# Extensions 1→N→G→Q→1 with N=C54 and Q=C2×C4

Direct product G=N×Q with N=C54 and Q=C2×C4
dρLabelID
C22×C108432C2^2xC108432,53

Semidirect products G=N:Q with N=C54 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C541(C2×C4) = C2×C4×D27φ: C2×C4/C4C2 ⊆ Aut C54216C54:1(C2xC4)432,44
C542(C2×C4) = C22×Dic27φ: C2×C4/C22C2 ⊆ Aut C54432C54:2(C2xC4)432,51

Non-split extensions G=N.Q with N=C54 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C54.1(C2×C4) = C8×D27φ: C2×C4/C4C2 ⊆ Aut C542162C54.1(C2xC4)432,5
C54.2(C2×C4) = C8⋊D27φ: C2×C4/C4C2 ⊆ Aut C542162C54.2(C2xC4)432,6
C54.3(C2×C4) = C4×Dic27φ: C2×C4/C4C2 ⊆ Aut C54432C54.3(C2xC4)432,11
C54.4(C2×C4) = Dic27⋊C4φ: C2×C4/C4C2 ⊆ Aut C54432C54.4(C2xC4)432,12
C54.5(C2×C4) = D54⋊C4φ: C2×C4/C4C2 ⊆ Aut C54216C54.5(C2xC4)432,14
C54.6(C2×C4) = C2×C27⋊C8φ: C2×C4/C22C2 ⊆ Aut C54432C54.6(C2xC4)432,9
C54.7(C2×C4) = C4.Dic27φ: C2×C4/C22C2 ⊆ Aut C542162C54.7(C2xC4)432,10
C54.8(C2×C4) = C4⋊Dic27φ: C2×C4/C22C2 ⊆ Aut C54432C54.8(C2xC4)432,13
C54.9(C2×C4) = C54.D4φ: C2×C4/C22C2 ⊆ Aut C54216C54.9(C2xC4)432,19
C54.10(C2×C4) = C22⋊C4×C27central extension (φ=1)216C54.10(C2xC4)432,21
C54.11(C2×C4) = C4⋊C4×C27central extension (φ=1)432C54.11(C2xC4)432,22
C54.12(C2×C4) = M4(2)×C27central extension (φ=1)2162C54.12(C2xC4)432,24

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