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Extensions 1→N→G→Q→1 with N=C22 and Q=S3×C2×C10

Direct product G=N×Q with N=C22 and Q=S3×C2×C10
dρLabelID
S3×C23×C10240S3xC2^3xC10480,1211

Semidirect products G=N:Q with N=C22 and Q=S3×C2×C10
extensionφ:Q→Aut NdρLabelID
C22⋊(S3×C2×C10) = C2×C10×S4φ: S3×C2×C10/C2×C10 → S3 ⊆ Aut C2260C2^2:(S3xC2xC10)480,1198
C22⋊2(S3×C2×C10) = S3×D4×C10φ: S3×C2×C10/S3×C10 → C2 ⊆ Aut C22120C2^2:2(S3xC2xC10)480,1154
C22⋊3(S3×C2×C10) = C2×C10×C3⋊D4φ: S3×C2×C10/C2×C30 → C2 ⊆ Aut C22240C2^2:3(S3xC2xC10)480,1164

Non-split extensions G=N.Q with N=C22 and Q=S3×C2×C10
extensionφ:Q→Aut NdρLabelID
C22.1(S3×C2×C10) = C10×D4⋊2S3φ: S3×C2×C10/S3×C10 → C2 ⊆ Aut C22240C2^2.1(S3xC2xC10)480,1155
C22.2(S3×C2×C10) = C5×D4⋊6D6φ: S3×C2×C10/S3×C10 → C2 ⊆ Aut C221204C2^2.2(S3xC2xC10)480,1156
C22.3(S3×C2×C10) = C5×S3×C4○D4φ: S3×C2×C10/S3×C10 → C2 ⊆ Aut C221204C2^2.3(S3xC2xC10)480,1160
C22.4(S3×C2×C10) = C5×D4○D12φ: S3×C2×C10/S3×C10 → C2 ⊆ Aut C221204C2^2.4(S3xC2xC10)480,1161
C22.5(S3×C2×C10) = C5×Q8○D12φ: S3×C2×C10/S3×C10 → C2 ⊆ Aut C222404C2^2.5(S3xC2xC10)480,1162
C22.6(S3×C2×C10) = C10×C4○D12φ: S3×C2×C10/C2×C30 → C2 ⊆ Aut C22240C2^2.6(S3xC2xC10)480,1153
C22.7(S3×C2×C10) = C5×Q8.15D6φ: S3×C2×C10/C2×C30 → C2 ⊆ Aut C222404C2^2.7(S3xC2xC10)480,1159
C22.8(S3×C2×C10) = C20×Dic6central extension (φ=1)480C2^2.8(S3xC2xC10)480,747
C22.9(S3×C2×C10) = S3×C4×C20central extension (φ=1)240C2^2.9(S3xC2xC10)480,750
C22.10(S3×C2×C10) = C5×C42⋊2S3central extension (φ=1)240C2^2.10(S3xC2xC10)480,751
C22.11(S3×C2×C10) = C20×D12central extension (φ=1)240C2^2.11(S3xC2xC10)480,752
C22.12(S3×C2×C10) = C5×C23.16D6central extension (φ=1)240C2^2.12(S3xC2xC10)480,756
C22.13(S3×C2×C10) = C5×S3×C22⋊C4central extension (φ=1)120C2^2.13(S3xC2xC10)480,759
C22.14(S3×C2×C10) = C5×Dic3⋊4D4central extension (φ=1)240C2^2.14(S3xC2xC10)480,760
C22.15(S3×C2×C10) = C5×Dic6⋊C4central extension (φ=1)480C2^2.15(S3xC2xC10)480,766
C22.16(S3×C2×C10) = C5×S3×C4⋊C4central extension (φ=1)240C2^2.16(S3xC2xC10)480,770
C22.17(S3×C2×C10) = C5×C4⋊C4⋊7S3central extension (φ=1)240C2^2.17(S3xC2xC10)480,771
C22.18(S3×C2×C10) = C5×Dic3⋊5D4central extension (φ=1)240C2^2.18(S3xC2xC10)480,772
C22.19(S3×C2×C10) = Dic3×C2×C20central extension (φ=1)480C2^2.19(S3xC2xC10)480,801
C22.20(S3×C2×C10) = C10×Dic3⋊C4central extension (φ=1)480C2^2.20(S3xC2xC10)480,802
C22.21(S3×C2×C10) = C10×C4⋊Dic3central extension (φ=1)480C2^2.21(S3xC2xC10)480,804
C22.22(S3×C2×C10) = C5×C23.26D6central extension (φ=1)240C2^2.22(S3xC2xC10)480,805
C22.23(S3×C2×C10) = C10×D6⋊C4central extension (φ=1)240C2^2.23(S3xC2xC10)480,806
C22.24(S3×C2×C10) = C20×C3⋊D4central extension (φ=1)240C2^2.24(S3xC2xC10)480,807
C22.25(S3×C2×C10) = C5×D4×Dic3central extension (φ=1)240C2^2.25(S3xC2xC10)480,813
C22.26(S3×C2×C10) = C5×Q8×Dic3central extension (φ=1)480C2^2.26(S3xC2xC10)480,824
C22.27(S3×C2×C10) = C10×C6.D4central extension (φ=1)240C2^2.27(S3xC2xC10)480,831
C22.28(S3×C2×C10) = C2×C10×Dic6central extension (φ=1)480C2^2.28(S3xC2xC10)480,1150
C22.29(S3×C2×C10) = S3×C22×C20central extension (φ=1)240C2^2.29(S3xC2xC10)480,1151
C22.30(S3×C2×C10) = C2×C10×D12central extension (φ=1)240C2^2.30(S3xC2xC10)480,1152
