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

Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C4×S3

Direct product G=N×Q with N=C3×C6 and Q=C4×S3
dρLabelID
S3×C6×C12144S3xC6xC12432,701

Semidirect products G=N:Q with N=C3×C6 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1(C4×S3) = C2×C6.S32φ: C4×S3/C2 → D6 ⊆ Aut C3×C672(C3xC6):1(C4xS3)432,317
(C3×C6)⋊2(C4×S3) = C2×He3⋊(C2×C4)φ: C4×S3/C2 → D6 ⊆ Aut C3×C672(C3xC6):2(C4xS3)432,321
(C3×C6)⋊3(C4×S3) = C2×C4×C32⋊C6φ: C4×S3/C4 → S3 ⊆ Aut C3×C672(C3xC6):3(C4xS3)432,349
(C3×C6)⋊4(C4×S3) = C2×C4×He3⋊C2φ: C4×S3/C4 → S3 ⊆ Aut C3×C672(C3xC6):4(C4xS3)432,385
(C3×C6)⋊5(C4×S3) = C2×S3×C32⋊C4φ: C4×S3/S3 → C4 ⊆ Aut C3×C6248+(C3xC6):5(C4xS3)432,753
(C3×C6)⋊6(C4×S3) = C2×Dic3×C3⋊S3φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6):6(C4xS3)432,677
(C3×C6)⋊7(C4×S3) = C2×C33⋊9(C2×C4)φ: C4×S3/C6 → C22 ⊆ Aut C3×C648(C3xC6):7(C4xS3)432,692
(C3×C6)⋊8(C4×S3) = C6×C6.D6φ: C4×S3/Dic3 → C2 ⊆ Aut C3×C648(C3xC6):8(C4xS3)432,654
(C3×C6)⋊9(C4×S3) = C2×C33⋊8(C2×C4)φ: C4×S3/Dic3 → C2 ⊆ Aut C3×C672(C3xC6):9(C4xS3)432,679
(C3×C6)⋊10(C4×S3) = C3⋊S3×C2×C12φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6):10(C4xS3)432,711
(C3×C6)⋊11(C4×S3) = C2×C4×C33⋊C2φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6):11(C4xS3)432,721
(C3×C6)⋊12(C4×S3) = S3×C6×Dic3φ: C4×S3/D6 → C2 ⊆ Aut C3×C648(C3xC6):12(C4xS3)432,651
(C3×C6)⋊13(C4×S3) = C2×S3×C3⋊Dic3φ: C4×S3/D6 → C2 ⊆ Aut C3×C6144(C3xC6):13(C4xS3)432,674

Non-split extensions G=N.Q with N=C3×C6 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C4×S3) = C32⋊C6⋊C8φ: C4×S3/C2 → D6 ⊆ Aut C3×C6726(C3xC6).1(C4xS3)432,76
(C3×C6).2(C4×S3) = He3⋊M4(2)φ: C4×S3/C2 → D6 ⊆ Aut C3×C6726(C3xC6).2(C4xS3)432,77
(C3×C6).3(C4×S3) = C12.89S32φ: C4×S3/C2 → D6 ⊆ Aut C3×C6726(C3xC6).3(C4xS3)432,81
(C3×C6).4(C4×S3) = He3⋊3M4(2)φ: C4×S3/C2 → D6 ⊆ Aut C3×C6726(C3xC6).4(C4xS3)432,82
(C3×C6).5(C4×S3) = He3⋊C42φ: C4×S3/C2 → D6 ⊆ Aut C3×C6144(C3xC6).5(C4xS3)432,94
(C3×C6).6(C4×S3) = C62.D6φ: C4×S3/C2 → D6 ⊆ Aut C3×C6144(C3xC6).6(C4xS3)432,95
(C3×C6).7(C4×S3) = C62.3D6φ: C4×S3/C2 → D6 ⊆ Aut C3×C6144(C3xC6).7(C4xS3)432,96
(C3×C6).8(C4×S3) = C62.4D6φ: C4×S3/C2 → D6 ⊆ Aut C3×C672(C3xC6).8(C4xS3)432,97
(C3×C6).9(C4×S3) = C62.5D6φ: C4×S3/C2 → D6 ⊆ Aut C3×C672(C3xC6).9(C4xS3)432,98
(C3×C6).10(C4×S3) = C8×C32⋊C6φ: C4×S3/C4 → S3 ⊆ Aut C3×C6726(C3xC6).10(C4xS3)432,115
(C3×C6).11(C4×S3) = He3⋊5M4(2)φ: C4×S3/C4 → S3 ⊆ Aut C3×C6726(C3xC6).11(C4xS3)432,116
(C3×C6).12(C4×S3) = C8×C9⋊C6φ: C4×S3/C4 → S3 ⊆ Aut C3×C6726(C3xC6).12(C4xS3)432,120
(C3×C6).13(C4×S3) = C72⋊C6φ: C4×S3/C4 → S3 ⊆ Aut C3×C6726(C3xC6).13(C4xS3)432,121
