C2×C4).10(C5×Q8) = C5×C23.63C23φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).10(C5xQ8)320,888
(C2×C4).11(C5×Q8) = C5×C23.65C23φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).11(C5xQ8)320,890
(C2×C4).12(C5×Q8) = C5×C42⋊6C4φ: C5×Q8/C20 → C2 ⊆ Aut C2×C480(C2xC4).12(C5xQ8)320,144
(C2×C4).13(C5×Q8) = C5×C22.4Q16φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).13(C5xQ8)320,145
(C2×C4).14(C5×Q8) = C5×C42⋊8C4φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).14(C5xQ8)320,883
(C2×C4).15(C5×Q8) = C5×C42⋊9C4φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).15(C5xQ8)320,885
(C2×C4).16(C5×Q8) = C5×C4⋊M4(2)φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4160(C2xC4).16(C5xQ8)320,924
(C2×C4).17(C5×Q8) = C5×C42.6C22φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4160(C2xC4).17(C5xQ8)320,925
(C2×C4).18(C5×Q8) = C10×C4.Q8φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).18(C5xQ8)320,926
(C2×C4).19(C5×Q8) = C10×C2.D8φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).19(C5xQ8)320,927
(C2×C4).20(C5×Q8) = C5×C23.25D4φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4160(C2xC4).20(C5xQ8)320,928
(C2×C4).21(C5×Q8) = C10×C8.C4φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4160(C2xC4).21(C5xQ8)320,930
(C2×C4).22(C5×Q8) = C10×C42.C2φ: C5×Q8/C20 → C2 ⊆ Aut C2×C4320(C2xC4).22(C5xQ8)320,1529
(C2×C4).23(C5×Q8) = C5×C22.7C42central extension (φ=1)320(C2xC4).23(C5xQ8)320,141
(C2×C4).24(C5×Q8) = C4⋊C4×C20central extension (φ=1)320(C2xC4).24(C5xQ8)320,879
(C2×C4).25(C5×Q8) = C10×C4⋊C8central extension (φ=1)320(C2xC4).25(C5xQ8)320,923

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