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

Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C4×S3

Direct product G=N×Q with N=C2×C10 and Q=C4×S3
dρLabelID
S3×C22×C20240S3xC2^2xC20480,1151

Semidirect products G=N:Q with N=C2×C10 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C4×S3) = F5×S4φ: C4×S3/C1 → C4×S3 ⊆ Aut C2×C102012+(C2xC10):(C4xS3)480,1189
(C2×C10)⋊2(C4×S3) = Dic5×S4φ: C4×S3/C2 → D6 ⊆ Aut C2×C10606-(C2xC10):2(C4xS3)480,976
(C2×C10)⋊3(C4×S3) = Dic5⋊2S4φ: C4×S3/C2 → D6 ⊆ Aut C2×C10606(C2xC10):3(C4xS3)480,977
(C2×C10)⋊4(C4×S3) = F5×C3⋊D4φ: C4×S3/C3 → C2×C4 ⊆ Aut C2×C10608(C2xC10):4(C4xS3)480,1010
(C2×C10)⋊5(C4×S3) = C3⋊D4⋊F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C2×C10608(C2xC10):5(C4xS3)480,1012
(C2×C10)⋊6(C4×S3) = C20×S4φ: C4×S3/C4 → S3 ⊆ Aut C2×C10603(C2xC10):6(C4xS3)480,1014
(C2×C10)⋊7(C4×S3) = C4×C5⋊S4φ: C4×S3/C4 → S3 ⊆ Aut C2×C10606(C2xC10):7(C4xS3)480,1025
(C2×C10)⋊8(C4×S3) = S3×C22⋊F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C10608+(C2xC10):8(C4xS3)480,1011
(C2×C10)⋊9(C4×S3) = C22×S3×F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C1060(C2xC10):9(C4xS3)480,1197
(C2×C10)⋊10(C4×S3) = Dic5×C3⋊D4φ: C4×S3/C6 → C22 ⊆ Aut C2×C10240(C2xC10):10(C4xS3)480,627
(C2×C10)⋊11(C4×S3) = C15⋊26(C4×D4)φ: C4×S3/C6 → C22 ⊆ Aut C2×C10240(C2xC10):11(C4xS3)480,628
(C2×C10)⋊12(C4×S3) = Dic15⋊17D4φ: C4×S3/C6 → C22 ⊆ Aut C2×C10240(C2xC10):12(C4xS3)480,636
(C2×C10)⋊13(C4×S3) = D30.45D4φ: C4×S3/C6 → C22 ⊆ Aut C2×C10120(C2xC10):13(C4xS3)480,637
(C2×C10)⋊14(C4×S3) = C22⋊C4×D15φ: C4×S3/C6 → C22 ⊆ Aut C2×C10120(C2xC10):14(C4xS3)480,845
(C2×C10)⋊15(C4×S3) = Dic15⋊19D4φ: C4×S3/C6 → C22 ⊆ Aut C2×C10240(C2xC10):15(C4xS3)480,846
(C2×C10)⋊16(C4×S3) = C5×Dic3⋊4D4φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10):16(C4xS3)480,760
(C2×C10)⋊17(C4×S3) = C15⋊28(C4×D4)φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10):17(C4xS3)480,632
(C2×C10)⋊18(C4×S3) = C22×D30.C2φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10):18(C4xS3)480,1117
(C2×C10)⋊19(C4×S3) = C20×C3⋊D4φ: C4×S3/C12 → C2 ⊆ Aut C2×C10240(C2xC10):19(C4xS3)480,807
(C2×C10)⋊20(C4×S3) = C4×C15⋊7D4φ: C4×S3/C12 → C2 ⊆ Aut C2×C10240(C2xC10):20(C4xS3)480,893
