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Extensions 1→N→G→Q→1 with N=C23 and Q=M4(2)

Direct product G=N×Q with N=C23 and Q=M4(2)
dρLabelID
C23×M4(2)64C2^3xM4(2)128,2302

Semidirect products G=N:Q with N=C23 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
C23⋊1M4(2) = C23⋊M4(2)φ: M4(2)/C4 → C4 ⊆ Aut C2332C2^3:1M4(2)128,197
C23⋊2M4(2) = C23⋊2M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2364C2^3:2M4(2)128,602
C23⋊3M4(2) = C23⋊3M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2332C2^3:3M4(2)128,1705
C23⋊4M4(2) = C25.3C4φ: M4(2)/C22 → C4 ⊆ Aut C2316C2^3:4M4(2)128,194
C23⋊5M4(2) = C2×C8⋊9D4φ: M4(2)/C8 → C2 ⊆ Aut C2364C2^3:5M4(2)128,1659
C23⋊6M4(2) = C2×C24.4C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2332C2^3:6M4(2)128,1609

Non-split extensions G=N.Q with N=C23 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
C23.1M4(2) = C23.1M4(2)φ: M4(2)/C4 → C4 ⊆ Aut C23324C2^3.1M4(2)128,53
C23.2M4(2) = C23.2M4(2)φ: M4(2)/C4 → C4 ⊆ Aut C2332C2^3.2M4(2)128,58
C23.3M4(2) = C42.43D4φ: M4(2)/C4 → C4 ⊆ Aut C2332C2^3.3M4(2)128,198
C23.4M4(2) = C8.19M4(2)φ: M4(2)/C4 → C4 ⊆ Aut C23324C2^3.4M4(2)128,898
C23.5M4(2) = C23.21C42φ: M4(2)/C4 → C22 ⊆ Aut C2332C2^3.5M4(2)128,14
C23.6M4(2) = C23.M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2364C2^3.6M4(2)128,47
C23.7M4(2) = C23.7M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2364C2^3.7M4(2)128,55
C23.8M4(2) = C23.8M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2332C2^3.8M4(2)128,191
C23.9M4(2) = C23.9M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2364C2^3.9M4(2)128,656
C23.10M4(2) = C42.109D4φ: M4(2)/C4 → C22 ⊆ Aut C2364C2^3.10M4(2)128,687
C23.11M4(2) = C8.23C42φ: M4(2)/C4 → C22 ⊆ Aut C23324C2^3.11M4(2)128,842
C23.12M4(2) = M5(2)⋊12C22φ: M4(2)/C4 → C22 ⊆ Aut C23324C2^3.12M4(2)128,849
C23.13M4(2) = M4(2).1C8φ: M4(2)/C4 → C22 ⊆ Aut C23324C2^3.13M4(2)128,885
C23.14M4(2) = C24⋊C8φ: M4(2)/C22 → C4 ⊆ Aut C2316C2^3.14M4(2)128,48
C23.15M4(2) = C23.15M4(2)φ: M4(2)/C22 → C4 ⊆ Aut C2332C2^3.15M4(2)128,49
C23.16M4(2) = C42.C8φ: M4(2)/C22 → C4 ⊆ Aut C23164C2^3.16M4(2)128,59
C23.17M4(2) = C42.42D4φ: M4(2)/C22 → C4 ⊆ Aut C2332C2^3.17M4(2)128,196
C23.18M4(2) = C8.5M4(2)φ: M4(2)/C22 → C4 ⊆ Aut C23164C2^3.18M4(2)128,897
C23.19M4(2) = M5(2)⋊7C4φ: M4(2)/C8 → C2 ⊆ Aut C2364C2^3.19M4(2)128,111
C23.20M4(2) = C23.36C42φ: M4(2)/C8 → C2 ⊆ Aut C2364C2^3.20M4(2)128,484
C23.21M4(2) = C23.21M4(2)φ: M4(2)/C8 → C2 ⊆ Aut C2364C2^3.21M4(2)128,582
C23.22M4(2) = C23.22M4(2)φ: M4(2)/C8 → C2 ⊆ Aut C2364C2^3.22M4(2)128,601
C23.23M4(2) = C2×D4.C8φ: M4(2)/C8 → C2 ⊆ Aut C2364C2^3.23M4(2)128,848
C23.24M4(2) = C23.19C42φ: M4(2)/C2×C4 → C2 ⊆ Aut C2364C2^3.24M4(2)128,12
C23.25M4(2) = C42.2C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2332C2^3.25M4(2)128,107
C23.26M4(2) = C42.7C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2332C2^3.26M4(2)128,108
C23.27M4(2) = C2×C23⋊C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2332C2^3.27M4(2)128,188
C23.28M4(2) = C2×C22.M4(2)φ: M4(2)/C2×C4 → C2 ⊆ Aut C2364C2^3.28M4(2)128,189
C23.29M4(2) = C42.378D4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2364C2^3.29M4(2)128,481
C23.30M4(2) = C24⋊3C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2332C2^3.30M4(2)128,511
C23.31M4(2) = C42.425D4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2364C2^3.31M4(2)128,529
C23.32M4(2) = C23.32M4(2)φ: M4(2)/C2×C4 → C2 ⊆ Aut C2364C2^3.32M4(2)128,549
C23.33M4(2) = C2×C16⋊C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2332C2^3.33M4(2)128,841
C23.34M4(2) = C2×C8.C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2332C2^3.34M4(2)128,884
C23.35M4(2) = C2×C42.6C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2364C2^3.35M4(2)128,1650
C23.36M4(2) = C2×C22.7C42central extension (φ=1)128C2^3.36M4(2)128,459
C23.37M4(2) = C22×C8⋊C4central extension (φ=1)128C2^3.37M4(2)128,1602
C23.38M4(2) = C22×C22⋊C8central extension (φ=1)64C2^3.38M4(2)128,1608
C23.39M4(2) = C22×C4⋊C8central extension (φ=1)128C2^3.39M4(2)128,1634

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