# Extensions 1→N→G→Q→1 with N=C6 and Q=C23

Direct product G=N×Q with N=C6 and Q=C23
dρLabelID
C23×C648C2^3xC648,52

Semidirect products G=N:Q with N=C6 and Q=C23
extensionφ:Q→Aut NdρLabelID
C6⋊C23 = S3×C23φ: C23/C22C2 ⊆ Aut C624C6:C2^348,51

Non-split extensions G=N.Q with N=C6 and Q=C23
extensionφ:Q→Aut NdρLabelID
C6.1C23 = C2×Dic6φ: C23/C22C2 ⊆ Aut C648C6.1C2^348,34
C6.2C23 = S3×C2×C4φ: C23/C22C2 ⊆ Aut C624C6.2C2^348,35
C6.3C23 = C2×D12φ: C23/C22C2 ⊆ Aut C624C6.3C2^348,36
C6.4C23 = C4○D12φ: C23/C22C2 ⊆ Aut C6242C6.4C2^348,37
C6.5C23 = S3×D4φ: C23/C22C2 ⊆ Aut C6124+C6.5C2^348,38
C6.6C23 = D42S3φ: C23/C22C2 ⊆ Aut C6244-C6.6C2^348,39
C6.7C23 = S3×Q8φ: C23/C22C2 ⊆ Aut C6244-C6.7C2^348,40
C6.8C23 = Q83S3φ: C23/C22C2 ⊆ Aut C6244+C6.8C2^348,41
C6.9C23 = C22×Dic3φ: C23/C22C2 ⊆ Aut C648C6.9C2^348,42
C6.10C23 = C2×C3⋊D4φ: C23/C22C2 ⊆ Aut C624C6.10C2^348,43
C6.11C23 = C6×D4central extension (φ=1)24C6.11C2^348,45
C6.12C23 = C6×Q8central extension (φ=1)48C6.12C2^348,46
C6.13C23 = C3×C4○D4central extension (φ=1)242C6.13C2^348,47

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