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C₄×C₅×C₈×C₁₉ #72182787

order	3040
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9216
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄×C₅×C₈×C₁₉
multiplicative	(ℤ/3805)ˣ, (ℤ/7610)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₅×C₁₉
socle, prime radical	C₂²×C₅×C₁₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅×C₁₆×C₁₉, C₅×C₈²×C₁₉, C₂×C₄×C₅×C₈×C₁₉, …
maximal normal subgroup of	C₄×C₅×C₁₆×C₁₉, C₅×C₈²×C₁₉, C₂×C₄×C₅×C₈×C₁₉, …
maximal quotient of	C₄×C₅×C₁₆×C₁₉, C₅×C₈²×C₁₉, C₂×C₄×C₅×C₈×C₁₉, …
automorphism group of	C₅×C₇₆₁, C₂×C₅×C₇₆₁
outer automorphism group of	C₅×C₇₆₁, C₂×C₅×C₇₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.