(C3×C6).14(C4×S3) = C4×C32⋊C12φ: C4×S3/C4 → S3 ⊆ Aut C3×C6144(C3xC6).14(C4xS3)432,138
(C3×C6).15(C4×S3) = C62.19D6φ: C4×S3/C4 → S3 ⊆ Aut C3×C6144(C3xC6).15(C4xS3)432,139
(C3×C6).16(C4×S3) = C62.21D6φ: C4×S3/C4 → S3 ⊆ Aut C3×C672(C3xC6).16(C4xS3)432,141
(C3×C6).17(C4×S3) = C4×C9⋊C12φ: C4×S3/C4 → S3 ⊆ Aut C3×C6144(C3xC6).17(C4xS3)432,144
(C3×C6).18(C4×S3) = Dic9⋊C12φ: C4×S3/C4 → S3 ⊆ Aut C3×C6144(C3xC6).18(C4xS3)432,145
(C3×C6).19(C4×S3) = D18⋊C12φ: C4×S3/C4 → S3 ⊆ Aut C3×C672(C3xC6).19(C4xS3)432,147
(C3×C6).20(C4×S3) = C8×He3⋊C2φ: C4×S3/C4 → S3 ⊆ Aut C3×C6723(C3xC6).20(C4xS3)432,173
(C3×C6).21(C4×S3) = He3⋊6M4(2)φ: C4×S3/C4 → S3 ⊆ Aut C3×C6726(C3xC6).21(C4xS3)432,174
(C3×C6).22(C4×S3) = C4×He3⋊3C4φ: C4×S3/C4 → S3 ⊆ Aut C3×C6144(C3xC6).22(C4xS3)432,186
(C3×C6).23(C4×S3) = C62.29D6φ: C4×S3/C4 → S3 ⊆ Aut C3×C6144(C3xC6).23(C4xS3)432,187
(C3×C6).24(C4×S3) = C62.31D6φ: C4×S3/C4 → S3 ⊆ Aut C3×C672(C3xC6).24(C4xS3)432,189
(C3×C6).25(C4×S3) = C2×C4×C9⋊C6φ: C4×S3/C4 → S3 ⊆ Aut C3×C672(C3xC6).25(C4xS3)432,353
(C3×C6).26(C4×S3) = Dic3×C32⋊C4φ: C4×S3/S3 → C4 ⊆ Aut C3×C6488-(C3xC6).26(C4xS3)432,567
(C3×C6).27(C4×S3) = D6⋊(C32⋊C4)φ: C4×S3/S3 → C4 ⊆ Aut C3×C6248+(C3xC6).27(C4xS3)432,568
(C3×C6).28(C4×S3) = C33⋊(C4⋊C4)φ: C4×S3/S3 → C4 ⊆ Aut C3×C6488-(C3xC6).28(C4xS3)432,569
(C3×C6).29(C4×S3) = S3×C32⋊2C8φ: C4×S3/S3 → C4 ⊆ Aut C3×C6488-(C3xC6).29(C4xS3)432,570
(C3×C6).30(C4×S3) = C33⋊5(C2×C8)φ: C4×S3/S3 → C4 ⊆ Aut C3×C6248+(C3xC6).30(C4xS3)432,571
(C3×C6).31(C4×S3) = C33⋊M4(2)φ: C4×S3/S3 → C4 ⊆ Aut C3×C6488-(C3xC6).31(C4xS3)432,572
(C3×C6).32(C4×S3) = C33⋊2M4(2)φ: C4×S3/S3 → C4 ⊆ Aut C3×C6248+(C3xC6).32(C4xS3)432,573
(C3×C6).33(C4×S3) = D9×C3⋊C8φ: C4×S3/C6 → C22 ⊆ Aut C3×C61444(C3xC6).33(C4xS3)432,58
(C3×C6).34(C4×S3) = C36.38D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C6724(C3xC6).34(C4xS3)432,59
(C3×C6).35(C4×S3) = C36.39D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C61444(C3xC6).35(C4xS3)432,60
(C3×C6).36(C4×S3) = C36.40D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C6724(C3xC6).36(C4xS3)432,61
(C3×C6).37(C4×S3) = Dic3×Dic9φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).37(C4xS3)432,87
(C3×C6).38(C4×S3) = Dic9⋊Dic3φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).38(C4xS3)432,88
(C3×C6).39(C4×S3) = C18.Dic6φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).39(C4xS3)432,89
(C3×C6).40(C4×S3) = D18⋊Dic3φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).40(C4xS3)432,91
(C3×C6).41(C4×S3) = C6.18D36φ: C4×S3/C6 → C22 ⊆ Aut C3×C672(C3xC6).41(C4xS3)432,92
(C3×C6).42(C4×S3) = C2×Dic3×D9φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).42(C4xS3)432,304
