# Extensions 1→N→G→Q→1 with N=C6 and Q=C23×C10

Direct product G=N×Q with N=C6 and Q=C23×C10
dρLabelID
C24×C30480C2^4xC30480,1213

Semidirect products G=N:Q with N=C6 and Q=C23×C10
extensionφ:Q→Aut NdρLabelID
C6⋊(C23×C10) = S3×C23×C10φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6:(C2^3xC10)480,1211

Non-split extensions G=N.Q with N=C6 and Q=C23×C10
extensionφ:Q→Aut NdρLabelID
C6.1(C23×C10) = C2×C10×Dic6φ: C23×C10/C22×C10C2 ⊆ Aut C6480C6.1(C2^3xC10)480,1150
C6.2(C23×C10) = S3×C22×C20φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6.2(C2^3xC10)480,1151
C6.3(C23×C10) = C2×C10×D12φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6.3(C2^3xC10)480,1152
C6.4(C23×C10) = C10×C4○D12φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6.4(C2^3xC10)480,1153
C6.5(C23×C10) = S3×D4×C10φ: C23×C10/C22×C10C2 ⊆ Aut C6120C6.5(C2^3xC10)480,1154
C6.6(C23×C10) = C10×D42S3φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6.6(C2^3xC10)480,1155
C6.7(C23×C10) = C5×D46D6φ: C23×C10/C22×C10C2 ⊆ Aut C61204C6.7(C2^3xC10)480,1156
C6.8(C23×C10) = S3×Q8×C10φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6.8(C2^3xC10)480,1157
C6.9(C23×C10) = C10×Q83S3φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6.9(C2^3xC10)480,1158
C6.10(C23×C10) = C5×Q8.15D6φ: C23×C10/C22×C10C2 ⊆ Aut C62404C6.10(C2^3xC10)480,1159
C6.11(C23×C10) = C5×S3×C4○D4φ: C23×C10/C22×C10C2 ⊆ Aut C61204C6.11(C2^3xC10)480,1160
C6.12(C23×C10) = C5×D4○D12φ: C23×C10/C22×C10C2 ⊆ Aut C61204C6.12(C2^3xC10)480,1161
C6.13(C23×C10) = C5×Q8○D12φ: C23×C10/C22×C10C2 ⊆ Aut C62404C6.13(C2^3xC10)480,1162
C6.14(C23×C10) = Dic3×C22×C10φ: C23×C10/C22×C10C2 ⊆ Aut C6480C6.14(C2^3xC10)480,1163
C6.15(C23×C10) = C2×C10×C3⋊D4φ: C23×C10/C22×C10C2 ⊆ Aut C6240C6.15(C2^3xC10)480,1164
C6.16(C23×C10) = D4×C2×C30central extension (φ=1)240C6.16(C2^3xC10)480,1181
C6.17(C23×C10) = Q8×C2×C30central extension (φ=1)480C6.17(C2^3xC10)480,1182
C6.18(C23×C10) = C4○D4×C30central extension (φ=1)240C6.18(C2^3xC10)480,1183
C6.19(C23×C10) = C15×2+ 1+4central extension (φ=1)1204C6.19(C2^3xC10)480,1184
C6.20(C23×C10) = C15×2- 1+4central extension (φ=1)2404C6.20(C2^3xC10)480,1185

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