(C2×C10)⋊21(C4×S3) = C22×C4×D15φ: C4×S3/C12 → C2 ⊆ Aut C2×C10240(C2xC10):21(C4xS3)480,1166
(C2×C10)⋊22(C4×S3) = C5×S3×C22⋊C4φ: C4×S3/D6 → C2 ⊆ Aut C2×C10120(C2xC10):22(C4xS3)480,759
(C2×C10)⋊23(C4×S3) = S3×C23.D5φ: C4×S3/D6 → C2 ⊆ Aut C2×C10120(C2xC10):23(C4xS3)480,630
(C2×C10)⋊24(C4×S3) = C22×S3×Dic5φ: C4×S3/D6 → C2 ⊆ Aut C2×C10240(C2xC10):24(C4xS3)480,1115

Non-split extensions G=N.Q with N=C2×C10 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C4×S3) = C5⋊C8.D6φ: C4×S3/C3 → C2×C4 ⊆ Aut C2×C102408(C2xC10).1(C4xS3)480,1003
(C2×C10).2(C4×S3) = D15⋊C8⋊C2φ: C4×S3/C3 → C2×C4 ⊆ Aut C2×C102408(C2xC10).2(C4xS3)480,1005
(C2×C10).3(C4×S3) = D10.20D12φ: C4×S3/S3 → C4 ⊆ Aut C2×C10120(C2xC10).3(C4xS3)480,243
(C2×C10).4(C4×S3) = Dic3×C5⋊C8φ: C4×S3/S3 → C4 ⊆ Aut C2×C10480(C2xC10).4(C4xS3)480,244
(C2×C10).5(C4×S3) = C30.M4(2)φ: C4×S3/S3 → C4 ⊆ Aut C2×C10480(C2xC10).5(C4xS3)480,245
(C2×C10).6(C4×S3) = Dic5.22D12φ: C4×S3/S3 → C4 ⊆ Aut C2×C10240(C2xC10).6(C4xS3)480,246
(C2×C10).7(C4×S3) = D30⋊C8φ: C4×S3/S3 → C4 ⊆ Aut C2×C10240(C2xC10).7(C4xS3)480,247
(C2×C10).8(C4×S3) = D10.D12φ: C4×S3/S3 → C4 ⊆ Aut C2×C101208-(C2xC10).8(C4xS3)480,248
(C2×C10).9(C4×S3) = D10.4D12φ: C4×S3/S3 → C4 ⊆ Aut C2×C101208+(C2xC10).9(C4xS3)480,249
(C2×C10).10(C4×S3) = Dic5.D12φ: C4×S3/S3 → C4 ⊆ Aut C2×C101208+(C2xC10).10(C4xS3)480,250
(C2×C10).11(C4×S3) = Dic5.4D12φ: C4×S3/S3 → C4 ⊆ Aut C2×C102408-(C2xC10).11(C4xS3)480,251
(C2×C10).12(C4×S3) = C30.4M4(2)φ: C4×S3/S3 → C4 ⊆ Aut C2×C10480(C2xC10).12(C4xS3)480,252
(C2×C10).13(C4×S3) = Dic15⋊C8φ: C4×S3/S3 → C4 ⊆ Aut C2×C10480(C2xC10).13(C4xS3)480,253
(C2×C10).14(C4×S3) = C2×Dic3×F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C10120(C2xC10).14(C4xS3)480,998
(C2×C10).15(C4×S3) = C22⋊F5.S3φ: C4×S3/S3 → C4 ⊆ Aut C2×C101208-(C2xC10).15(C4xS3)480,999
(C2×C10).16(C4×S3) = C2×D6⋊F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C10120(C2xC10).16(C4xS3)480,1000
(C2×C10).17(C4×S3) = C2×Dic3⋊F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C10120(C2xC10).17(C4xS3)480,1001
(C2×C10).18(C4×S3) = C2×S3×C5⋊C8φ: C4×S3/S3 → C4 ⊆ Aut C2×C10240(C2xC10).18(C4xS3)480,1002
