Finite Group Databasebeta

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D₃×#10937 #72249223

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

Splittings

Fitting	C₃×#10937 ⋊ C₂
Sylow	C₃ ⋊ C₂×#10937

Subgroups

	subgroup	G/H
center	C₂×C₄	D₃×#120
commutator	C₂³×C₃	C₂²×C₄²
Frattini	C₂³×C₄	C₂³×D₃
Fitting	C₃×#10937	C₂
socle	C₂²×C₃	C₂×#386
prime radical	C₂⁵×D₃	C₂×C₄
cosocle	C₂³×C₃×C₄	C₂⁴
hypercenter	#10937	D₃
hypocenter	C₃	C₂×#10937
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #10937

6876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#417774, D₃×#364592, D₃×#383145, …
maximal normal subgroup of	D₃×#417774, D₃×#364592, D₃×#383145, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.