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

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

Semidirect products G=N:Q with N=C6 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C6⋊1(C5⋊D4) = C2×C5⋊D12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C6120C6:1(C5:D4)240,147
C6⋊2(C5⋊D4) = C2×C15⋊D4φ: C5⋊D4/D10 → C2 ⊆ Aut C6120C6:2(C5:D4)240,145
C6⋊3(C5⋊D4) = C2×C15⋊7D4φ: C5⋊D4/C2×C10 → 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/C2×C10 → C2 ⊆ Aut C6240C6.14(C5:D4)240,73
C6.15(C5⋊D4) = D30⋊3C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C6120C6.15(C5:D4)240,75
C6.16(C5⋊D4) = D4⋊D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C61204+C6.16(C5:D4)240,76
C6.17(C5⋊D4) = D4.D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C61204-C6.17(C5:D4)240,77
C6.18(C5⋊D4) = Q8⋊2D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C61204+C6.18(C5:D4)240,78
C6.19(C5⋊D4) = C15⋊7Q16φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C62404-C6.19(C5:D4)240,79
C6.20(C5⋊D4) = C30.38D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C6120C6.20(C5:D4)240,80
C6.21(C5⋊D4) = C3×C10.D4central extension (φ=1)240C6.21(C5:D4)240,41
C6.22(C5⋊D4) = C3×D10⋊C4central extension (φ=1)120C6.22(C5:D4)240,43
C6.23(C5⋊D4) = C3×D4⋊D5central extension (φ=1)1204C6.23(C5:D4)240,44
C6.24(C5⋊D4) = C3×D4.D5central extension (φ=1)1204C6.24(C5:D4)240,45
C6.25(C5⋊D4) = C3×Q8⋊D5central extension (φ=1)1204C6.25(C5:D4)240,46
C6.26(C5⋊D4) = C3×C5⋊Q16central extension (φ=1)2404C6.26(C5:D4)240,47
C6.27(C5⋊D4) = C3×C23.D5central extension (φ=1)120C6.27(C5:D4)240,48

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