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C₄×D₃×C₄⋊(C₃⋊D₃) #13175393

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₄×D₃×C₄⋊(C₃⋊D₃)

Splittings

Fitting	C₃³×C₄² ⋊ C₂²
Sylow	C₃³ ⋊ C₂×C₄×D₄

Subgroups

2932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#10592410, C₄×D₃×D₄×C₃⋊D₃, D₃×#10592713
maximal normal subgroup of	D₃×#10592410, C₄×D₃×D₄×C₃⋊D₃, D₃×#10592713
maximal quotient of	D₃×#10592410

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 41456);