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

Extensions 1→N→G→Q→1 with N=C23 and Q=C3⋊D4

Direct product G=N×Q with N=C23 and Q=C3⋊D4
dρLabelID
C23×C3⋊D496C2^3xC3:D4192,1529

Semidirect products G=N:Q with N=C23 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C23⋊1(C3⋊D4) = C24⋊6D6φ: C3⋊D4/C3 → D4 ⊆ Aut C23244C2^3:1(C3:D4)192,591
C23⋊2(C3⋊D4) = 2+ 1+4⋊7S3φ: C3⋊D4/C3 → D4 ⊆ Aut C23248+C2^3:2(C3:D4)192,803
C23⋊3(C3⋊D4) = C2×A4⋊D4φ: C3⋊D4/C22 → S3 ⊆ Aut C2324C2^3:3(C3:D4)192,1488
C23⋊4(C3⋊D4) = C24.32D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3:4(C3:D4)192,782
C23⋊5(C3⋊D4) = C24⋊12D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2348C2^3:5(C3:D4)192,1363
C23⋊6(C3⋊D4) = C2×C23.14D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3:6(C3:D4)192,1361
C23⋊7(C3⋊D4) = C2×C23⋊2D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3:7(C3:D4)192,1358
C23⋊8(C3⋊D4) = C2×C24⋊4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3:8(C3:D4)192,1399

