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C₂×C₄×C₁₉×C₄₁ #72185396

order	6232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5760
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₁₉×C₄₁
multiplicative	(ℤ/7795)ˣ, (ℤ/15590)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₁₉×C₄₁
socle, prime radical	C₂²×C₁₉×C₄₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₁₉×C₄₁, C₄²×C₁₉×C₄₁, C₂²×C₄×C₁₉×C₄₁, …
maximal normal subgroup of	C₂×C₈×C₁₉×C₄₁, C₄²×C₁₉×C₄₁, C₂²×C₄×C₁₉×C₄₁, …
maximal quotient of	C₂×C₈×C₁₉×C₄₁, C₄²×C₁₉×C₄₁, C₂²×C₄×C₁₉×C₄₁, …
automorphism group of	C₅×C₁₅₅₉
outer automorphism group of	C₅×C₁₅₅₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.