Finite Group Databasebeta

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D₃×#10591522 #72220385

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

D₃×#10591522

Splittings

Fitting	C₂×C₃³×D₄ ⋊ C₂³
Sylow	C₃³ ⋊ C₂×#453

Subgroups

	subgroup	G/H
center	C₂	D₃×#63983
commutator, cosocle	C₂×C₃³×C₄	C₂⁴
Frattini	C₂×C₄	C₂×D₃³
Fitting	C₂×C₃³×D₄	C₂³
socle	C₂×C₃³	C₂×#120
hypercenter	C₂×D₄	D₃³
hypocenter	C₃³	C₂×#453
LCS	G ▷ C₂×C₃³×C₄ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

4318 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal normal subgroup of

D₃×#11864777

GAP

Past the SmallGroups library coverage — no SmallGroups id.