Non-split extensions G=N.Q with N=C23 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C23.1(C3⋊D4) = C3⋊C2≀C4φ: C3⋊D4/C3 → D4 ⊆ Aut C23248+C2^3.1(C3:D4)192,30
C23.2(C3⋊D4) = (C2×D4).D6φ: C3⋊D4/C3 → D4 ⊆ Aut C23488-C2^3.2(C3:D4)192,31
C23.3(C3⋊D4) = C23.D12φ: C3⋊D4/C3 → D4 ⊆ Aut C23488-C2^3.3(C3:D4)192,32
C23.4(C3⋊D4) = C23.2D12φ: C3⋊D4/C3 → D4 ⊆ Aut C23248+C2^3.4(C3:D4)192,33
C23.5(C3⋊D4) = C24⋊5Dic3φ: C3⋊D4/C3 → D4 ⊆ Aut C23244C2^3.5(C3:D4)192,95
C23.6(C3⋊D4) = (C22×C12)⋊C4φ: C3⋊D4/C3 → D4 ⊆ Aut C23484C2^3.6(C3:D4)192,98
C23.7(C3⋊D4) = C42⋊4Dic3φ: C3⋊D4/C3 → D4 ⊆ Aut C23484C2^3.7(C3:D4)192,100
C23.8(C3⋊D4) = C42⋊5Dic3φ: C3⋊D4/C3 → D4 ⊆ Aut C23244C2^3.8(C3:D4)192,104
C23.9(C3⋊D4) = C22⋊C4⋊D6φ: C3⋊D4/C3 → D4 ⊆ Aut C23484C2^3.9(C3:D4)192,612
C23.10(C3⋊D4) = C42⋊7D6φ: C3⋊D4/C3 → D4 ⊆ Aut C23484C2^3.10(C3:D4)192,620
C23.11(C3⋊D4) = C42⋊8D6φ: C3⋊D4/C3 → D4 ⊆ Aut C23244C2^3.11(C3:D4)192,636
C23.12(C3⋊D4) = 2+ 1+4⋊6S3φ: C3⋊D4/C3 → D4 ⊆ Aut C23248+C2^3.12(C3:D4)192,800
C23.13(C3⋊D4) = 2+ 1+4.4S3φ: C3⋊D4/C3 → D4 ⊆ Aut C23488-C2^3.13(C3:D4)192,801
C23.14(C3⋊D4) = 2+ 1+4.5S3φ: C3⋊D4/C3 → D4 ⊆ Aut C23488-C2^3.14(C3:D4)192,802
C23.15(C3⋊D4) = C24.3D6φ: C3⋊D4/C22 → S3 ⊆ Aut C2348C2^3.15(C3:D4)192,970
C23.16(C3⋊D4) = C24.5D6φ: C3⋊D4/C22 → S3 ⊆ Aut C2324C2^3.16(C3:D4)192,972
C23.17(C3⋊D4) = A4⋊SD16φ: C3⋊D4/C22 → S3 ⊆ Aut C23246C2^3.17(C3:D4)192,973
C23.18(C3⋊D4) = D4⋊S4φ: C3⋊D4/C22 → S3 ⊆ Aut C23246+C2^3.18(C3:D4)192,974
C23.19(C3⋊D4) = A4⋊2Q16φ: C3⋊D4/C22 → S3 ⊆ Aut C23486-C2^3.19(C3:D4)192,975
C23.20(C3⋊D4) = Q8⋊3S4φ: C3⋊D4/C22 → S3 ⊆ Aut C23246C2^3.20(C3:D4)192,976
C23.21(C3⋊D4) = C25.S3φ: C3⋊D4/C22 → S3 ⊆ Aut C2324C2^3.21(C3:D4)192,991
C23.22(C3⋊D4) = C24.13D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2348C2^3.22(C3:D4)192,86
C23.23(C3⋊D4) = C42⋊3Dic3φ: C3⋊D4/C6 → C22 ⊆ Aut C23484C2^3.23(C3:D4)192,90
C23.24(C3⋊D4) = C24.20D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.24(C3:D4)192,511
C23.25(C3⋊D4) = C24.25D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.25(C3:D4)192,518
C23.26(C3⋊D4) = C4⋊C4.233D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.26(C3:D4)192,555
C23.27(C3⋊D4) = C4⋊C4.236D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.27(C3:D4)192,562
C23.28(C3⋊D4) = C42⋊6D6φ: C3⋊D4/C6 → C22 ⊆ Aut C23484C2^3.28(C3:D4)192,564
C23.29(C3⋊D4) = C6.Q16⋊C2φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.29(C3:D4)192,594
C23.30(C3⋊D4) = D12⋊17D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.30(C3:D4)192,596
C23.31(C3⋊D4) = C4⋊D4⋊S3φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.31(C3:D4)192,598
C23.32(C3⋊D4) = C3⋊C8⋊5D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.32(C3:D4)192,601
C23.33(C3⋊D4) = (C2×Q8).51D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.33(C3:D4)192,604
C23.34(C3⋊D4) = D12.37D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.34(C3:D4)192,606
C23.35(C3⋊D4) = C3⋊C8⋊6D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.35(C3:D4)192,608
C23.36(C3⋊D4) = C3⋊C8.6D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.36(C3:D4)192,611
C23.37(C3⋊D4) = C24.31D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.37(C3:D4)192,781
C23.38(C3⋊D4) = (C6×D4)⋊9C4φ: C3⋊D4/C6 → C22 ⊆ Aut C23484C2^3.38(C3:D4)192,795
C23.39(C3⋊D4) = (C3×D4)⋊14D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.39(C3:D4)192,797
C23.40(C3⋊D4) = (C3×D4).32D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2396C2^3.40(C3:D4)192,798
C23.41(C3⋊D4) = C12.C24φ: C3⋊D4/C6 → C22 ⊆ Aut C23484C2^3.41(C3:D4)192,1381
C23.42(C3⋊D4) = C24.55D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.42(C3:D4)192,501
C23.43(C3⋊D4) = C24.60D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.43(C3:D4)192,517
C23.44(C3⋊D4) = C4⋊C4.234D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.44(C3:D4)192,557
C23.45(C3⋊D4) = C4.(C2×D12)φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.45(C3:D4)192,561
C23.46(C3⋊D4) = C3⋊C8⋊22D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.46(C3:D4)192,597
C23.47(C3⋊D4) = C3⋊C8⋊23D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.47(C3:D4)192,600
C23.48(C3⋊D4) = C3⋊C8⋊24D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.48(C3:D4)192,607
C23.49(C3⋊D4) = C3⋊C8.29D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.49(C3:D4)192,610
C23.50(C3⋊D4) = C24.29D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.50(C3:D4)192,779
C23.51(C3⋊D4) = C4○D4⋊4Dic3φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.51(C3:D4)192,792
C23.52(C3⋊D4) = C2×Q8.13D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2396C2^3.52(C3:D4)192,1380
C23.53(C3⋊D4) = C24.12D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.53(C3:D4)192,85
C23.54(C3⋊D4) = C12.2C42φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.54(C3:D4)192,91
C23.55(C3⋊D4) = (C6×D4)⋊C4φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.55(C3:D4)192,96
C23.56(C3⋊D4) = (C6×Q8)⋊C4φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.56(C3:D4)192,97
C23.57(C3⋊D4) = C24.56D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.57(C3:D4)192,502
C23.58(C3⋊D4) = C24.57D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.58(C3:D4)192,505
C23.59(C3⋊D4) = C24.59D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.59(C3:D4)192,514
