Finite Group Databasebeta

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C₃×#763336 #72271604

order	1536
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂⁹×C₄²

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂⁵
commutator, Frattini, cosocle	C₂⁴	C₂⁵×C₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ G

18480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

276 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	D₃×#763336, #72271623
maximal subgroup of	D₃×#763336, #72271623, C₃×#72214271
maximal normal subgroup of	D₃×#763336, #72271623, C₃×#72214271

GAP

Past the SmallGroups library coverage — no SmallGroups id.