Finite Group Databasebeta

← Prev (#13181733) Next (#13181735) →

C₂²×C₃×D₄×C₃⋊D₃ #13181734

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂²×C₃×D₄×C₃⋊D₃

Splittings

Fitting	C₂²×C₃³×D₄ ⋊ C₂
Sylow	C₃³ ⋊ C₂³×D₄

Subgroups

9116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂²×D₃×D₄×C₃⋊D₃, C₂×D₄×C₃⋊D₃×AGL(1,𝔽₇), C₂×C₃×#10595100, …
maximal normal subgroup of	C₂²×D₃×D₄×C₃⋊D₃, C₂×C₃×#10595100, C₂×C₃×C₃⋊D₃×#127, …
maximal quotient of	C₂×D₄×C₃⋊D₃×AGL(1,𝔽₇), C₂×C₃×C₃⋊D₃×#127, C₂×C₃×C₃⋊D₃×#120, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47797);