C23.60(C3⋊D4) = C4⋊C4.232D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.60(C3:D4)192,554
C23.61(C3⋊D4) = C4⋊C4⋊36D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.61(C3:D4)192,560
C23.62(C3⋊D4) = C4⋊C4.237D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.62(C3:D4)192,563
C23.63(C3⋊D4) = (C2×C6).D8φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.63(C3:D4)192,592
C23.64(C3⋊D4) = C4⋊D4.S3φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.64(C3:D4)192,593
C23.65(C3⋊D4) = D12⋊16D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.65(C3:D4)192,595
C23.66(C3⋊D4) = Dic6⋊17D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.66(C3:D4)192,599
C23.67(C3⋊D4) = (C2×Q8).49D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.67(C3:D4)192,602
C23.68(C3⋊D4) = (C2×C6).Q16φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.68(C3:D4)192,603
C23.69(C3⋊D4) = D12.36D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.69(C3:D4)192,605
C23.70(C3⋊D4) = Dic6.37D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.70(C3:D4)192,609
C23.71(C3⋊D4) = C2×C23.7D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.71(C3:D4)192,778
C23.72(C3⋊D4) = C4○D4⋊3Dic3φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.72(C3:D4)192,791
C23.73(C3⋊D4) = C2×Q8⋊3Dic3φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.73(C3:D4)192,794
C23.74(C3⋊D4) = C2×C23.23D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.74(C3:D4)192,1355
C23.75(C3⋊D4) = C2×D4⋊D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2348C2^3.75(C3:D4)192,1379
C23.76(C3⋊D4) = C2×Q8.14D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2396C2^3.76(C3:D4)192,1382
C23.77(C3⋊D4) = C6.C4≀C2φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.77(C3:D4)192,10
C23.78(C3⋊D4) = C4⋊Dic3⋊C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.78(C3:D4)192,11
C23.79(C3⋊D4) = C12.8C42φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.79(C3:D4)192,82
C23.80(C3⋊D4) = C2×C42⋊4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.80(C3:D4)192,486
C23.81(C3⋊D4) = C2×C23.6D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.81(C3:D4)192,513
C23.82(C3⋊D4) = C4⋊C4.225D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.82(C3:D4)192,523
C23.83(C3⋊D4) = C4○D12⋊C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.83(C3:D4)192,525
C23.84(C3⋊D4) = (C2×C6).40D8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.84(C3:D4)192,526
C23.85(C3⋊D4) = C4⋊C4.228D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.85(C3:D4)192,527
C23.86(C3⋊D4) = C4⋊C4.230D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.86(C3:D4)192,529
C23.87(C3⋊D4) = C4⋊C4.231D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.87(C3:D4)192,530
C23.88(C3⋊D4) = C24.73D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.88(C3:D4)192,769
C23.89(C3⋊D4) = C24.74D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.89(C3:D4)192,770
C23.90(C3⋊D4) = C24.76D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.90(C3:D4)192,772
C23.91(C3⋊D4) = (C6×D4)⋊6C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.91(C3:D4)192,774
C23.92(C3⋊D4) = (C2×C6)⋊8D8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.92(C3:D4)192,776
C23.93(C3⋊D4) = (C3×D4).31D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.93(C3:D4)192,777
C23.94(C3⋊D4) = (C6×Q8)⋊6C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.94(C3:D4)192,784
C23.95(C3⋊D4) = (C3×Q8)⋊13D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.95(C3:D4)192,786
C23.96(C3⋊D4) = (C2×C6)⋊8Q16φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.96(C3:D4)192,787
C23.97(C3⋊D4) = C25.4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.97(C3:D4)192,806
C23.98(C3⋊D4) = C2×C23.28D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.98(C3:D4)192,1348
C23.99(C3⋊D4) = C2×D12⋊6C22φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2348C2^3.99(C3:D4)192,1352
C23.100(C3⋊D4) = C2×Q8.11D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2396C2^3.100(C3:D4)192,1367
C23.101(C3⋊D4) = C12.C42central extension (φ=1)192C2^3.101(C3:D4)192,88
C23.102(C3⋊D4) = C2×C6.Q16central extension (φ=1)192C2^3.102(C3:D4)192,521
C23.103(C3⋊D4) = C2×C12.Q8central extension (φ=1)192C2^3.103(C3:D4)192,522
C23.104(C3⋊D4) = C2×C6.D8central extension (φ=1)96C2^3.104(C3:D4)192,524
C23.105(C3⋊D4) = C2×C6.SD16central extension (φ=1)192C2^3.105(C3:D4)192,528
C23.106(C3⋊D4) = C2×C6.C42central extension (φ=1)192C2^3.106(C3:D4)192,767
C23.107(C3⋊D4) = C2×D4⋊Dic3central extension (φ=1)96C2^3.107(C3:D4)192,773
C23.108(C3⋊D4) = C2×Q8⋊2Dic3central extension (φ=1)192C2^3.108(C3:D4)192,783
C23.109(C3⋊D4) = C22×Dic3⋊C4central extension (φ=1)192C2^3.109(C3:D4)192,1342
C23.110(C3⋊D4) = C22×D6⋊C4central extension (φ=1)96C2^3.110(C3:D4)192,1346
C23.111(C3⋊D4) = C22×D4⋊S3central extension (φ=1)96C2^3.111(C3:D4)192,1351
C23.112(C3⋊D4) = C22×D4.S3central extension (φ=1)96C2^3.112(C3:D4)192,1353
C23.113(C3⋊D4) = C22×Q8⋊2S3central extension (φ=1)96C2^3.113(C3:D4)192,1366
C23.114(C3⋊D4) = C22×C3⋊Q16central extension (φ=1)192C2^3.114(C3:D4)192,1368
C23.115(C3⋊D4) = C22×C6.D4central extension (φ=1)96C2^3.115(C3:D4)192,1398

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