Finite Group Databasebeta

← Prev (#72231787) Next (#72231789) →

D₃×#7310 #72231788

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

Splittings

Fitting	C₃×#7310 ⋊ C₂
Sylow	C₃ ⋊ C₂×#7310

Subgroups

	subgroup	G/H
center	C₂	D₃×#1304
commutator	C₂⁴×C₃	C₂×C₄²
Frattini	C₂³×D₄	C₂²×D₃
Fitting	C₃×#7310	C₂
socle	C₂×C₃	C₂×#1304
prime radical	C₂³×D₃×D₄	C₂²
cosocle	C₂³×C₃×D₄	C₂³
hypercenter	#7310	D₃
hypocenter	C₃	C₂×#7310
LCS	G ▷ C₂⁴×C₃ ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×D₄ ◁ #7310

4148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#139750, D₃×#144378, D₃×#139743, …
maximal normal subgroup of	D₃×#139750, D₃×#144378, D₃×#139743, …
maximal quotient of	C₂×D₃×#7310

GAP

Past the SmallGroups library coverage — no SmallGroups id.