Finite Group Databasebeta

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D₃×#11714174 #72275027

order	4608
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁷

Aliases

D₃×#11714174

Splittings

C₃×#3027 ⋊ C₂×D₃

Subgroups

	subgroup	G/H
center	C₂	C₂×D₃×#1020⋊C₂
commutator, cosocle, hypocenter	C₃×#997	C₂⁴
Frattini	C₂³	C₂²×D₃×S₄
Fitting	C₃×#3027	C₂×D₃
socle	C₂×C₃	C₂²×#1020⋊C₂
hypercenter	C₄	D₃×#1020⋊C₂
LCS	G ▷ C₃×#997
UCS	C₁ ◁ C₂ ◁ C₄

7541 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72217027
maximal normal subgroup of	D₃×#72217027

GAP

Past the SmallGroups library coverage — no SmallGroups id.