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C₂²×C₃×C₅×C₁₈₁ #24925803

order	10860
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₅×C₁₈₁
multiplicative	(ℤ/11957)ˣ, (ℤ/12677)ˣ, (ℤ/16293)ˣ, (ℤ/16299)ˣ, (ℤ/21724)ˣ, (ℤ/23914)ˣ, (ℤ/25354)ˣ, (ℤ/32586)ˣ, (ℤ/32598)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₅×C₉×C₁₈₁, C₅×C₂²⋊#13108656, C₅×C₂²⋊C₉×C₁₈₁, …
maximal normal subgroup of	C₂²×C₅×C₉×C₁₈₁, C₅×C₂²⋊#13108656, C₅×C₂²⋊C₉×C₁₈₁, …
maximal quotient of	C₂²×C₅×C₉×C₁₈₁, C₂²×C₃²×C₅×C₁₈₁, C₂×C₃×C₅×D₃×C₁₈₁, …
automorphism group of	C₁₁×C₁₀₈₇, C₇×C₁₈₁₁
outer automorphism group of	C₁₁×C₁₀₈₇, C₇×C₁₈₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 19);