Extensions 1→N→G→Q→1 with N=C6 and Q=S3×D5

Direct product G=N×Q with N=C6 and Q=S3×D5
dρLabelID
S3×C6×D5604S3xC6xD5360,151

Semidirect products G=N:Q with N=C6 and Q=S3×D5
extensionφ:Q→Aut NdρLabelID
C61(S3×D5) = C2×S3×D15φ: S3×D5/C5×S3C2 ⊆ Aut C6604+C6:1(S3xD5)360,154
C62(S3×D5) = C2×D5×C3⋊S3φ: S3×D5/C3×D5C2 ⊆ Aut C690C6:2(S3xD5)360,152
C63(S3×D5) = C2×D15⋊S3φ: S3×D5/D15C2 ⊆ Aut C6604C6:3(S3xD5)360,155

Non-split extensions G=N.Q with N=C6 and Q=S3×D5
extensionφ:Q→Aut NdρLabelID
C6.1(S3×D5) = Dic3×D15φ: S3×D5/C5×S3C2 ⊆ Aut C61204-C6.1(S3xD5)360,77
C6.2(S3×D5) = S3×Dic15φ: S3×D5/C5×S3C2 ⊆ Aut C61204-C6.2(S3xD5)360,78
C6.3(S3×D5) = C6.D30φ: S3×D5/C5×S3C2 ⊆ Aut C6604+C6.3(S3xD5)360,79
C6.4(S3×D5) = D6⋊D15φ: S3×D5/C5×S3C2 ⊆ Aut C61204-C6.4(S3xD5)360,80
C6.5(S3×D5) = C3⋊D60φ: S3×D5/C5×S3C2 ⊆ Aut C6604+C6.5(S3xD5)360,81
C6.6(S3×D5) = D62D15φ: S3×D5/C5×S3C2 ⊆ Aut C6604+C6.6(S3xD5)360,82
C6.7(S3×D5) = C3⋊Dic30φ: S3×D5/C5×S3C2 ⊆ Aut C61204-C6.7(S3xD5)360,83
C6.8(S3×D5) = C45⋊Q8φ: S3×D5/C3×D5C2 ⊆ Aut C63604-C6.8(S3xD5)360,7
C6.9(S3×D5) = D9×Dic5φ: S3×D5/C3×D5C2 ⊆ Aut C61804-C6.9(S3xD5)360,8
C6.10(S3×D5) = D90.C2φ: S3×D5/C3×D5C2 ⊆ Aut C61804+C6.10(S3xD5)360,9
C6.11(S3×D5) = C5⋊D36φ: S3×D5/C3×D5C2 ⊆ Aut C61804+C6.11(S3xD5)360,10
C6.12(S3×D5) = D5×Dic9φ: S3×D5/C3×D5C2 ⊆ Aut C61804-C6.12(S3xD5)360,11
C6.13(S3×D5) = C45⋊D4φ: S3×D5/C3×D5C2 ⊆ Aut C61804-C6.13(S3xD5)360,12
C6.14(S3×D5) = C9⋊D20φ: S3×D5/C3×D5C2 ⊆ Aut C61804+C6.14(S3xD5)360,13
C6.15(S3×D5) = C2×D5×D9φ: S3×D5/C3×D5C2 ⊆ Aut C6904+C6.15(S3xD5)360,45
C6.16(S3×D5) = D5×C3⋊Dic3φ: S3×D5/C3×D5C2 ⊆ Aut C6180C6.16(S3xD5)360,65
C6.17(S3×D5) = C3⋊S3×Dic5φ: S3×D5/C3×D5C2 ⊆ Aut C6180C6.17(S3xD5)360,66
C6.18(S3×D5) = C30.D6φ: S3×D5/C3×D5C2 ⊆ Aut C6180C6.18(S3xD5)360,67
C6.19(S3×D5) = C30.12D6φ: S3×D5/C3×D5C2 ⊆ Aut C6180C6.19(S3xD5)360,68
C6.20(S3×D5) = C327D20φ: S3×D5/C3×D5C2 ⊆ Aut C6180C6.20(S3xD5)360,69
C6.21(S3×D5) = C15⋊D12φ: S3×D5/C3×D5C2 ⊆ Aut C6180C6.21(S3xD5)360,70
C6.22(S3×D5) = C15⋊Dic6φ: S3×D5/C3×D5C2 ⊆ Aut C6360C6.22(S3xD5)360,71
C6.23(S3×D5) = D30.S3φ: S3×D5/D15C2 ⊆ Aut C61204C6.23(S3xD5)360,84
C6.24(S3×D5) = Dic15⋊S3φ: S3×D5/D15C2 ⊆ Aut C6604C6.24(S3xD5)360,85
C6.25(S3×D5) = D30⋊S3φ: S3×D5/D15C2 ⊆ Aut C6604C6.25(S3xD5)360,86
C6.26(S3×D5) = C323D20φ: S3×D5/D15C2 ⊆ Aut C61204C6.26(S3xD5)360,87
C6.27(S3×D5) = C323Dic10φ: S3×D5/D15C2 ⊆ Aut C61204C6.27(S3xD5)360,88
C6.28(S3×D5) = C3×D5×Dic3central extension (φ=1)604C6.28(S3xD5)360,58
C6.29(S3×D5) = C3×S3×Dic5central extension (φ=1)1204C6.29(S3xD5)360,59
C6.30(S3×D5) = C3×D30.C2central extension (φ=1)1204C6.30(S3xD5)360,60
C6.31(S3×D5) = C3×C15⋊D4central extension (φ=1)604C6.31(S3xD5)360,61
C6.32(S3×D5) = C3×C3⋊D20central extension (φ=1)604C6.32(S3xD5)360,62
C6.33(S3×D5) = C3×C5⋊D12central extension (φ=1)1204C6.33(S3xD5)360,63
C6.34(S3×D5) = C3×C15⋊Q8central extension (φ=1)1204C6.34(S3xD5)360,64

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