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Extensions 1→N→G→Q→1 with N=C4 and Q=C2xC4:C4

Direct product G=NxQ with N=C4 and Q=C2xC4:C4
dρLabelID
C2xC4xC4:C4128C2xC4xC4:C4128,1001

Semidirect products G=N:Q with N=C4 and Q=C2xC4:C4
extensionφ:Q→Aut NdρLabelID
C4:1(C2xC4:C4) = D4xC4:C4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4:1(C2xC4:C4)128,1080
C4:2(C2xC4:C4) = C2xC42:9C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4:2(C2xC4:C4)128,1016
C4:3(C2xC4:C4) = C2xC23.65C23φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4:3(C2xC4:C4)128,1023

Non-split extensions G=N.Q with N=C4 and Q=C2xC4:C4
extensionφ:Q→Aut NdρLabelID
C4.1(C2xC4:C4) = C42.98D4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.1(C2xC4:C4)128,534
C4.2(C2xC4:C4) = C42.99D4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4128C4.2(C2xC4:C4)128,535
C4.3(C2xC4:C4) = C42.100D4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.3(C2xC4:C4)128,536
C4.4(C2xC4:C4) = C42.101D4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4128C4.4(C2xC4:C4)128,537
C4.5(C2xC4:C4) = C42.102D4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C432C4.5(C2xC4:C4)128,538
C4.6(C2xC4:C4) = C8oD4:C4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4324C4.6(C2xC4:C4)128,546
C4.7(C2xC4:C4) = C4oD4.4Q8φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.7(C2xC4:C4)128,547
C4.8(C2xC4:C4) = C4oD4.5Q8φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.8(C2xC4:C4)128,548
C4.9(C2xC4:C4) = C4wrC2:C4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C432C4.9(C2xC4:C4)128,591
C4.10(C2xC4:C4) = C42:9(C2xC4)φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C432C4.10(C2xC4:C4)128,592
C4.11(C2xC4:C4) = M4(2).41D4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4164C4.11(C2xC4:C4)128,593
C4.12(C2xC4:C4) = C2.(C4xD8)φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.12(C2xC4:C4)128,594
C4.13(C2xC4:C4) = Q8:(C4:C4)φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4128C4.13(C2xC4:C4)128,595
C4.14(C2xC4:C4) = D4:(C4:C4)φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.14(C2xC4:C4)128,596
C4.15(C2xC4:C4) = Q8:C4:C4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4128C4.15(C2xC4:C4)128,597
C4.16(C2xC4:C4) = M4(2).42D4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C432C4.16(C2xC4:C4)128,598
C4.17(C2xC4:C4) = C23.231C24φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.17(C2xC4:C4)128,1081
C4.18(C2xC4:C4) = Q8xC4:C4φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4128C4.18(C2xC4:C4)128,1082
C4.19(C2xC4:C4) = C23.233C24φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4128C4.19(C2xC4:C4)128,1083
C4.20(C2xC4:C4) = C42.674C23φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.20(C2xC4:C4)128,1638
C4.21(C2xC4:C4) = C4oD4.7Q8φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.21(C2xC4:C4)128,1644
C4.22(C2xC4:C4) = C4oD4.8Q8φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C464C4.22(C2xC4:C4)128,1645
C4.23(C2xC4:C4) = M4(2).29C23φ: C2xC4:C4/C4:C4 → C2 ⊆ Aut C4324C4.23(C2xC4:C4)128,1648
C4.24(C2xC4:C4) = C2xC4.9C42φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.24(C2xC4:C4)128,462
C4.25(C2xC4:C4) = C24.63D4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.25(C2xC4:C4)128,465
C4.26(C2xC4:C4) = C2xC22.4Q16φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.26(C2xC4:C4)128,466
C4.27(C2xC4:C4) = C24.132D4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.27(C2xC4:C4)128,467
C4.28(C2xC4:C4) = C24.152D4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.28(C2xC4:C4)128,468
C4.29(C2xC4:C4) = C2xC22.C42φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.29(C2xC4:C4)128,473
C4.30(C2xC4:C4) = C23.15C42φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.30(C2xC4:C4)128,474
C4.31(C2xC4:C4) = C2xM4(2):4C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.31(C2xC4:C4)128,475
C4.32(C2xC4:C4) = C8.(C4:C4)φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4324C4.32(C2xC4:C4)128,565
C4.33(C2xC4:C4) = C42.58Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.33(C2xC4:C4)128,576
C4.34(C2xC4:C4) = C42.59Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.34(C2xC4:C4)128,577
C4.35(C2xC4:C4) = C42.60Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.35(C2xC4:C4)128,578
C4.36(C2xC4:C4) = C42.26Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.36(C2xC4:C4)128,579
C4.37(C2xC4:C4) = C42.324D4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.37(C2xC4:C4)128,580
