# Extensions 1→N→G→Q→1 with N=C6 and Q=C10.D4

Direct product G=N×Q with N=C6 and Q=C10.D4
dρLabelID
C6×C10.D4480C6xC10.D4480,716

Semidirect products G=N:Q with N=C6 and Q=C10.D4
extensionφ:Q→Aut NdρLabelID
C61(C10.D4) = C2×C30.Q8φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6:1(C10.D4)480,617
C62(C10.D4) = C2×Dic155C4φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6:2(C10.D4)480,620
C63(C10.D4) = C2×C30.4Q8φ: C10.D4/C2×C20C2 ⊆ Aut C6480C6:3(C10.D4)480,888

Non-split extensions G=N.Q with N=C6 and Q=C10.D4
extensionφ:Q→Aut NdρLabelID
C6.1(C10.D4) = C60.13Q8φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6.1(C10.D4)480,58
C6.2(C10.D4) = C60.14Q8φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6.2(C10.D4)480,59
C6.3(C10.D4) = C60.7Q8φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6.3(C10.D4)480,61
C6.4(C10.D4) = C30.SD16φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6.4(C10.D4)480,62
C6.5(C10.D4) = C60.8Q8φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6.5(C10.D4)480,64
C6.6(C10.D4) = C30.20D8φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6.6(C10.D4)480,65
C6.7(C10.D4) = C60.105D4φ: C10.D4/C2×Dic5C2 ⊆ Aut C62404C6.7(C10.D4)480,67
C6.8(C10.D4) = C60.D4φ: C10.D4/C2×Dic5C2 ⊆ Aut C62404C6.8(C10.D4)480,68
C6.9(C10.D4) = C30.24C42φ: C10.D4/C2×Dic5C2 ⊆ Aut C6480C6.9(C10.D4)480,70
C6.10(C10.D4) = C60.1Q8φ: C10.D4/C2×C20C2 ⊆ Aut C6480C6.10(C10.D4)480,167
C6.11(C10.D4) = C60.2Q8φ: C10.D4/C2×C20C2 ⊆ Aut C6480C6.11(C10.D4)480,168
C6.12(C10.D4) = C60.26Q8φ: C10.D4/C2×C20C2 ⊆ Aut C6480C6.12(C10.D4)480,174
C6.13(C10.D4) = C60.210D4φ: C10.D4/C2×C20C2 ⊆ Aut C62404C6.13(C10.D4)480,182
C6.14(C10.D4) = C30.29C42φ: C10.D4/C2×C20C2 ⊆ Aut C6480C6.14(C10.D4)480,191
C6.15(C10.D4) = C3×C10.D8central extension (φ=1)480C6.15(C10.D4)480,85
C6.16(C10.D4) = C3×C20.Q8central extension (φ=1)480C6.16(C10.D4)480,86
C6.17(C10.D4) = C3×C20.8Q8central extension (φ=1)480C6.17(C10.D4)480,92
C6.18(C10.D4) = C3×C20.53D4central extension (φ=1)2404C6.18(C10.D4)480,100
C6.19(C10.D4) = C3×C10.10C42central extension (φ=1)480C6.19(C10.D4)480,109

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