Finite Group Databasebeta

← Prev (#72271391) Next (#72271393) →

C₃×#772785 #72271392

order	1536
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂¹²

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

22724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	D₃×#772785, #72271447
maximal subgroup of	D₃×#772785, #72271447, C₃×#72214271
maximal normal subgroup of	D₃×#772785, #72271447, C₃×#72214271

GAP

Past the SmallGroups library coverage — no SmallGroups id.