C4.38(C2xC4:C4) = C42.106D4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.38(C2xC4:C4)128,581
C4.39(C2xC4:C4) = C8:7(C4:C4)φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.39(C2xC4:C4)128,673
C4.40(C2xC4:C4) = C8:5(C4:C4)φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.40(C2xC4:C4)128,674
C4.41(C2xC4:C4) = C4.(C4xQ8)φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.41(C2xC4:C4)128,675
C4.42(C2xC4:C4) = C8:(C4:C4)φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.42(C2xC4:C4)128,676
C4.43(C2xC4:C4) = C42.62Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.43(C2xC4:C4)128,677
C4.44(C2xC4:C4) = C42.28Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.44(C2xC4:C4)128,678
C4.45(C2xC4:C4) = M4(2).5Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.45(C2xC4:C4)128,683
C4.46(C2xC4:C4) = M4(2).6Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.46(C2xC4:C4)128,684
C4.47(C2xC4:C4) = M4(2).27D4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4324C4.47(C2xC4:C4)128,685
C4.48(C2xC4:C4) = C2xC8.Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.48(C2xC4:C4)128,886
C4.49(C2xC4:C4) = M5(2):3C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4324C4.49(C2xC4:C4)128,887
C4.50(C2xC4:C4) = C2xC16:3C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.50(C2xC4:C4)128,888
C4.51(C2xC4:C4) = C2xC16:4C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.51(C2xC4:C4)128,889
C4.52(C2xC4:C4) = C23.25D8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.52(C2xC4:C4)128,890
C4.53(C2xC4:C4) = M5(2):1C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.53(C2xC4:C4)128,891
C4.54(C2xC4:C4) = C2xC8.4Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.54(C2xC4:C4)128,892
C4.55(C2xC4:C4) = M5(2).1C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4324C4.55(C2xC4:C4)128,893
C4.56(C2xC4:C4) = C2xC42:8C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.56(C2xC4:C4)128,1013
C4.57(C2xC4:C4) = C23.178C24φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.57(C2xC4:C4)128,1028
C4.58(C2xC4:C4) = C24.545C23φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.58(C2xC4:C4)128,1048
C4.59(C2xC4:C4) = C23.199C24φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.59(C2xC4:C4)128,1049
C4.60(C2xC4:C4) = C2xC4:M4(2)φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.60(C2xC4:C4)128,1635
C4.61(C2xC4:C4) = C2xC42.6C22φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.61(C2xC4:C4)128,1636
C4.62(C2xC4:C4) = C42.257C23φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.62(C2xC4:C4)128,1637
C4.63(C2xC4:C4) = C22xC4.Q8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.63(C2xC4:C4)128,1639
C4.64(C2xC4:C4) = C22xC2.D8φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C4128C4.64(C2xC4:C4)128,1640
C4.65(C2xC4:C4) = C2xM4(2):C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.65(C2xC4:C4)128,1642
C4.66(C2xC4:C4) = C24.100D4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.66(C2xC4:C4)128,1643
C4.67(C2xC4:C4) = C22xC8.C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C464C4.67(C2xC4:C4)128,1646
C4.68(C2xC4:C4) = C2xM4(2).C4φ: C2xC4:C4/C22xC4 → C2 ⊆ Aut C432C4.68(C2xC4:C4)128,1647
C4.69(C2xC4:C4) = C2xC22.7C42central extension (φ=1)128C4.69(C2xC4:C4)128,459
C4.70(C2xC4:C4) = C23.28C42central extension (φ=1)64C4.70(C2xC4:C4)128,460
C4.71(C2xC4:C4) = C23.29C42central extension (φ=1)64C4.71(C2xC4:C4)128,461
C4.72(C2xC4:C4) = C2xC42:6C4central extension (φ=1)32C4.72(C2xC4:C4)128,464
C4.73(C2xC4:C4) = C8xC4:C4central extension (φ=1)128C4.73(C2xC4:C4)128,501
C4.74(C2xC4:C4) = C4:C8:13C4central extension (φ=1)128C4.74(C2xC4:C4)128,502
C4.75(C2xC4:C4) = C4:C8:14C4central extension (φ=1)128C4.75(C2xC4:C4)128,503
C4.76(C2xC4:C4) = C8.14C42central extension (φ=1)32C4.76(C2xC4:C4)128,504
C4.77(C2xC4:C4) = C8.5C42central extension (φ=1)32C4.77(C2xC4:C4)128,505
C4.78(C2xC4:C4) = C2xC4:C16central extension (φ=1)128C4.78(C2xC4:C4)128,881
C4.79(C2xC4:C4) = C4:M5(2)central extension (φ=1)64C4.79(C2xC4:C4)128,882
C4.80(C2xC4:C4) = C4:C4.7C8central extension (φ=1)64C4.80(C2xC4:C4)128,883
C4.81(C2xC4:C4) = C2xC8.C8central extension (φ=1)32C4.81(C2xC4:C4)128,884
C4.82(C2xC4:C4) = M4(2).1C8central extension (φ=1)324C4.82(C2xC4:C4)128,885
C4.83(C2xC4:C4) = C23.167C24central extension (φ=1)64C4.83(C2xC4:C4)128,1017
C4.84(C2xC4:C4) = C22xC4:C8central extension (φ=1)128C4.84(C2xC4:C4)128,1634
C4.85(C2xC4:C4) = C2xC23.25D4central extension (φ=1)64C4.85(C2xC4:C4)128,1641

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