Finite Group Databasebeta

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D₃×#21249 #72255125

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

Splittings

Fitting	C₃×#21249 ⋊ C₂
Sylow	C₃ ⋊ C₂×#21249

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#121
commutator	C₂×C₃×C₄	C₂⁴×C₄
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₃×#21249	C₂
socle	C₂²×C₃	C₂²×#121
prime radical	C₂²×D₃×AGL(1,ℤ/8)	C₂
cosocle	C₂²×C₃×C₄	C₂⁵
hypercenter	#21249	D₃
hypocenter	C₃	C₂×#21249
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #21249

11020 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×#383145, D₃×#421068, D₃×#6442584
maximal normal subgroup of	D₃×#383145, D₃×#421068, D₃×#6442584

GAP

Past the SmallGroups library coverage — no SmallGroups id.