(C3×C6).43(C4×S3) = C2×C18.D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C672(C3xC6).43(C4xS3)432,306
(C3×C6).44(C4×S3) = C3⋊S3×C3⋊C8φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).44(C4xS3)432,431
(C3×C6).45(C4×S3) = C12.69S32φ: C4×S3/C6 → C22 ⊆ Aut C3×C672(C3xC6).45(C4xS3)432,432
(C3×C6).46(C4×S3) = C33⋊8M4(2)φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).46(C4xS3)432,434
(C3×C6).47(C4×S3) = C33⋊9M4(2)φ: C4×S3/C6 → C22 ⊆ Aut C3×C672(C3xC6).47(C4xS3)432,435
(C3×C6).48(C4×S3) = Dic3×C3⋊Dic3φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).48(C4xS3)432,448
(C3×C6).49(C4×S3) = C62.78D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).49(C4xS3)432,450
(C3×C6).50(C4×S3) = C62.79D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C672(C3xC6).50(C4xS3)432,451
(C3×C6).51(C4×S3) = C62.81D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).51(C4xS3)432,453
(C3×C6).52(C4×S3) = C62.82D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C6144(C3xC6).52(C4xS3)432,454
(C3×C6).53(C4×S3) = C12.93S32φ: C4×S3/C6 → C22 ⊆ Aut C3×C6484(C3xC6).53(C4xS3)432,455
(C3×C6).54(C4×S3) = C33⋊10M4(2)φ: C4×S3/C6 → C22 ⊆ Aut C3×C6484(C3xC6).54(C4xS3)432,456
(C3×C6).55(C4×S3) = C33⋊6C42φ: C4×S3/C6 → C22 ⊆ Aut C3×C648(C3xC6).55(C4xS3)432,460
(C3×C6).56(C4×S3) = C62.84D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C648(C3xC6).56(C4xS3)432,461
(C3×C6).57(C4×S3) = C62.85D6φ: C4×S3/C6 → C22 ⊆ Aut C3×C648(C3xC6).57(C4xS3)432,462
(C3×C6).58(C4×S3) = C3×C12.29D6φ: C4×S3/Dic3 → C2 ⊆ Aut C3×C6484(C3xC6).58(C4xS3)432,415
(C3×C6).59(C4×S3) = C3×C12.31D6φ: C4×S3/Dic3 → C2 ⊆ Aut C3×C6484(C3xC6).59(C4xS3)432,417
(C3×C6).60(C4×S3) = C3×Dic32φ: C4×S3/Dic3 → C2 ⊆ Aut C3×C648(C3xC6).60(C4xS3)432,425
(C3×C6).61(C4×S3) = C3×C6.D12φ: C4×S3/Dic3 → C2 ⊆ Aut C3×C648(C3xC6).61(C4xS3)432,427
(C3×C6).62(C4×S3) = C3×C62.C22φ: C4×S3/Dic3 → C2 ⊆ Aut C3×C648(C3xC6).62(C4xS3)432,429
(C3×C6).63(C4×S3) = D9×C24φ: C4×S3/C12 → C2 ⊆ Aut C3×C61442(C3xC6).63(C4xS3)432,105
(C3×C6).64(C4×S3) = C3×C8⋊D9φ: C4×S3/C12 → C2 ⊆ Aut C3×C61442(C3xC6).64(C4xS3)432,106
(C3×C6).65(C4×S3) = C12×Dic9φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).65(C4xS3)432,128
(C3×C6).66(C4×S3) = C3×Dic9⋊C4φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).66(C4xS3)432,129
(C3×C6).67(C4×S3) = C3×D18⋊C4φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).67(C4xS3)432,134
(C3×C6).68(C4×S3) = C8×C9⋊S3φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6).68(C4xS3)432,169
(C3×C6).69(C4×S3) = C72⋊S3φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6).69(C4xS3)432,170
