Finite Group Databasebeta

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D₃×#33388 #72258507

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

Aliases

Splittings

Fitting	C₃×#33388 ⋊ C₂
Sylow	C₃ ⋊ C₂×#33388

Subgroups

	subgroup	G/H
center	C₂	C₂²×D₃×#102
commutator	C₃×C₈	C₂⁴×C₄
Frattini	C₂×C₈	C₂⁴×D₃
Fitting	C₃×#33388	C₂
socle	C₂×C₃	C₂³×#102
prime radical	D₃×#3584	C₂
cosocle	C₂×C₃×C₈	C₂⁵
hypercenter	#33388	D₃
hypocenter	C₃	C₂×#33388
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#131 ◁ #33388

7916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#7622637
maximal normal subgroup of	D₃×#7622637

GAP

Past the SmallGroups library coverage — no SmallGroups id.