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C₄×C₄⋊#1084 #13144257

order	1728
isoclinism	isoclinic class of #6229
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄×C₄⋊#1084

Splittings

H(3,𝔽₃) ⋊ C₄×C₄⋊C₄

Subgroups

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×C₃⋊D₃
commutator	C₂×H(3,𝔽₃)	C₂×C₄²
Frattini, socle	C₂³×C₃	C₂²×C₃⋊D₃
Fitting	C₂×C₄²×H(3,𝔽₃)	C₂
prime radical, cosocle	C₂³×H(3,𝔽₃)	C₂³
hypercenter	C₂×C₃×C₄²	C₃⋊D₃
hypocenter	H(3,𝔽₃)	C₄×C₄⋊C₄
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄²

1067 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 576

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10320);