Finite Group Databasebeta

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C₅×C₈×C₁₁×C₃₇ #72194232

order	16280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄²×C₅×C₉ (order 5760) · Inn(G) = C₁ · Out(G) = C₂³×C₄²×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₂₈₀
abelian	C₅×C₈×C₁₁×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₁₁×C₃₇
socle, prime radical	C₂×C₅×C₁₁×C₃₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16280 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₂₈₀, D₃₂₅₆₀
Fitting subgroup of	Dic₈₁₄₀, D₁₆₂₈₀
maximal subgroup of	C₅×C₁₁×C₁₆×C₃₇, C₂×C₅×C₈×C₁₁×C₃₇, Dic₈₁₄₀, …
maximal normal subgroup of	C₅×C₁₁×C₁₆×C₃₇, C₂×C₅×C₈×C₁₁×C₃₇, Dic₈₁₄₀, …
maximal quotient of	C₅×C₁₁×C₁₆×C₃₇, C₂×C₅×C₈×C₁₁×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.