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Extensions 1→N→G→Q→1 with N=C6 and Q=C22xDic5

Direct product G=NxQ with N=C6 and Q=C22xDic5
dρLabelID
Dic5xC22xC6480Dic5xC2^2xC6480,1148

Semidirect products G=N:Q with N=C6 and Q=C22xDic5
extensionφ:Q→Aut NdρLabelID
C6:1(C22xDic5) = C22xS3xDic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6:1(C2^2xDic5)480,1115
C6:2(C22xDic5) = C23xDic15φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6480C6:2(C2^2xDic5)480,1178

Non-split extensions G=N.Q with N=C6 and Q=C22xDic5
extensionφ:Q→Aut NdρLabelID
C6.1(C22xDic5) = C2xS3xC5:2C8φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.1(C2^2xDic5)480,361
C6.2(C22xDic5) = D12.2Dic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C62404C6.2(C2^2xDic5)480,362
C6.3(C22xDic5) = S3xC4.Dic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C61204C6.3(C2^2xDic5)480,363
C6.4(C22xDic5) = D12.Dic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C62404C6.4(C2^2xDic5)480,364
C6.5(C22xDic5) = C2xD6.Dic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.5(C2^2xDic5)480,370
C6.6(C22xDic5) = Dic5xDic6φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6480C6.6(C2^2xDic5)480,408
C6.7(C22xDic5) = (S3xC20):5C4φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.7(C2^2xDic5)480,414
C6.8(C22xDic5) = Dic15:7Q8φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6480C6.8(C2^2xDic5)480,420
C6.9(C22xDic5) = (S3xC20):7C4φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.9(C2^2xDic5)480,447
C6.10(C22xDic5) = C4xS3xDic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.10(C2^2xDic5)480,473
C6.11(C22xDic5) = Dic5xD12φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.11(C2^2xDic5)480,491
C6.12(C22xDic5) = S3xC4:Dic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.12(C2^2xDic5)480,502
C6.13(C22xDic5) = Dic15:8D4φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.13(C2^2xDic5)480,511
C6.14(C22xDic5) = C2xDic3xDic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6480C6.14(C2^2xDic5)480,603
C6.15(C22xDic5) = C23.26(S3xD5)φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.15(C2^2xDic5)480,605
C6.16(C22xDic5) = C2xD6:Dic5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.16(C2^2xDic5)480,614
C6.17(C22xDic5) = C2xC6.Dic10φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6480C6.17(C2^2xDic5)480,621
C6.18(C22xDic5) = Dic5xC3:D4φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.18(C2^2xDic5)480,627
C6.19(C22xDic5) = S3xC23.D5φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6120C6.19(C2^2xDic5)480,630
C6.20(C22xDic5) = Dic15:17D4φ: C22xDic5/C2xDic5 → C2 ⊆ Aut C6240C6.20(C2^2xDic5)480,636
C6.21(C22xDic5) = C22xC15:3C8φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6480C6.21(C2^2xDic5)480,885
C6.22(C22xDic5) = C2xC60.7C4φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6240C6.22(C2^2xDic5)480,886
C6.23(C22xDic5) = C2xC4xDic15φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6480C6.23(C2^2xDic5)480,887
C6.24(C22xDic5) = C2xC60:5C4φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6480C6.24(C2^2xDic5)480,890
C6.25(C22xDic5) = C23.26D30φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6240C6.25(C2^2xDic5)480,891
C6.26(C22xDic5) = D4xDic15φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6240C6.26(C2^2xDic5)480,899
C6.27(C22xDic5) = Q8xDic15φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6480C6.27(C2^2xDic5)480,910
C6.28(C22xDic5) = D4.Dic15φ: C22xDic5/C22xC10 → C2 ⊆ Aut C62404C6.28(C2^2xDic5)480,913
C6.29(C22xDic5) = C2xC30.38D4φ: C22xDic5/C22xC10 → C2 ⊆ Aut C6240C6.29(C2^2xDic5)480,917
C6.30(C22xDic5) = C2xC6xC5:2C8central extension (φ=1)480C6.30(C2^2xDic5)480,713
C6.31(C22xDic5) = C6xC4.Dic5central extension (φ=1)240C6.31(C2^2xDic5)480,714
C6.32(C22xDic5) = Dic5xC2xC12central extension (φ=1)480C6.32(C2^2xDic5)480,715
C6.33(C22xDic5) = C6xC4:Dic5central extension (φ=1)480C6.33(C2^2xDic5)480,718
C6.34(C22xDic5) = C3xC23.21D10central extension (φ=1)240C6.34(C2^2xDic5)480,719
C6.35(C22xDic5) = C3xD4xDic5central extension (φ=1)240C6.35(C2^2xDic5)480,727
C6.36(C22xDic5) = C3xQ8xDic5central extension (φ=1)480C6.36(C2^2xDic5)480,738
C6.37(C22xDic5) = C3xD4.Dic5central extension (φ=1)2404C6.37(C2^2xDic5)480,741
C6.38(C22xDic5) = C6xC23.D5central extension (φ=1)240C6.38(C2^2xDic5)480,745

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