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D₃×#1867 #10796265

order	768
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

Splittings

Fitting	C₃×#1867 ⋊ C₂
Sylow	C₃ ⋊ C₂×#1867

Subgroups

	subgroup	G/H
center	C₂²	D₃×#120
commutator	C₂³×C₃	C₂³×C₄
Frattini	C₂⁴	C₂³×D₃
Fitting	C₃×#1867	C₂
socle	C₂²×C₃	C₂×#120
prime radical	C₂²×D₃×D₄	C₂²
cosocle	C₂⁴×C₃	C₂⁴
hypercenter	#1867	D₃
hypocenter	C₃	C₂×#1867
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #1867

1994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#10603919, C₄×D₃×B(4,𝔽₂), D₃×#24404, …
maximal normal subgroup of	C₄×D₃×B(4,𝔽₂), D₃×#24404, D₃×#33020, …
maximal quotient of	D₃×#10603919, D₃×#10745, #72260305, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 170646);