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C₂×C₅×C₈×C₉×C₁₉ #72191886

order	13680
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₅×C₈×C₉×C₁₉
multiplicative	(ℤ/13943)ˣ, (ℤ/14459)ˣ, (ℤ/14801)ˣ, (ℤ/20523)ˣ, (ℤ/20547)ˣ, (ℤ/27364)ˣ, (ℤ/27886)ˣ, (ℤ/28918)ˣ, (ℤ/29602)ˣ, (ℤ/41046)ˣ, (ℤ/41094)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃×C₅×C₁₉
socle, prime radical	C₂²×C₃×C₅×C₁₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₉×C₁₆×C₁₉, C₄×C₅×C₈×C₉×C₁₉, C₂²×C₅×C₈×C₉×C₁₉
maximal normal subgroup of	C₂×C₅×C₉×C₁₆×C₁₉, C₄×C₅×C₈×C₉×C₁₉, C₂²×C₅×C₈×C₉×C₁₉
maximal quotient of	C₂×C₅×C₉×C₁₆×C₁₉, C₄×C₅×C₈×C₉×C₁₉, C₂²×C₅×C₈×C₉×C₁₉
automorphism group of	C₇₃×C₁₉₁, C₁₉×C₇₆₁
outer automorphism group of	C₇₃×C₁₉₁, C₁₉×C₇₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.