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D₃²×GL(2,ℤ/4) #72220747

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁷

Aliases

D₃²×GL(2,ℤ/4)

Splittings

C₂⁴×C₃² ⋊ C₂²×D₃

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂×D₃²×S₄
commutator, cosocle	C₂×C₃²×A₄	C₂⁴
Fitting	C₂⁴×C₃²	C₂²×D₃
socle	C₂³×C₃²	C₂³×D₃
hypercenter	C₂²	D₃²×S₄
hypocenter	C₃²×A₄	C₂²×D₄
LCS	G ▷ C₂×C₃²×A₄ ▷ C₃²×A₄
UCS	C₁ ◁ C₂ ◁ C₂²

6963 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

D₃²×A₄⋊S₄

GAP

Past the SmallGroups library coverage — no SmallGroups id.