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Extensions 1→N→G→Q→1 with N=C6 and Q=C24⋊C2

Direct product G=N×Q with N=C6 and Q=C24⋊C2
dρLabelID
C6×C24⋊C296C6xC24:C2288,673

Semidirect products G=N:Q with N=C6 and Q=C24⋊C2
extensionφ:Q→Aut NdρLabelID
C6⋊1(C24⋊C2) = C2×C24⋊2S3φ: C24⋊C2/C24 → C2 ⊆ Aut C6144C6:1(C24:C2)288,759
C6⋊2(C24⋊C2) = C2×C32⋊5SD16φ: C24⋊C2/Dic6 → C2 ⊆ Aut C648C6:2(C24:C2)288,480
C6⋊3(C24⋊C2) = C2×D12.S3φ: C24⋊C2/D12 → C2 ⊆ Aut C696C6:3(C24:C2)288,476

Non-split extensions G=N.Q with N=C6 and Q=C24⋊C2
extensionφ:Q→Aut NdρLabelID
C6.1(C24⋊C2) = C36.45D4φ: C24⋊C2/C24 → C2 ⊆ Aut C6288C6.1(C24:C2)288,24
C6.2(C24⋊C2) = C8⋊Dic9φ: C24⋊C2/C24 → C2 ⊆ Aut C6288C6.2(C24:C2)288,25
C6.3(C24⋊C2) = C2.D72φ: C24⋊C2/C24 → C2 ⊆ Aut C6144C6.3(C24:C2)288,28
C6.4(C24⋊C2) = C2×C72⋊C2φ: C24⋊C2/C24 → C2 ⊆ Aut C6144C6.4(C24:C2)288,113
C6.5(C24⋊C2) = C6.4Dic12φ: C24⋊C2/C24 → C2 ⊆ Aut C6288C6.5(C24:C2)288,291
C6.6(C24⋊C2) = C24⋊2Dic3φ: C24⋊C2/C24 → C2 ⊆ Aut C6288C6.6(C24:C2)288,292
C6.7(C24⋊C2) = C62.84D4φ: C24⋊C2/C24 → C2 ⊆ Aut C6144C6.7(C24:C2)288,296
C6.8(C24⋊C2) = C6.17D24φ: C24⋊C2/Dic6 → C2 ⊆ Aut C648C6.8(C24:C2)288,212
C6.9(C24⋊C2) = C6.Dic12φ: C24⋊C2/Dic6 → C2 ⊆ Aut C696C6.9(C24:C2)288,214
C6.10(C24⋊C2) = C6.16D24φ: C24⋊C2/D12 → C2 ⊆ Aut C696C6.10(C24:C2)288,211
C6.11(C24⋊C2) = C12.73D12φ: C24⋊C2/D12 → C2 ⊆ Aut C696C6.11(C24:C2)288,215
C6.12(C24⋊C2) = C12.Dic6φ: C24⋊C2/D12 → C2 ⊆ Aut C696C6.12(C24:C2)288,221
C6.13(C24⋊C2) = C3×C2.Dic12central extension (φ=1)96C6.13(C24:C2)288,250
C6.14(C24⋊C2) = C3×C8⋊Dic3central extension (φ=1)96C6.14(C24:C2)288,251
C6.15(C24⋊C2) = C3×C2.D24central extension (φ=1)96C6.15(C24:C2)288,255

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