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D₃×#41×C₃⋊D₃ #13181636

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₃

Aliases

D₃×#41×C₃⋊D₃

Splittings

Fitting	C₃³×#41 ⋊ C₂²
Sylow	C₃³ ⋊ C₂²×#41

Subgroups

	subgroup	G/H
center	C₄	C₂²×D₃×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃³	C₂⁵
Frattini	C₂	C₂³×D₃×C₃⋊D₃
Fitting	C₃³×#41	C₂²
hypercenter	#41	D₃×C₃⋊D₃
hypocenter	C₃³	C₂²×#41
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₄ ◁ #41

5996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₃⋊D₃×AGL(1,ℤ/8), C₂×D₃×#41×C₃⋊D₃
maximal normal subgroup of	D₃×C₃⋊D₃×AGL(1,ℤ/8), C₂×D₃×#41×C₃⋊D₃
maximal quotient of	C₄×D₃×D₄×C₃⋊D₃, C₂×D₃×#41×C₃⋊D₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47699);