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C₂×C₄×C₉×C₁₁×C₁₉ #72193103

order	15048
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₉×C₁₁×C₁₉
multiplicative	(ℤ/15503)ˣ, (ℤ/31006)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₁₁×C₁₉
socle, prime radical	C₂²×C₃×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₉×C₁₁×C₁₉, C₄²×C₉×C₁₁×C₁₉, C₂²×C₄×C₉×C₁₁×C₁₉
maximal normal subgroup of	C₂×C₈×C₉×C₁₁×C₁₉, C₄²×C₉×C₁₁×C₁₉, C₂²×C₄×C₉×C₁₁×C₁₉
maximal quotient of	C₂×C₈×C₉×C₁₁×C₁₉, C₄²×C₉×C₁₁×C₁₉, C₂²×C₄×C₉×C₁₁×C₁₉
automorphism group of	C₃₇×C₄₁₉
outer automorphism group of	C₃₇×C₄₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.