(C2×C10).19(C4×S3) = S3×C22.F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C101208-(C2xC10).19(C4xS3)480,1004
(C2×C10).20(C4×S3) = C2×D15⋊C8φ: C4×S3/S3 → C4 ⊆ Aut C2×C10240(C2xC10).20(C4xS3)480,1006
(C2×C10).21(C4×S3) = D15⋊2M4(2)φ: C4×S3/S3 → C4 ⊆ Aut C2×C101208+(C2xC10).21(C4xS3)480,1007
(C2×C10).22(C4×S3) = C2×D6.F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C10240(C2xC10).22(C4xS3)480,1008
(C2×C10).23(C4×S3) = C2×Dic3.F5φ: C4×S3/S3 → C4 ⊆ Aut C2×C10240(C2xC10).23(C4xS3)480,1009
(C2×C10).24(C4×S3) = C60.29D4φ: C4×S3/C6 → C22 ⊆ Aut C2×C101204+(C2xC10).24(C4xS3)480,36
(C2×C10).25(C4×S3) = C60.31D4φ: C4×S3/C6 → C22 ⊆ Aut C2×C102404-(C2xC10).25(C4xS3)480,39
(C2×C10).26(C4×S3) = C15⋊9(C23⋊C4)φ: C4×S3/C6 → C22 ⊆ Aut C2×C101204(C2xC10).26(C4xS3)480,73
(C2×C10).27(C4×S3) = C23.6D30φ: C4×S3/C6 → C22 ⊆ Aut C2×C101204(C2xC10).27(C4xS3)480,166
(C2×C10).28(C4×S3) = M4(2)⋊D15φ: C4×S3/C6 → C22 ⊆ Aut C2×C101204+(C2xC10).28(C4xS3)480,183
(C2×C10).29(C4×S3) = C4.D60φ: C4×S3/C6 → C22 ⊆ Aut C2×C102404-(C2xC10).29(C4xS3)480,184
(C2×C10).30(C4×S3) = D12.2Dic5φ: C4×S3/C6 → C22 ⊆ Aut C2×C102404(C2xC10).30(C4xS3)480,362
(C2×C10).31(C4×S3) = D12.Dic5φ: C4×S3/C6 → C22 ⊆ Aut C2×C102404(C2xC10).31(C4xS3)480,364
(C2×C10).32(C4×S3) = D60.5C4φ: C4×S3/C6 → C22 ⊆ Aut C2×C102404(C2xC10).32(C4xS3)480,366
(C2×C10).33(C4×S3) = D15⋊4M4(2)φ: C4×S3/C6 → C22 ⊆ Aut C2×C101204(C2xC10).33(C4xS3)480,368
(C2×C10).34(C4×S3) = C23.48(S3×D5)φ: C4×S3/C6 → C22 ⊆ Aut C2×C10240(C2xC10).34(C4xS3)480,608
(C2×C10).35(C4×S3) = C23.15D30φ: C4×S3/C6 → C22 ⊆ Aut C2×C10240(C2xC10).35(C4xS3)480,842
(C2×C10).36(C4×S3) = M4(2)×D15φ: C4×S3/C6 → C22 ⊆ Aut C2×C101204(C2xC10).36(C4xS3)480,871
(C2×C10).37(C4×S3) = D60.3C4φ: C4×S3/C6 → C22 ⊆ Aut C2×C102404(C2xC10).37(C4xS3)480,872
(C2×C10).38(C4×S3) = C5×D12.C4φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C102404(C2xC10).38(C4xS3)480,786
(C2×C10).39(C4×S3) = Dic15⋊4C8φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).39(C4xS3)480,27
(C2×C10).40(C4×S3) = C30.23C42φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).40(C4xS3)480,30
(C2×C10).41(C4×S3) = D30⋊4C8φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).41(C4xS3)480,33
(C2×C10).42(C4×S3) = C60.14Q8φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).42(C4xS3)480,59
