Extensions 1→N→G→Q→1 with N=C6 and Q=C4×Dic5

Direct product G=N×Q with N=C6 and Q=C4×Dic5
dρLabelID
Dic5×C2×C12480Dic5xC2xC12480,715

Semidirect products G=N:Q with N=C6 and Q=C4×Dic5
extensionφ:Q→Aut NdρLabelID
C61(C4×Dic5) = C2×Dic3×Dic5φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6:1(C4xDic5)480,603
C62(C4×Dic5) = C2×C4×Dic15φ: C4×Dic5/C2×C20C2 ⊆ Aut C6480C6:2(C4xDic5)480,887

Non-split extensions G=N.Q with N=C6 and Q=C4×Dic5
extensionφ:Q→Aut NdρLabelID
C6.1(C4×Dic5) = Dic5×C3⋊C8φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6.1(C4xDic5)480,25
C6.2(C4×Dic5) = Dic3×C52C8φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6.2(C4xDic5)480,26
C6.3(C4×Dic5) = Dic154C8φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6.3(C4xDic5)480,27
C6.4(C4×Dic5) = C30.21C42φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6.4(C4xDic5)480,28
C6.5(C4×Dic5) = C30.22C42φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6.5(C4xDic5)480,29
C6.6(C4×Dic5) = C30.23C42φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6.6(C4xDic5)480,30
C6.7(C4×Dic5) = C30.24C42φ: C4×Dic5/C2×Dic5C2 ⊆ Aut C6480C6.7(C4xDic5)480,70
C6.8(C4×Dic5) = C4×C153C8φ: C4×Dic5/C2×C20C2 ⊆ Aut C6480C6.8(C4xDic5)480,162
C6.9(C4×Dic5) = C42.D15φ: C4×Dic5/C2×C20C2 ⊆ Aut C6480C6.9(C4xDic5)480,163
C6.10(C4×Dic5) = C8×Dic15φ: C4×Dic5/C2×C20C2 ⊆ Aut C6480C6.10(C4xDic5)480,173
C6.11(C4×Dic5) = C12013C4φ: C4×Dic5/C2×C20C2 ⊆ Aut C6480C6.11(C4xDic5)480,175
C6.12(C4×Dic5) = C30.29C42φ: C4×Dic5/C2×C20C2 ⊆ Aut C6480C6.12(C4xDic5)480,191
C6.13(C4×Dic5) = C12×C52C8central extension (φ=1)480C6.13(C4xDic5)480,80
C6.14(C4×Dic5) = C3×C42.D5central extension (φ=1)480C6.14(C4xDic5)480,81
C6.15(C4×Dic5) = Dic5×C24central extension (φ=1)480C6.15(C4xDic5)480,91
C6.16(C4×Dic5) = C3×C408C4central extension (φ=1)480C6.16(C4xDic5)480,93
C6.17(C4×Dic5) = C3×C10.10C42central extension (φ=1)480C6.17(C4xDic5)480,109

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