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C₂×C₃×C₈×C₉×C₁₉ #72187151

order	8208
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 31104
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃×C₈×C₉×C₁₉
multiplicative	(ℤ/8683)ˣ, (ℤ/12339)ˣ, (ℤ/17366)ˣ, (ℤ/24678)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃²×C₁₉
socle, prime radical	C₂²×C₃²×C₁₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8208 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₉×C₁₆×C₁₉, C₃×C₄×C₈×C₉×C₁₉, C₂²×C₃×C₈×C₉×C₁₉, …
maximal normal subgroup of	C₂×C₃×C₉×C₁₆×C₁₉, C₃×C₄×C₈×C₉×C₁₉, C₂²×C₃×C₈×C₉×C₁₉, …
maximal quotient of	C₂×C₃×C₉×C₁₆×C₁₉, C₃×C₄×C₈×C₉×C₁₉, C₂²×C₃×C₈×C₉×C₁₉, …
automorphism group of	C₁₉×C₄₅₇, C₂×C₂₇×C₄₅₇
outer automorphism group of	C₁₉×C₄₅₇, C₂×C₂₇×C₄₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.