(C2×C10).43(C4×S3) = C30.24C42φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).43(C4xS3)480,70
(C2×C10).44(C4×S3) = C2×D15⋊2C8φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).44(C4xS3)480,365
(C2×C10).45(C4×S3) = D60.4C4φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C102404(C2xC10).45(C4xS3)480,367
(C2×C10).46(C4×S3) = C2×D30.5C4φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).46(C4xS3)480,371
(C2×C10).47(C4×S3) = C2×Dic3×Dic5φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).47(C4xS3)480,603
(C2×C10).48(C4×S3) = C2×D30⋊4C4φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).48(C4xS3)480,616
(C2×C10).49(C4×S3) = C2×Dic15⋊5C4φ: C4×S3/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).49(C4xS3)480,620
(C2×C10).50(C4×S3) = C5×C8○D12φ: C4×S3/C12 → C2 ⊆ Aut C2×C102402(C2xC10).50(C4xS3)480,780
(C2×C10).51(C4×S3) = C8×Dic15φ: C4×S3/C12 → C2 ⊆ Aut C2×C10480(C2xC10).51(C4xS3)480,173
(C2×C10).52(C4×S3) = C60.26Q8φ: C4×S3/C12 → C2 ⊆ Aut C2×C10480(C2xC10).52(C4xS3)480,174
(C2×C10).53(C4×S3) = C120⋊13C4φ: C4×S3/C12 → C2 ⊆ Aut C2×C10480(C2xC10).53(C4xS3)480,175
(C2×C10).54(C4×S3) = D30⋊3C8φ: C4×S3/C12 → C2 ⊆ Aut C2×C10240(C2xC10).54(C4xS3)480,180
(C2×C10).55(C4×S3) = C30.29C42φ: C4×S3/C12 → C2 ⊆ Aut C2×C10480(C2xC10).55(C4xS3)480,191
(C2×C10).56(C4×S3) = C2×C8×D15φ: C4×S3/C12 → C2 ⊆ Aut C2×C10240(C2xC10).56(C4xS3)480,864
(C2×C10).57(C4×S3) = C2×C40⋊S3φ: C4×S3/C12 → C2 ⊆ Aut C2×C10240(C2xC10).57(C4xS3)480,865
(C2×C10).58(C4×S3) = D60.6C4φ: C4×S3/C12 → C2 ⊆ Aut C2×C102402(C2xC10).58(C4xS3)480,866
(C2×C10).59(C4×S3) = C2×C4×Dic15φ: C4×S3/C12 → C2 ⊆ Aut C2×C10480(C2xC10).59(C4xS3)480,887
(C2×C10).60(C4×S3) = C2×C30.4Q8φ: C4×S3/C12 → C2 ⊆ Aut C2×C10480(C2xC10).60(C4xS3)480,888
(C2×C10).61(C4×S3) = C2×D30⋊3C4φ: C4×S3/C12 → C2 ⊆ Aut C2×C10240(C2xC10).61(C4xS3)480,892
(C2×C10).62(C4×S3) = C5×C23.6D6φ: C4×S3/D6 → C2 ⊆ Aut C2×C101204(C2xC10).62(C4xS3)480,125
(C2×C10).63(C4×S3) = C5×C12.46D4φ: C4×S3/D6 → C2 ⊆ Aut C2×C101204(C2xC10).63(C4xS3)480,142
(C2×C10).64(C4×S3) = C5×C12.47D4φ: C4×S3/D6 → C2 ⊆ Aut C2×C102404(C2xC10).64(C4xS3)480,143
