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D₃×SD₁₆×C₃⋊D₃ #13176731

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

D₃×SD₁₆×C₃⋊D₃

Splittings

Fitting	C₃³×SD₁₆ ⋊ C₂²
Sylow	C₃³ ⋊ C₂²×SD₁₆

Subgroups

2060 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×SD₁₆×C₃⋊D₃
maximal normal subgroup of	D₃×C₃⋊D₃×AGL(1,ℤ/8), C₂×D₃×SD₁₆×C₃⋊D₃
maximal quotient of	C₂×D₃×SD₁₆×C₃⋊D₃, D₃×C₃⋊D₃×#106, D₃×C₃⋊D₃×#102

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 42794);