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

Direct product G=N×Q with N=C6 and Q=C23×C6
dρLabelID
C23×C62288C2^3xC6^2288,1045

Semidirect products G=N:Q with N=C6 and Q=C23×C6
extensionφ:Q→Aut NdρLabelID
C6⋊(C23×C6) = S3×C23×C6φ: C23×C6/C22×C6 → C2 ⊆ Aut C696C6:(C2^3xC6)288,1043

Non-split extensions G=N.Q with N=C6 and Q=C23×C6
extensionφ:Q→Aut NdρLabelID
C6.1(C23×C6) = C2×C6×Dic6φ: C23×C6/C22×C6 → C2 ⊆ Aut C696C6.1(C2^3xC6)288,988
C6.2(C23×C6) = S3×C22×C12φ: C23×C6/C22×C6 → C2 ⊆ Aut C696C6.2(C2^3xC6)288,989
C6.3(C23×C6) = C2×C6×D12φ: C23×C6/C22×C6 → C2 ⊆ Aut C696C6.3(C2^3xC6)288,990
C6.4(C23×C6) = C6×C4○D12φ: C23×C6/C22×C6 → C2 ⊆ Aut C648C6.4(C2^3xC6)288,991
C6.5(C23×C6) = S3×C6×D4φ: C23×C6/C22×C6 → C2 ⊆ Aut C648C6.5(C2^3xC6)288,992
C6.6(C23×C6) = C6×D4⋊2S3φ: C23×C6/C22×C6 → C2 ⊆ Aut C648C6.6(C2^3xC6)288,993
C6.7(C23×C6) = C3×D4⋊6D6φ: C23×C6/C22×C6 → C2 ⊆ Aut C6244C6.7(C2^3xC6)288,994
C6.8(C23×C6) = S3×C6×Q8φ: C23×C6/C22×C6 → C2 ⊆ Aut C696C6.8(C2^3xC6)288,995
C6.9(C23×C6) = C6×Q8⋊3S3φ: C23×C6/C22×C6 → C2 ⊆ Aut C696C6.9(C2^3xC6)288,996
C6.10(C23×C6) = C3×Q8.15D6φ: C23×C6/C22×C6 → C2 ⊆ Aut C6484C6.10(C2^3xC6)288,997
C6.11(C23×C6) = C3×S3×C4○D4φ: C23×C6/C22×C6 → C2 ⊆ Aut C6484C6.11(C2^3xC6)288,998
C6.12(C23×C6) = C3×D4○D12φ: C23×C6/C22×C6 → C2 ⊆ Aut C6484C6.12(C2^3xC6)288,999
C6.13(C23×C6) = C3×Q8○D12φ: C23×C6/C22×C6 → C2 ⊆ Aut C6484C6.13(C2^3xC6)288,1000
C6.14(C23×C6) = Dic3×C22×C6φ: C23×C6/C22×C6 → C2 ⊆ Aut C696C6.14(C2^3xC6)288,1001
C6.15(C23×C6) = C2×C6×C3⋊D4φ: C23×C6/C22×C6 → C2 ⊆ Aut C648C6.15(C2^3xC6)288,1002
C6.16(C23×C6) = D4×C2×C18central extension (φ=1)144C6.16(C2^3xC6)288,368
C6.17(C23×C6) = Q8×C2×C18central extension (φ=1)288C6.17(C2^3xC6)288,369
C6.18(C23×C6) = C4○D4×C18central extension (φ=1)144C6.18(C2^3xC6)288,370
C6.19(C23×C6) = C9×2+ 1+4central extension (φ=1)724C6.19(C2^3xC6)288,371
C6.20(C23×C6) = C9×2- 1+4central extension (φ=1)1444C6.20(C2^3xC6)288,372
C6.21(C23×C6) = D4×C62central extension (φ=1)144C6.21(C2^3xC6)288,1019
C6.22(C23×C6) = Q8×C62central extension (φ=1)288C6.22(C2^3xC6)288,1020
C6.23(C23×C6) = C4○D4×C3×C6central extension (φ=1)144C6.23(C2^3xC6)288,1021
C6.24(C23×C6) = C32×2+ 1+4central extension (φ=1)72C6.24(C2^3xC6)288,1022
C6.25(C23×C6) = C32×2- 1+4central extension (φ=1)144C6.25(C2^3xC6)288,1023

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