(C2×C10).65(C4×S3) = C5×C23.16D6φ: C4×S3/D6 → C2 ⊆ Aut C2×C10240(C2xC10).65(C4xS3)480,756
(C2×C10).66(C4×S3) = C5×S3×M4(2)φ: C4×S3/D6 → C2 ⊆ Aut C2×C101204(C2xC10).66(C4xS3)480,785
(C2×C10).67(C4×S3) = Dic3×C5⋊2C8φ: C4×S3/D6 → C2 ⊆ Aut C2×C10480(C2xC10).67(C4xS3)480,26
(C2×C10).68(C4×S3) = C30.22C42φ: C4×S3/D6 → C2 ⊆ Aut C2×C10480(C2xC10).68(C4xS3)480,29
(C2×C10).69(C4×S3) = C60.94D4φ: C4×S3/D6 → C2 ⊆ Aut C2×C10240(C2xC10).69(C4xS3)480,32
(C2×C10).70(C4×S3) = C20.5D12φ: C4×S3/D6 → C2 ⊆ Aut C2×C101204(C2xC10).70(C4xS3)480,35
(C2×C10).71(C4×S3) = C60.54D4φ: C4×S3/D6 → C2 ⊆ Aut C2×C102404(C2xC10).71(C4xS3)480,38
(C2×C10).72(C4×S3) = C60.15Q8φ: C4×S3/D6 → C2 ⊆ Aut C2×C10480(C2xC10).72(C4xS3)480,60
(C2×C10).73(C4×S3) = C15⋊8(C23⋊C4)φ: C4×S3/D6 → C2 ⊆ Aut C2×C101204(C2xC10).73(C4xS3)480,72
(C2×C10).74(C4×S3) = C2×S3×C5⋊2C8φ: C4×S3/D6 → C2 ⊆ Aut C2×C10240(C2xC10).74(C4xS3)480,361
(C2×C10).75(C4×S3) = S3×C4.Dic5φ: C4×S3/D6 → C2 ⊆ Aut C2×C101204(C2xC10).75(C4xS3)480,363
(C2×C10).76(C4×S3) = C2×D6.Dic5φ: C4×S3/D6 → C2 ⊆ Aut C2×C10240(C2xC10).76(C4xS3)480,370
(C2×C10).77(C4×S3) = C23.26(S3×D5)φ: C4×S3/D6 → C2 ⊆ Aut C2×C10240(C2xC10).77(C4xS3)480,605
(C2×C10).78(C4×S3) = C2×D6⋊Dic5φ: C4×S3/D6 → C2 ⊆ Aut C2×C10240(C2xC10).78(C4xS3)480,614
(C2×C10).79(C4×S3) = C2×C6.Dic10φ: C4×S3/D6 → C2 ⊆ Aut C2×C10480(C2xC10).79(C4xS3)480,621
(C2×C10).80(C4×S3) = Dic3×C40central extension (φ=1)480(C2xC10).80(C4xS3)480,132
(C2×C10).81(C4×S3) = C5×Dic3⋊C8central extension (φ=1)480(C2xC10).81(C4xS3)480,133
(C2×C10).82(C4×S3) = C5×C24⋊C4central extension (φ=1)480(C2xC10).82(C4xS3)480,134
(C2×C10).83(C4×S3) = C5×D6⋊C8central extension (φ=1)240(C2xC10).83(C4xS3)480,139
(C2×C10).84(C4×S3) = C5×C6.C42central extension (φ=1)480(C2xC10).84(C4xS3)480,150
(C2×C10).85(C4×S3) = S3×C2×C40central extension (φ=1)240(C2xC10).85(C4xS3)480,778
(C2×C10).86(C4×S3) = C10×C8⋊S3central extension (φ=1)240(C2xC10).86(C4xS3)480,779
(C2×C10).87(C4×S3) = Dic3×C2×C20central extension (φ=1)480(C2xC10).87(C4xS3)480,801
(C2×C10).88(C4×S3) = C10×Dic3⋊C4central extension (φ=1)480(C2xC10).88(C4xS3)480,802
(C2×C10).89(C4×S3) = C10×D6⋊C4central extension (φ=1)240(C2xC10).89(C4xS3)480,806

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