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D₃×C₂²⋊C₄×C₃⋊D₃ #13175907

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷×C₃

Aliases

D₃×C₂²⋊C₄×C₃⋊D₃

Splittings

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

Subgroups

4572 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×#120, C₄×D₃×D₄×C₃⋊D₃, D₃×#10590404
maximal normal subgroup of	D₃×C₃⋊D₃×#120, C₄×D₃×D₄×C₃⋊D₃, D₃×#10590404
maximal quotient of	D₃×C₃⋊D₃×#102

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 41970);