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D₃×D₈×C₃⋊D₃ #13176711

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

D₃×D₈×C₃⋊D₃

Splittings

Fitting	C₃³×D₈ ⋊ C₂²
Sylow	C₃³ ⋊ C₂²×D₈

Subgroups

	subgroup	G/H
center	C₂	D₃×D₄×C₃⋊D₃
commutator, cosocle	C₃³×C₄	C₂⁴
Frattini	C₄	C₂²×D₃×C₃⋊D₃
Fitting	C₃³×D₈	C₂²
socle	C₂×C₃³	C₂²×D₄
hypercenter	D₈	D₃×C₃⋊D₃
hypocenter	C₃³	C₂²×D₈
LCS	G ▷ C₃³×C₄ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

2332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₃⋊D₃×AGL(1,ℤ/8), C₂×D₃×D₈×C₃⋊D₃
maximal normal subgroup of	D₃×C₃⋊D₃×AGL(1,ℤ/8), C₂×D₃×D₈×C₃⋊D₃
maximal quotient of	C₂×D₃×D₈×C₃⋊D₃, D₃×C₃⋊D₃×#102

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 42774);