Finite Group Databasebeta

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D₃×#14820 #72248242

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

Splittings

Fitting	C₃×#14820 ⋊ C₂
Sylow	C₃ ⋊ C₂×#14820

Subgroups

	subgroup	G/H
center, Frattini	C₂⁴	C₂⁴×D₃
commutator, socle, cosocle	C₂⁴×C₃	C₂⁵
Fitting	C₃×#14820	C₂
prime radical	C₂⁶×D₃	C₂²
hypercenter	#14820	D₃
hypocenter	C₃	C₂×#14820
LCS	G ▷ C₂⁴×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ #14820

28236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#846041, D₃×#1420724, D₃×#4421184
maximal normal subgroup of	D₃×#846041, D₃×#1420724, D₃×#4421184
maximal quotient of	D₃×#401626

GAP

Past the SmallGroups library coverage — no SmallGroups id.