# Extensions 1→N→G→Q→1 with N=C2×C54 and Q=C22

Direct product G=N×Q with N=C2×C54 and Q=C22
dρLabelID
C23×C54432C2^3xC54432,228

Semidirect products G=N:Q with N=C2×C54 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C54)⋊C22 = D4×D27φ: C22/C1C22 ⊆ Aut C2×C541084+(C2xC54):C2^2432,47
(C2×C54)⋊2C22 = D4×C54φ: C22/C2C2 ⊆ Aut C2×C54216(C2xC54):2C2^2432,54
(C2×C54)⋊3C22 = C2×C27⋊D4φ: C22/C2C2 ⊆ Aut C2×C54216(C2xC54):3C2^2432,52
(C2×C54)⋊4C22 = C23×D27φ: C22/C2C2 ⊆ Aut C2×C54216(C2xC54):4C2^2432,227

Non-split extensions G=N.Q with N=C2×C54 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C54).C22 = D42D27φ: C22/C1C22 ⊆ Aut C2×C542164-(C2xC54).C2^2432,48
(C2×C54).2C22 = C4○D4×C27φ: C22/C2C2 ⊆ Aut C2×C542162(C2xC54).2C2^2432,56
(C2×C54).3C22 = C4×Dic27φ: C22/C2C2 ⊆ Aut C2×C54432(C2xC54).3C2^2432,11
(C2×C54).4C22 = Dic27⋊C4φ: C22/C2C2 ⊆ Aut C2×C54432(C2xC54).4C2^2432,12
(C2×C54).5C22 = C4⋊Dic27φ: C22/C2C2 ⊆ Aut C2×C54432(C2xC54).5C2^2432,13
(C2×C54).6C22 = D54⋊C4φ: C22/C2C2 ⊆ Aut C2×C54216(C2xC54).6C2^2432,14
(C2×C54).7C22 = C54.D4φ: C22/C2C2 ⊆ Aut C2×C54216(C2xC54).7C2^2432,19
(C2×C54).8C22 = C2×Dic54φ: C22/C2C2 ⊆ Aut C2×C54432(C2xC54).8C2^2432,43
(C2×C54).9C22 = C2×C4×D27φ: C22/C2C2 ⊆ Aut C2×C54216(C2xC54).9C2^2432,44
(C2×C54).10C22 = C2×D108φ: C22/C2C2 ⊆ Aut C2×C54216(C2xC54).10C2^2432,45
(C2×C54).11C22 = D1085C2φ: C22/C2C2 ⊆ Aut C2×C542162(C2xC54).11C2^2432,46
(C2×C54).12C22 = C22×Dic27φ: C22/C2C2 ⊆ Aut C2×C54432(C2xC54).12C2^2432,51
(C2×C54).13C22 = C22⋊C4×C27central extension (φ=1)216(C2xC54).13C2^2432,21
(C2×C54).14C22 = C4⋊C4×C27central extension (φ=1)432(C2xC54).14C2^2432,22
(C2×C54).15C22 = Q8×C54central extension (φ=1)432(C2xC54).15C2^2432,55

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