Finite Group Databasebeta

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D₃×#20983 #72249232

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

Aliases

Splittings

Fitting	C₃×#20983 ⋊ C₂
Sylow	C₃ ⋊ C₂×#20983

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×D₃×C₂²⋊C₄
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂⁴	C₂⁴×D₃
Fitting	C₃×#20983	C₂
socle	C₂²×C₃	C₂³×C₂²⋊C₄
prime radical	C₂×D₃×#525	C₂
cosocle	C₂⁴×C₃	C₂⁵
hypercenter	#20983	D₃
hypocenter	C₃	C₂×#20983
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ #20983

14460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#359639, D₃×#374114, D₃×#364424, …
maximal normal subgroup of	D₃×#359639, D₃×#374114, D₃×#364424, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.