# Extensions 1→N→G→Q→1 with N=C10 and Q=C2×C3⋊S3

Direct product G=N×Q with N=C10 and Q=C2×C3⋊S3
dρLabelID
C3⋊S3×C2×C10180C3:S3xC2xC10360,160

Semidirect products G=N:Q with N=C10 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C101(C2×C3⋊S3) = C2×D5×C3⋊S3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C1090C10:1(C2xC3:S3)360,152
C102(C2×C3⋊S3) = C22×C3⋊D15φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C10180C10:2(C2xC3:S3)360,161

Non-split extensions G=N.Q with N=C10 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C10.1(C2×C3⋊S3) = D5×C3⋊Dic3φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C10180C10.1(C2xC3:S3)360,65
C10.2(C2×C3⋊S3) = C3⋊S3×Dic5φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C10180C10.2(C2xC3:S3)360,66
C10.3(C2×C3⋊S3) = C30.D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C10180C10.3(C2xC3:S3)360,67
C10.4(C2×C3⋊S3) = C30.12D6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C10180C10.4(C2xC3:S3)360,68
C10.5(C2×C3⋊S3) = C327D20φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C10180C10.5(C2xC3:S3)360,69
C10.6(C2×C3⋊S3) = C15⋊D12φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C10180C10.6(C2xC3:S3)360,70
C10.7(C2×C3⋊S3) = C15⋊Dic6φ: C2×C3⋊S3/C3⋊S3C2 ⊆ Aut C10360C10.7(C2xC3:S3)360,71
C10.8(C2×C3⋊S3) = C12.D15φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C10360C10.8(C2xC3:S3)360,110
C10.9(C2×C3⋊S3) = C4×C3⋊D15φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C10180C10.9(C2xC3:S3)360,111
C10.10(C2×C3⋊S3) = C60⋊S3φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C10180C10.10(C2xC3:S3)360,112
C10.11(C2×C3⋊S3) = C2×C3⋊Dic15φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C10360C10.11(C2xC3:S3)360,113
C10.12(C2×C3⋊S3) = C62⋊D5φ: C2×C3⋊S3/C3×C6C2 ⊆ Aut C10180C10.12(C2xC3:S3)360,114
C10.13(C2×C3⋊S3) = C5×C324Q8central extension (φ=1)360C10.13(C2xC3:S3)360,105
C10.14(C2×C3⋊S3) = C3⋊S3×C20central extension (φ=1)180C10.14(C2xC3:S3)360,106
C10.15(C2×C3⋊S3) = C5×C12⋊S3central extension (φ=1)180C10.15(C2xC3:S3)360,107
C10.16(C2×C3⋊S3) = C10×C3⋊Dic3central extension (φ=1)360C10.16(C2xC3:S3)360,108
C10.17(C2×C3⋊S3) = C5×C327D4central extension (φ=1)180C10.17(C2xC3:S3)360,109

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