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D₃×C₄⋊C₄×C₃⋊D₃ #13176520

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

Aliases

D₃×C₄⋊C₄×C₃⋊D₃

Splittings

Fitting	C₃³×C₄⋊C₄ ⋊ C₂²
Sylow	C₃³ ⋊ C₂²×C₄⋊C₄

Subgroups

2876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₃⋊D₃×#106, C₄×D₃×D₄×C₃⋊D₃, D₃×C₃⋊D₃×#102
maximal normal subgroup of	D₃×C₃⋊D₃×#106, C₄×D₃×D₄×C₃⋊D₃, D₃×C₃⋊D₃×#102
maximal quotient of	D₃×C₃⋊D₃×#106

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 42583);