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

Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C4×D5

Direct product G=N×Q with N=C2×C6 and Q=C4×D5
dρLabelID
D5×C22×C12240D5xC2^2xC12480,1136

Semidirect products G=N:Q with N=C2×C6 and Q=C4×D5
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C4×D5) = Dic3×C5⋊D4φ: C4×D5/C10 → C22 ⊆ Aut C2×C6240(C2xC6):1(C4xD5)480,629
(C2×C6)⋊2(C4×D5) = C15⋊28(C4×D4)φ: C4×D5/C10 → C22 ⊆ Aut C2×C6240(C2xC6):2(C4xD5)480,632
(C2×C6)⋊3(C4×D5) = Dic15⋊16D4φ: C4×D5/C10 → C22 ⊆ Aut C2×C6240(C2xC6):3(C4xD5)480,635
(C2×C6)⋊4(C4×D5) = D30.45D4φ: C4×D5/C10 → C22 ⊆ Aut C2×C6120(C2xC6):4(C4xD5)480,637
(C2×C6)⋊5(C4×D5) = C22⋊C4×D15φ: C4×D5/C10 → C22 ⊆ Aut C2×C6120(C2xC6):5(C4xD5)480,845
(C2×C6)⋊6(C4×D5) = Dic15⋊19D4φ: C4×D5/C10 → C22 ⊆ Aut C2×C6240(C2xC6):6(C4xD5)480,846
(C2×C6)⋊7(C4×D5) = C3×Dic5⋊4D4φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):7(C4xD5)480,674
(C2×C6)⋊8(C4×D5) = C15⋊26(C4×D4)φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):8(C4xD5)480,628
(C2×C6)⋊9(C4×D5) = C22×D30.C2φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):9(C4xD5)480,1117
(C2×C6)⋊10(C4×D5) = C12×C5⋊D4φ: C4×D5/C20 → C2 ⊆ Aut C2×C6240(C2xC6):10(C4xD5)480,721
(C2×C6)⋊11(C4×D5) = C4×C15⋊7D4φ: C4×D5/C20 → C2 ⊆ Aut C2×C6240(C2xC6):11(C4xD5)480,893
(C2×C6)⋊12(C4×D5) = C22×C4×D15φ: C4×D5/C20 → C2 ⊆ Aut C2×C6240(C2xC6):12(C4xD5)480,1166
(C2×C6)⋊13(C4×D5) = C3×D5×C22⋊C4φ: C4×D5/D10 → C2 ⊆ Aut C2×C6120(C2xC6):13(C4xD5)480,673
(C2×C6)⋊14(C4×D5) = D5×C6.D4φ: C4×D5/D10 → C2 ⊆ Aut C2×C6120(C2xC6):14(C4xD5)480,623
(C2×C6)⋊15(C4×D5) = C22×D5×Dic3φ: C4×D5/D10 → C2 ⊆ Aut C2×C6240(C2xC6):15(C4xD5)480,1112