C22.31(S3×C2×C10) = S3×Q8×C10central extension (φ=1)240C2^2.31(S3xC2xC10)480,1157
C22.32(S3×C2×C10) = C10×Q8⋊3S3central extension (φ=1)240C2^2.32(S3xC2xC10)480,1158
C22.33(S3×C2×C10) = Dic3×C22×C10central extension (φ=1)480C2^2.33(S3xC2xC10)480,1163
C22.34(S3×C2×C10) = C5×C12⋊2Q8central stem extension (φ=1)480C2^2.34(S3xC2xC10)480,748
C22.35(S3×C2×C10) = C5×C12.6Q8central stem extension (φ=1)480C2^2.35(S3xC2xC10)480,749
C22.36(S3×C2×C10) = C5×C4⋊D12central stem extension (φ=1)240C2^2.36(S3xC2xC10)480,753
C22.37(S3×C2×C10) = C5×C42⋊7S3central stem extension (φ=1)240C2^2.37(S3xC2xC10)480,754
C22.38(S3×C2×C10) = C5×C42⋊3S3central stem extension (φ=1)240C2^2.38(S3xC2xC10)480,755
C22.39(S3×C2×C10) = C5×Dic3.D4central stem extension (φ=1)240C2^2.39(S3xC2xC10)480,757
C22.40(S3×C2×C10) = C5×C23.8D6central stem extension (φ=1)240C2^2.40(S3xC2xC10)480,758
C22.41(S3×C2×C10) = C5×D6⋊D4central stem extension (φ=1)120C2^2.41(S3xC2xC10)480,761
C22.42(S3×C2×C10) = C5×C23.9D6central stem extension (φ=1)240C2^2.42(S3xC2xC10)480,762
C22.43(S3×C2×C10) = C5×Dic3⋊D4central stem extension (φ=1)240C2^2.43(S3xC2xC10)480,763
C22.44(S3×C2×C10) = C5×C23.11D6central stem extension (φ=1)240C2^2.44(S3xC2xC10)480,764
C22.45(S3×C2×C10) = C5×C23.21D6central stem extension (φ=1)240C2^2.45(S3xC2xC10)480,765
C22.46(S3×C2×C10) = C5×C12⋊Q8central stem extension (φ=1)480C2^2.46(S3xC2xC10)480,767
C22.47(S3×C2×C10) = C5×Dic3.Q8central stem extension (φ=1)480C2^2.47(S3xC2xC10)480,768
C22.48(S3×C2×C10) = C5×C4.Dic6central stem extension (φ=1)480C2^2.48(S3xC2xC10)480,769
C22.49(S3×C2×C10) = C5×D6.D4central stem extension (φ=1)240C2^2.49(S3xC2xC10)480,773
C22.50(S3×C2×C10) = C5×C12⋊D4central stem extension (φ=1)240C2^2.50(S3xC2xC10)480,774
C22.51(S3×C2×C10) = C5×D6⋊Q8central stem extension (φ=1)240C2^2.51(S3xC2xC10)480,775
C22.52(S3×C2×C10) = C5×C4.D12central stem extension (φ=1)240C2^2.52(S3xC2xC10)480,776
C22.53(S3×C2×C10) = C5×C4⋊C4⋊S3central stem extension (φ=1)240C2^2.53(S3xC2xC10)480,777
C22.54(S3×C2×C10) = C5×C12.48D4central stem extension (φ=1)240C2^2.54(S3xC2xC10)480,803
C22.55(S3×C2×C10) = C5×C23.28D6central stem extension (φ=1)240C2^2.55(S3xC2xC10)480,808
C22.56(S3×C2×C10) = C5×C12⋊7D4central stem extension (φ=1)240C2^2.56(S3xC2xC10)480,809
C22.57(S3×C2×C10) = C5×C23.23D6central stem extension (φ=1)240C2^2.57(S3xC2xC10)480,814
C22.58(S3×C2×C10) = C5×C23.12D6central stem extension (φ=1)240C2^2.58(S3xC2xC10)480,815
C22.59(S3×C2×C10) = C5×C23⋊2D6central stem extension (φ=1)120C2^2.59(S3xC2xC10)480,816
C22.60(S3×C2×C10) = C5×D6⋊3D4central stem extension (φ=1)240C2^2.60(S3xC2xC10)480,817
C22.61(S3×C2×C10) = C5×C23.14D6central stem extension (φ=1)240C2^2.61(S3xC2xC10)480,818
C22.62(S3×C2×C10) = C5×C12⋊3D4central stem extension (φ=1)240C2^2.62(S3xC2xC10)480,819
C22.63(S3×C2×C10) = C5×Dic3⋊Q8central stem extension (φ=1)480C2^2.63(S3xC2xC10)480,823
C22.64(S3×C2×C10) = C5×D6⋊3Q8central stem extension (φ=1)240C2^2.64(S3xC2xC10)480,825
C22.65(S3×C2×C10) = C5×C12.23D4central stem extension (φ=1)240C2^2.65(S3xC2xC10)480,826
C22.66(S3×C2×C10) = C5×C24⋊4S3central stem extension (φ=1)120C2^2.66(S3xC2xC10)480,832

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