# Extensions 1→N→G→Q→1 with N=C10 and Q=C22×C6

Direct product G=N×Q with N=C10 and Q=C22×C6
dρLabelID
C23×C30240C2^3xC30240,208

Semidirect products G=N:Q with N=C10 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C10⋊(C22×C6) = D5×C22×C6φ: C22×C6/C2×C6C2 ⊆ Aut C10120C10:(C2^2xC6)240,205

Non-split extensions G=N.Q with N=C10 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C10.1(C22×C6) = C6×Dic10φ: C22×C6/C2×C6C2 ⊆ Aut C10240C10.1(C2^2xC6)240,155
C10.2(C22×C6) = D5×C2×C12φ: C22×C6/C2×C6C2 ⊆ Aut C10120C10.2(C2^2xC6)240,156
C10.3(C22×C6) = C6×D20φ: C22×C6/C2×C6C2 ⊆ Aut C10120C10.3(C2^2xC6)240,157
C10.4(C22×C6) = C3×C4○D20φ: C22×C6/C2×C6C2 ⊆ Aut C101202C10.4(C2^2xC6)240,158
C10.5(C22×C6) = C3×D4×D5φ: C22×C6/C2×C6C2 ⊆ Aut C10604C10.5(C2^2xC6)240,159
C10.6(C22×C6) = C3×D42D5φ: C22×C6/C2×C6C2 ⊆ Aut C101204C10.6(C2^2xC6)240,160
C10.7(C22×C6) = C3×Q8×D5φ: C22×C6/C2×C6C2 ⊆ Aut C101204C10.7(C2^2xC6)240,161
C10.8(C22×C6) = C3×Q82D5φ: C22×C6/C2×C6C2 ⊆ Aut C101204C10.8(C2^2xC6)240,162
C10.9(C22×C6) = C2×C6×Dic5φ: C22×C6/C2×C6C2 ⊆ Aut C10240C10.9(C2^2xC6)240,163
C10.10(C22×C6) = C6×C5⋊D4φ: C22×C6/C2×C6C2 ⊆ Aut C10120C10.10(C2^2xC6)240,164
C10.11(C22×C6) = D4×C30central extension (φ=1)120C10.11(C2^2xC6)240,186
C10.12(C22×C6) = Q8×C30central extension (φ=1)240C10.12(C2^2xC6)240,187
C10.13(C22×C6) = C15×C4○D4central extension (φ=1)1202C10.13(C2^2xC6)240,188

׿
×
𝔽