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D₃×#10596675 #72220391

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁴

Aliases

D₃×#10596675

Splittings

Fitting	C₂×C₃³×D₄ ⋊ C₂³
Sylow	C₃³ ⋊ C₂²×H(5,𝔽₂)

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂³×D₃³
commutator, socle, cosocle	C₂×C₃³	C₂⁶
Fitting	C₂×C₃³×D₄	C₂³
hypercenter	C₂×D₄	D₃³
hypocenter	C₃³	C₂²×H(5,𝔽₂)
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂×D₄

29634 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#11865254
maximal normal subgroup of	D₃×#11864777, D₃×#11865254
holomorph of	C₃×C₄×D₃, C₃×#67

GAP

Past the SmallGroups library coverage — no SmallGroups id.