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Extensions 1→N→G→Q→1 with N=C6 and Q=C5:D4

Direct product G=NxQ with N=C6 and Q=C5:D4
dρLabelID
C6xC5:D4120C6xC5:D4240,164

Semidirect products G=N:Q with N=C6 and Q=C5:D4
extensionφ:Q→Aut NdρLabelID
C6:1(C5:D4) = C2xC5:D12φ: C5:D4/Dic5 → C2 ⊆ Aut C6120C6:1(C5:D4)240,147
C6:2(C5:D4) = C2xC15:D4φ: C5:D4/D10 → C2 ⊆ Aut C6120C6:2(C5:D4)240,145
C6:3(C5:D4) = C2xC15:7D4φ: C5:D4/C2xC10 → C2 ⊆ Aut C6120C6:3(C5:D4)240,184

Non-split extensions G=N.Q with N=C6 and Q=C5:D4
extensionφ:Q→Aut NdρLabelID
C6.1(C5:D4) = C5:D24φ: C5:D4/Dic5 → C2 ⊆ Aut C61204+C6.1(C5:D4)240,15
C6.2(C5:D4) = D12.D5φ: C5:D4/Dic5 → C2 ⊆ Aut C61204-C6.2(C5:D4)240,20
C6.3(C5:D4) = Dic6:D5φ: C5:D4/Dic5 → C2 ⊆ Aut C61204+C6.3(C5:D4)240,21
C6.4(C5:D4) = C5:Dic12φ: C5:D4/Dic5 → C2 ⊆ Aut C62404-C6.4(C5:D4)240,24
C6.5(C5:D4) = D30:4C4φ: C5:D4/Dic5 → C2 ⊆ Aut C6120C6.5(C5:D4)240,28
C6.6(C5:D4) = C30.Q8φ: C5:D4/Dic5 → C2 ⊆ Aut C6240C6.6(C5:D4)240,29
C6.7(C5:D4) = C15:D8φ: C5:D4/D10 → C2 ⊆ Aut C61204C6.7(C5:D4)240,13
C6.8(C5:D4) = C30.D4φ: C5:D4/D10 → C2 ⊆ Aut C61204C6.8(C5:D4)240,16
C6.9(C5:D4) = C20.D6φ: C5:D4/D10 → C2 ⊆ Aut C61204C6.9(C5:D4)240,17
C6.10(C5:D4) = C15:Q16φ: C5:D4/D10 → C2 ⊆ Aut C62404C6.10(C5:D4)240,22
C6.11(C5:D4) = D10:Dic3φ: C5:D4/D10 → C2 ⊆ Aut C6120C6.11(C5:D4)240,26
C6.12(C5:D4) = D6:Dic5φ: C5:D4/D10 → C2 ⊆ Aut C6120C6.12(C5:D4)240,27
C6.13(C5:D4) = Dic15:5C4φ: C5:D4/D10 → C2 ⊆ Aut C6240C6.13(C5:D4)240,30
C6.14(C5:D4) = C30.4Q8φ: C5:D4/C2xC10 → C2 ⊆ Aut C6240C6.14(C5:D4)240,73
C6.15(C5:D4) = D30:3C4φ: C5:D4/C2xC10 → C2 ⊆ Aut C6120C6.15(C5:D4)240,75
C6.16(C5:D4) = D4:D15φ: C5:D4/C2xC10 → C2 ⊆ Aut C61204+C6.16(C5:D4)240,76
C6.17(C5:D4) = D4.D15φ: C5:D4/C2xC10 → C2 ⊆ Aut C61204-C6.17(C5:D4)240,77
C6.18(C5:D4) = Q8:2D15φ: C5:D4/C2xC10 → C2 ⊆ Aut C61204+C6.18(C5:D4)240,78
C6.19(C5:D4) = C15:7Q16φ: C5:D4/C2xC10 → C2 ⊆ Aut C62404-C6.19(C5:D4)240,79
C6.20(C5:D4) = C30.38D4φ: C5:D4/C2xC10 → C2 ⊆ Aut C6120C6.20(C5:D4)240,80
C6.21(C5:D4) = C3xC10.D4central extension (φ=1)240C6.21(C5:D4)240,41
C6.22(C5:D4) = C3xD10:C4central extension (φ=1)120C6.22(C5:D4)240,43
C6.23(C5:D4) = C3xD4:D5central extension (φ=1)1204C6.23(C5:D4)240,44
C6.24(C5:D4) = C3xD4.D5central extension (φ=1)1204C6.24(C5:D4)240,45
C6.25(C5:D4) = C3xQ8:D5central extension (φ=1)1204C6.25(C5:D4)240,46
C6.26(C5:D4) = C3xC5:Q16central extension (φ=1)2404C6.26(C5:D4)240,47
C6.27(C5:D4) = C3xC23.D5central extension (φ=1)120C6.27(C5:D4)240,48

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