Finite Group Databasebeta

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C₃²×C₅×C₁₆×C₁₉ #72191885

order	13680
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 27648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₅×C₁₆×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃²×C₅×C₁₉
socle, prime radical	C₂×C₃²×C₅×C₁₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₅×C₁₉×C₃₂, C₂×C₃²×C₅×C₁₆×C₁₉
maximal normal subgroup of	C₃²×C₅×C₁₉×C₃₂, C₂×C₃²×C₅×C₁₆×C₁₉
maximal quotient of	C₃²×C₅×C₁₉×C₃₂, C₂×C₃²×C₅×C₁₆×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.