Finite Group Databasebeta

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D₃×#13082 #72247979

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

Splittings

Fitting	C₃×#13082 ⋊ C₂
Sylow	C₃ ⋊ C₂×#13082

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#99
commutator	C₂⁴×C₃	C₂³×C₄
Frattini	C₂²×D₄	C₂³×D₃
Fitting	C₃×#13082	C₂
socle	C₂²×C₃	C₂²×#99
prime radical	D₃×#2403	C₂
cosocle	C₂²×C₃×D₄	C₂⁴
hypercenter	#13082	D₃
hypocenter	C₃	C₂×#13082
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ #13082

7428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#133356, D₃×#496225, D₃×#499832, …
maximal normal subgroup of	D₃×#133356, D₃×#496225, D₃×#499832, …
maximal quotient of	D₃×#147555

GAP

Past the SmallGroups library coverage — no SmallGroups id.