Finite Group Databasebeta

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C₅×C₁₆×C₁₃₇ #72189507

order	10960
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄²×C₈×C₁₇ (order 4352) · Inn(G) = C₁ · Out(G) = C₂×C₄²×C₈×C₁₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₉₆₀
abelian	C₅×C₁₆×C₁₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₁₃₇
socle, prime radical	C₂×C₅×C₁₃₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10960 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₉₆₀, D₂₁₉₂₀
maximal subgroup of	C₅×C₃₂×C₁₃₇, C₂×C₅×C₁₆×C₁₃₇, D₁₀₉₆₀, …
maximal normal subgroup of	C₅×C₃₂×C₁₃₇, C₂×C₅×C₁₆×C₁₃₇, D₁₀₉₆₀, …
maximal quotient of	C₅×C₃₂×C₁₃₇, C₂×C₅×C₁₆×C₁₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.