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D₃×D₄×#272 #72259887

order	2592
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

D₃×D₄×#272

Splittings

Fitting	C₃×D₄×H(3,𝔽₃) ⋊ C₂²
Sylow	C₃×H(3,𝔽₃) ⋊ C₂²×D₄

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₃	C₂²×D₃×C₃⋊D₃
commutator, cosocle	C₂×C₃×H(3,𝔽₃)	C₂⁴
Fitting	C₃×D₄×H(3,𝔽₃)	C₂²
socle	C₂×C₃²	C₂³×C₃⋊D₃
hypercenter	C₃×D₄	D₃×C₃⋊D₃
hypocenter	C₃×H(3,𝔽₃)	C₂²×D₄
LCS	G ▷ C₂×C₃×H(3,𝔽₃) ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

3055 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 72

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₄×#11757730
maximal quotient of	D₄×#11757730

GAP

Past the SmallGroups library coverage — no SmallGroups id.