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C₂×C₄×C₅×C₁₃×C₁₉ #72188576

order	9880
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₅×C₁₃×C₁₉
multiplicative	(ℤ/10123)ˣ, (ℤ/20246)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅×C₁₃×C₁₉
socle, prime radical	C₂²×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9880 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₈×C₁₃×C₁₉, C₄²×C₅×C₁₃×C₁₉, C₂²×C₄×C₅×C₁₃×C₁₉, …
maximal normal subgroup of	C₂×C₅×C₈×C₁₃×C₁₉, C₄²×C₅×C₁₃×C₁₉, C₂²×C₄×C₅×C₁₃×C₁₉, …
maximal quotient of	C₂×C₅×C₈×C₁₃×C₁₉, C₄²×C₅×C₁₃×C₁₉, C₂²×C₄×C₅×C₁₃×C₁₉, …
automorphism group of	C₅₃×C₁₉₁
outer automorphism group of	C₅₃×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.