Non-split extensions G=N.Q with N=C2×C6 and Q=C4×D5
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C4×D5) = C60.29D4φ: C4×D5/C10 → C22 ⊆ Aut C2×C61204+(C2xC6).1(C4xD5)480,36
(C2×C6).2(C4×D5) = C60.31D4φ: C4×D5/C10 → C22 ⊆ Aut C2×C62404-(C2xC6).2(C4xD5)480,39
(C2×C6).3(C4×D5) = C15⋊9(C23⋊C4)φ: C4×D5/C10 → C22 ⊆ Aut C2×C61204(C2xC6).3(C4xD5)480,73
(C2×C6).4(C4×D5) = C23.6D30φ: C4×D5/C10 → C22 ⊆ Aut C2×C61204(C2xC6).4(C4xD5)480,166
(C2×C6).5(C4×D5) = M4(2)⋊D15φ: C4×D5/C10 → C22 ⊆ Aut C2×C61204+(C2xC6).5(C4xD5)480,183
(C2×C6).6(C4×D5) = C4.D60φ: C4×D5/C10 → C22 ⊆ Aut C2×C62404-(C2xC6).6(C4xD5)480,184
(C2×C6).7(C4×D5) = D20.3Dic3φ: C4×D5/C10 → C22 ⊆ Aut C2×C62404(C2xC6).7(C4xD5)480,359
(C2×C6).8(C4×D5) = D20.2Dic3φ: C4×D5/C10 → C22 ⊆ Aut C2×C62404(C2xC6).8(C4xD5)480,360
(C2×C6).9(C4×D5) = D60.4C4φ: C4×D5/C10 → C22 ⊆ Aut C2×C62404(C2xC6).9(C4xD5)480,367
(C2×C6).10(C4×D5) = D15⋊4M4(2)φ: C4×D5/C10 → C22 ⊆ Aut C2×C61204(C2xC6).10(C4xD5)480,368
(C2×C6).11(C4×D5) = C23.48(S3×D5)φ: C4×D5/C10 → C22 ⊆ Aut C2×C6240(C2xC6).11(C4xD5)480,608
(C2×C6).12(C4×D5) = C23.15D30φ: C4×D5/C10 → C22 ⊆ Aut C2×C6240(C2xC6).12(C4xD5)480,842
(C2×C6).13(C4×D5) = M4(2)×D15φ: C4×D5/C10 → C22 ⊆ Aut C2×C61204(C2xC6).13(C4xD5)480,871
(C2×C6).14(C4×D5) = D60.3C4φ: C4×D5/C10 → C22 ⊆ Aut C2×C62404(C2xC6).14(C4xD5)480,872
(C2×C6).15(C4×D5) = C3×D20.2C4φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C62404(C2xC6).15(C4xD5)480,700
(C2×C6).16(C4×D5) = Dic15⋊4C8φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).16(C4xD5)480,27
(C2×C6).17(C4×D5) = C30.23C42φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).17(C4xD5)480,30
(C2×C6).18(C4×D5) = D30⋊4C8φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).18(C4xD5)480,33
(C2×C6).19(C4×D5) = C60.14Q8φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).19(C4xD5)480,59
(C2×C6).20(C4×D5) = C2×D15⋊2C8φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).20(C4xD5)480,365
(C2×C6).21(C4×D5) = D60.5C4φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C62404(C2xC6).21(C4xD5)480,366
(C2×C6).22(C4×D5) = C2×D30.5C4φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).22(C4xD5)480,371
(C2×C6).23(C4×D5) = C2×D30⋊4C4φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).23(C4xD5)480,616
(C2×C6).24(C4×D5) = C2×Dic15⋊5C4φ: C4×D5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).24(C4xD5)480,620
(C2×C6).25(C4×D5) = C3×D20.3C4φ: C4×D5/C20 → C2 ⊆ Aut C2×C62402(C2xC6).25(C4xD5)480,694
(C2×C6).26(C4×D5) = C8×Dic15φ: C4×D5/C20 → C2 ⊆ Aut C2×C6480(C2xC6).26(C4xD5)480,173
(C2×C6).27(C4×D5) = C60.26Q8φ: C4×D5/C20 → C2 ⊆ Aut C2×C6480(C2xC6).27(C4xD5)480,174
(C2×C6).28(C4×D5) = C120⋊13C4φ: C4×D5/C20 → C2 ⊆ Aut C2×C6480(C2xC6).28(C4xD5)480,175
(C2×C6).29(C4×D5) = D30⋊3C8φ: C4×D5/C20 → C2 ⊆ Aut C2×C6240(C2xC6).29(C4xD5)480,180
(C2×C6).30(C4×D5) = C30.29C42φ: C4×D5/C20 → C2 ⊆ Aut C2×C6480(C2xC6).30(C4xD5)480,191
(C2×C6).31(C4×D5) = C2×C8×D15φ: C4×D5/C20 → C2 ⊆ Aut C2×C6240(C2xC6).31(C4xD5)480,864
(C2×C6).32(C4×D5) = C2×C40⋊S3φ: C4×D5/C20 → C2 ⊆ Aut C2×C6240(C2xC6).32(C4xD5)480,865
(C2×C6).33(C4×D5) = D60.6C4φ: C4×D5/C20 → C2 ⊆ Aut C2×C62402(C2xC6).33(C4xD5)480,866
