Finite Group Databasebeta

← Prev (#11661529) Next (#11661531) →

D₃×#3003 #11661530

order	768
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₃×#3003 ⋊ C₂
Sylow	C₃ ⋊ C₂×#3003

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₃
Fitting	C₃×#3003	C₂
socle	C₂²×C₃	C₂³×D₄
hypercenter	#3003	D₃
hypocenter	C₃	C₂×#3003
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3003

7114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72214219, D₃×#23882, #72219800, …
maximal normal subgroup of	D₃×#23882, D₃×#61049, D₃×#23906, …
maximal quotient of	#72214219, D₃×#18524, #72219800, …
automorphism group of	#817, #818, #4717, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1035911);