Finite Group Databasebeta

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D₃×#83287 #72243763

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

Splittings

Fitting	C₃²×#532 ⋊ C₂²
Sylow	C₃² ⋊ C₂×#3151

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₃×#67
commutator, cosocle	C₂×C₃²×C₄	C₂⁵
Frattini	C₂×C₄	C₂³×D₃²
Fitting	C₃²×#532	C₂²
socle	C₂²×C₃²	C₂³×D₄
hypercenter	#532	D₃²
hypocenter	C₃²	C₂×#3151
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

8228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃²×#3151
maximal normal subgroup of	D₃²×#3151

GAP

Past the SmallGroups library coverage — no SmallGroups id.