Finite Group Databasebeta

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C₁₆×C₁₉×C₄₁ #72190809

order	12464
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₅×C₈×C₉ (order 5760) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₅×C₈×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₄₆₄
abelian	C₁₆×C₁₉×C₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₉×C₄₁
socle, prime radical	C₂×C₁₉×C₄₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12464 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₄₆₄, D₂₄₉₂₈
maximal subgroup of	C₁₉×C₃₂×C₄₁, C₂×C₁₆×C₁₉×C₄₁, D₁₂₄₆₄, …
maximal normal subgroup of	C₁₉×C₃₂×C₄₁, C₂×C₁₆×C₁₉×C₄₁, D₁₂₄₆₄, …
maximal quotient of	C₁₉×C₃₂×C₄₁, C₂×C₁₆×C₁₉×C₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.