Finite Group Databasebeta

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D₃×#107130 #72271383

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#107130 ⋊ C₂
Sylow	C₃ ⋊ C₂×#107130

Subgroups

	subgroup	G/H
center	C₂³	D₃×#379
commutator	C₂²×C₃×C₄	C₂²×C₄²
Frattini	C₂⁴×C₄	C₂³×D₃
Fitting	C₃×#107130	C₂
socle	C₂³×C₃	C₂×#379
prime radical	C₂⁴×D₃×D₄	C₂²
cosocle	C₂⁴×C₃×C₄	C₂⁴
hypercenter	#107130	D₃
hypocenter	C₃	C₂×#107130
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ #107130

51322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72219159, D₃×#72219163
maximal normal subgroup of	D₃×#72219159, D₃×#72219163

GAP

Past the SmallGroups library coverage — no SmallGroups id.