Finite Group Databasebeta

← Prev (#13047782) Next (#13047784) →

H(3,𝔽₃)×C₄²⋊C₃ #13047783

order	1296
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴×C₄

Aliases

H(3,𝔽₃)×C₄²⋊C₃

Splittings

Fitting	C₄²×H(3,𝔽₃) ⋊ C₃
Sylow	C₄² ⋊ C₃×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center	C₃	C₃²×C₄²⋊C₃
commutator, cosocle	C₃×C₄²	C₃³
Frattini, socle	C₂²×C₃	C₃²×A₄
Fitting	C₄²×H(3,𝔽₃)	C₃
hypercenter	H(3,𝔽₃)	C₄²⋊C₃
hypocenter	C₄²	C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₄² ▷ C₄²
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 108

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1501);