(C2×C6).34(C4×D5) = C2×C4×Dic15φ: C4×D5/C20 → C2 ⊆ Aut C2×C6480(C2xC6).34(C4xD5)480,887
(C2×C6).35(C4×D5) = C2×C30.4Q8φ: C4×D5/C20 → C2 ⊆ Aut C2×C6480(C2xC6).35(C4xD5)480,888
(C2×C6).36(C4×D5) = C2×D30⋊3C4φ: C4×D5/C20 → C2 ⊆ Aut C2×C6240(C2xC6).36(C4xD5)480,892
(C2×C6).37(C4×D5) = C3×C23.1D10φ: C4×D5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).37(C4xD5)480,84
(C2×C6).38(C4×D5) = C3×C20.46D4φ: C4×D5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).38(C4xD5)480,101
(C2×C6).39(C4×D5) = C3×C4.12D20φ: C4×D5/D10 → C2 ⊆ Aut C2×C62404(C2xC6).39(C4xD5)480,102
(C2×C6).40(C4×D5) = C3×C23.11D10φ: C4×D5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).40(C4xD5)480,670
(C2×C6).41(C4×D5) = C3×D5×M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).41(C4xD5)480,699
(C2×C6).42(C4×D5) = Dic5×C3⋊C8φ: C4×D5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).42(C4xD5)480,25
(C2×C6).43(C4×D5) = C30.21C42φ: C4×D5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).43(C4xD5)480,28
(C2×C6).44(C4×D5) = C60.93D4φ: C4×D5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).44(C4xD5)480,31
(C2×C6).45(C4×D5) = C60.28D4φ: C4×D5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).45(C4xD5)480,34
(C2×C6).46(C4×D5) = C12.6D20φ: C4×D5/D10 → C2 ⊆ Aut C2×C62404(C2xC6).46(C4xD5)480,37
(C2×C6).47(C4×D5) = C60.13Q8φ: C4×D5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).47(C4xD5)480,58
(C2×C6).48(C4×D5) = C30.24C42φ: C4×D5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).48(C4xD5)480,70
(C2×C6).49(C4×D5) = (C2×C6).D20φ: C4×D5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).49(C4xD5)480,71
(C2×C6).50(C4×D5) = C2×D5×C3⋊C8φ: C4×D5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).50(C4xD5)480,357
(C2×C6).51(C4×D5) = D5×C4.Dic3φ: C4×D5/D10 → C2 ⊆ Aut C2×C61204(C2xC6).51(C4xD5)480,358
(C2×C6).52(C4×D5) = C2×C20.32D6φ: C4×D5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).52(C4xD5)480,369
(C2×C6).53(C4×D5) = C2×Dic3×Dic5φ: C4×D5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).53(C4xD5)480,603
(C2×C6).54(C4×D5) = (C6×Dic5)⋊7C4φ: C4×D5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).54(C4xD5)480,604
(C2×C6).55(C4×D5) = C2×D10⋊Dic3φ: C4×D5/D10 → C2 ⊆ Aut C2×C6240(C2xC6).55(C4xD5)480,611
(C2×C6).56(C4×D5) = C2×C30.Q8φ: C4×D5/D10 → C2 ⊆ Aut C2×C6480(C2xC6).56(C4xD5)480,617
(C2×C6).57(C4×D5) = Dic5×C24central extension (φ=1)480(C2xC6).57(C4xD5)480,91
(C2×C6).58(C4×D5) = C3×C20.8Q8central extension (φ=1)480(C2xC6).58(C4xD5)480,92
(C2×C6).59(C4×D5) = C3×C40⋊8C4central extension (φ=1)480(C2xC6).59(C4xD5)480,93
(C2×C6).60(C4×D5) = C3×D10⋊1C8central extension (φ=1)240(C2xC6).60(C4xD5)480,98
(C2×C6).61(C4×D5) = C3×C10.10C42central extension (φ=1)480(C2xC6).61(C4xD5)480,109
(C2×C6).62(C4×D5) = D5×C2×C24central extension (φ=1)240(C2xC6).62(C4xD5)480,692
(C2×C6).63(C4×D5) = C6×C8⋊D5central extension (φ=1)240(C2xC6).63(C4xD5)480,693
(C2×C6).64(C4×D5) = Dic5×C2×C12central extension (φ=1)480(C2xC6).64(C4xD5)480,715
(C2×C6).65(C4×D5) = C6×C10.D4central extension (φ=1)480(C2xC6).65(C4xD5)480,716
(C2×C6).66(C4×D5) = C6×D10⋊C4central extension (φ=1)240(C2xC6).66(C4xD5)480,720

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