Finite Group Databasebeta

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C₃×C₁₃×C₁₆×C₁₉ #72190293

order	11856
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄²×C₉ (order 3456) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄²×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₈₅₆
abelian	C₃×C₁₃×C₁₆×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₁₃×C₁₉
socle, prime radical	C₂×C₃×C₁₃×C₁₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11856 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₈₅₆, D₂₃₇₁₂
maximal subgroup of	C₃×C₁₃×C₁₉×C₃₂, C₂×C₃×C₁₃×C₁₆×C₁₉, D₁₁₈₅₆, …
maximal normal subgroup of	C₃×C₁₃×C₁₉×C₃₂, C₂×C₃×C₁₃×C₁₆×C₁₉, D₁₁₈₅₆, …
maximal quotient of	C₃×C₁₃×C₁₉×C₃₂, C₂×C₃×C₁₃×C₁₆×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.