# Extensions 1→N→G→Q→1 with N=C6 and Q=C24

Direct product G=N×Q with N=C6 and Q=C24
dρLabelID
C24×C696C2^4xC696,231

Semidirect products G=N:Q with N=C6 and Q=C24
extensionφ:Q→Aut NdρLabelID
C6⋊C24 = S3×C24φ: C24/C23C2 ⊆ Aut C648C6:C2^496,230

Non-split extensions G=N.Q with N=C6 and Q=C24
extensionφ:Q→Aut NdρLabelID
C6.1C24 = C22×Dic6φ: C24/C23C2 ⊆ Aut C696C6.1C2^496,205
C6.2C24 = S3×C22×C4φ: C24/C23C2 ⊆ Aut C648C6.2C2^496,206
C6.3C24 = C22×D12φ: C24/C23C2 ⊆ Aut C648C6.3C2^496,207
C6.4C24 = C2×C4○D12φ: C24/C23C2 ⊆ Aut C648C6.4C2^496,208
C6.5C24 = C2×S3×D4φ: C24/C23C2 ⊆ Aut C624C6.5C2^496,209
C6.6C24 = C2×D42S3φ: C24/C23C2 ⊆ Aut C648C6.6C2^496,210
C6.7C24 = D46D6φ: C24/C23C2 ⊆ Aut C6244C6.7C2^496,211
C6.8C24 = C2×S3×Q8φ: C24/C23C2 ⊆ Aut C648C6.8C2^496,212
C6.9C24 = C2×Q83S3φ: C24/C23C2 ⊆ Aut C648C6.9C2^496,213
C6.10C24 = Q8.15D6φ: C24/C23C2 ⊆ Aut C6484C6.10C2^496,214
C6.11C24 = S3×C4○D4φ: C24/C23C2 ⊆ Aut C6244C6.11C2^496,215
C6.12C24 = D4○D12φ: C24/C23C2 ⊆ Aut C6244+C6.12C2^496,216
C6.13C24 = Q8○D12φ: C24/C23C2 ⊆ Aut C6484-C6.13C2^496,217
C6.14C24 = C23×Dic3φ: C24/C23C2 ⊆ Aut C696C6.14C2^496,218
C6.15C24 = C22×C3⋊D4φ: C24/C23C2 ⊆ Aut C648C6.15C2^496,219
C6.16C24 = D4×C2×C6central extension (φ=1)48C6.16C2^496,221
C6.17C24 = Q8×C2×C6central extension (φ=1)96C6.17C2^496,222
C6.18C24 = C6×C4○D4central extension (φ=1)48C6.18C2^496,223
C6.19C24 = C3×2+ 1+4central extension (φ=1)244C6.19C2^496,224
C6.20C24 = C3×2- 1+4central extension (φ=1)484C6.20C2^496,225

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