Finite Group Databasebeta

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D₃×#33348 #72255240

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₃×#33348 ⋊ C₂
Sylow	C₃ ⋊ C₂×#33348

Subgroups

	subgroup	G/H
center	C₂	C₂²×D₃×#99
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂×D₄	C₂⁴×D₃
Fitting	C₃×#33348	C₂
socle	C₂×C₃	C₂³×#99
prime radical	D₃×#3484	C₂
cosocle	C₂×C₃×D₄	C₂⁵
hypercenter	#33348	D₃
hypocenter	C₃	C₂×#33348
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×D₄ ◁ C₂×H(5,𝔽₂) ◁ #33348

9984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#7622880, D₃×#493635, D₃×#493474
maximal normal subgroup of	D₃×#7622880, D₃×#493635, D₃×#493474

GAP

Past the SmallGroups library coverage — no SmallGroups id.