# Extensions 1→N→G→Q→1 with N=C4 and Q=C24

Direct product G=N×Q with N=C4 and Q=C24
dρLabelID
C24×C464C2^4xC464,260

Semidirect products G=N:Q with N=C4 and Q=C24
extensionφ:Q→Aut NdρLabelID
C4⋊C24 = D4×C23φ: C24/C23C2 ⊆ Aut C432C4:C2^464,261

Non-split extensions G=N.Q with N=C4 and Q=C24
extensionφ:Q→Aut NdρLabelID
C4.1C24 = C22×D8φ: C24/C23C2 ⊆ Aut C432C4.1C2^464,250
C4.2C24 = C22×SD16φ: C24/C23C2 ⊆ Aut C432C4.2C2^464,251
C4.3C24 = C22×Q16φ: C24/C23C2 ⊆ Aut C464C4.3C2^464,252
C4.4C24 = C2×C4○D8φ: C24/C23C2 ⊆ Aut C432C4.4C2^464,253
C4.5C24 = C2×C8⋊C22φ: C24/C23C2 ⊆ Aut C416C4.5C2^464,254
C4.6C24 = C2×C8.C22φ: C24/C23C2 ⊆ Aut C432C4.6C2^464,255
C4.7C24 = D8⋊C22φ: C24/C23C2 ⊆ Aut C4164C4.7C2^464,256
C4.8C24 = D4○D8φ: C24/C23C2 ⊆ Aut C4164+C4.8C2^464,257
C4.9C24 = D4○SD16φ: C24/C23C2 ⊆ Aut C4164C4.9C2^464,258
C4.10C24 = Q8○D8φ: C24/C23C2 ⊆ Aut C4324-C4.10C2^464,259
C4.11C24 = Q8×C23φ: C24/C23C2 ⊆ Aut C464C4.11C2^464,262
C4.12C24 = C2×2+ 1+4φ: C24/C23C2 ⊆ Aut C416C4.12C2^464,264
C4.13C24 = C2×2- 1+4φ: C24/C23C2 ⊆ Aut C432C4.13C2^464,265
C4.14C24 = C2.C25φ: C24/C23C2 ⊆ Aut C4164C4.14C2^464,266
C4.15C24 = C22×M4(2)central extension (φ=1)32C4.15C2^464,247
C4.16C24 = C2×C8○D4central extension (φ=1)32C4.16C2^464,248
C4.17C24 = Q8○M4(2)central extension (φ=1)164C4.17C2^464,249
C4.18C24 = C22×C4○D4central extension (φ=1)32C4.18C2^464,263

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