Finite Group Databasebeta

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D₃×#146656 #72247995

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

Splittings

Fitting	C₃×#146656 ⋊ C₂
Sylow	C₃ ⋊ C₂×#146656

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1790
commutator	C₂×C₃×Q₈	C₂²×C₄²
Frattini	C₂²×#41	C₂³×D₃
Fitting	C₃×#146656	C₂
socle	C₂²×C₃	C₂×#1790
prime radical	C₂×D₃×#535	C₂²
cosocle	C₂²×C₃×#41	C₂⁴
hypercenter	#146656	D₃
hypocenter	C₃	C₂×#146656
LCS	G ▷ C₂×C₃×Q₈ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#41 ◁ #146656

At least 7124 conjugacy classes of subgroups; only the 1191 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72215601
maximal normal subgroup of	D₃×#72215601
maximal quotient of	D₃×#72213396

GAP

Past the SmallGroups library coverage — no SmallGroups id.