(C3×C6).70(C4×S3) = C4×C9⋊Dic3φ: C4×S3/C12 → C2 ⊆ Aut C3×C6432(C3xC6).70(C4xS3)432,180
(C3×C6).71(C4×S3) = C6.Dic18φ: C4×S3/C12 → C2 ⊆ Aut C3×C6432(C3xC6).71(C4xS3)432,181
(C3×C6).72(C4×S3) = C6.11D36φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6).72(C4xS3)432,183
(C3×C6).73(C4×S3) = D9×C2×C12φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).73(C4xS3)432,342
(C3×C6).74(C4×S3) = C2×C4×C9⋊S3φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6).74(C4xS3)432,381
(C3×C6).75(C4×S3) = C3⋊S3×C24φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).75(C4xS3)432,480
(C3×C6).76(C4×S3) = C3×C24⋊S3φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).76(C4xS3)432,481
(C3×C6).77(C4×S3) = C12×C3⋊Dic3φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).77(C4xS3)432,487
(C3×C6).78(C4×S3) = C3×C6.Dic6φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).78(C4xS3)432,488
(C3×C6).79(C4×S3) = C3×C6.11D12φ: C4×S3/C12 → C2 ⊆ Aut C3×C6144(C3xC6).79(C4xS3)432,490
(C3×C6).80(C4×S3) = C8×C33⋊C2φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6).80(C4xS3)432,496
(C3×C6).81(C4×S3) = C33⋊15M4(2)φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6).81(C4xS3)432,497
(C3×C6).82(C4×S3) = C4×C33⋊5C4φ: C4×S3/C12 → C2 ⊆ Aut C3×C6432(C3xC6).82(C4xS3)432,503
(C3×C6).83(C4×S3) = C62.146D6φ: C4×S3/C12 → C2 ⊆ Aut C3×C6432(C3xC6).83(C4xS3)432,504
(C3×C6).84(C4×S3) = C62.148D6φ: C4×S3/C12 → C2 ⊆ Aut C3×C6216(C3xC6).84(C4xS3)432,506
(C3×C6).85(C4×S3) = C3×S3×C3⋊C8φ: C4×S3/D6 → C2 ⊆ Aut C3×C6484(C3xC6).85(C4xS3)432,414
(C3×C6).86(C4×S3) = C3×D6.Dic3φ: C4×S3/D6 → C2 ⊆ Aut C3×C6484(C3xC6).86(C4xS3)432,416
(C3×C6).87(C4×S3) = C3×D6⋊Dic3φ: C4×S3/D6 → C2 ⊆ Aut C3×C648(C3xC6).87(C4xS3)432,426
(C3×C6).88(C4×S3) = C3×Dic3⋊Dic3φ: C4×S3/D6 → C2 ⊆ Aut C3×C648(C3xC6).88(C4xS3)432,428
(C3×C6).89(C4×S3) = S3×C32⋊4C8φ: C4×S3/D6 → C2 ⊆ Aut C3×C6144(C3xC6).89(C4xS3)432,430
(C3×C6).90(C4×S3) = C33⋊7M4(2)φ: C4×S3/D6 → C2 ⊆ Aut C3×C6144(C3xC6).90(C4xS3)432,433
(C3×C6).91(C4×S3) = C62.77D6φ: C4×S3/D6 → C2 ⊆ Aut C3×C6144(C3xC6).91(C4xS3)432,449
(C3×C6).92(C4×S3) = C62.80D6φ: C4×S3/D6 → C2 ⊆ Aut C3×C6144(C3xC6).92(C4xS3)432,452
(C3×C6).93(C4×S3) = S3×C3×C24central extension (φ=1)144(C3xC6).93(C4xS3)432,464
(C3×C6).94(C4×S3) = C32×C8⋊S3central extension (φ=1)144(C3xC6).94(C4xS3)432,465
(C3×C6).95(C4×S3) = Dic3×C3×C12central extension (φ=1)144(C3xC6).95(C4xS3)432,471
(C3×C6).96(C4×S3) = C32×Dic3⋊C4central extension (φ=1)144(C3xC6).96(C4xS3)432,472
(C3×C6).97(C4×S3) = C32×D6⋊C4central extension (φ=1)144(C3xC6).97(C4xS3)432,474

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