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C₂²×C₄×D₃×C₃⋊D₃ #13181597

order	1728
isoclinism	isoclinic class of D₃×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂²×C₄×D₃×C₃⋊D₃

Splittings

Fitting	C₂²×C₃³×C₄ ⋊ C₂²
derived, Sylow	C₃³ ⋊ C₂⁴×C₄

Subgroups

9116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Conjugacy classes & character table

288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×D₃×D₄×C₃⋊D₃, C₂×D₃×M₁₆×C₃⋊D₃, C₂²×D₃×C₃⋊D₃×AGL(1,𝔽₅), …
maximal normal subgroup of	C₂²×D₃×D₄×C₃⋊D₃, C₂×D₃×M₁₆×C₃⋊D₃, C₄×D₃×#3811, …
maximal quotient of	C₂×D₃×M₁₆×C₃⋊D₃, C₂²×D₃×C₃⋊D₃×AGL(1,𝔽₅), C₄×D₃×D₄×C₃⋊D₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47660);