Finite Group Databasebeta

← Prev (#72182141) Next (#72182143) →

C₅×C₁₆×C₂₇ #72182142

order	2160
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₉ (order 576) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₁₆₀
abelian	C₅×C₁₆×C₂₇
multiplicative	(ℤ/2161)ˣ, (ℤ/4322)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₉	C₂×C₃×C₅
socle, prime radical	C₂×C₃×C₅	C₈×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₂₇×C₃₂, C₂×C₅×C₁₆×C₂₇, C₅×C₁₆×C₈₁, …
maximal normal subgroup of	C₅×C₂₇×C₃₂, C₂×C₅×C₁₆×C₂₇, C₅×C₁₆×C₈₁, …
maximal quotient of	C₅×C₂₇×C₃₂, C₂×C₅×C₁₆×C₂₇, C₅×C₁₆×C₈₁, …
automorphism group of	C₂₁₆₁, C₂×C₂₁₆₁
outer automorphism group of	C₂₁₆₁, C₂×C₂₁₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.