Finite Group Databasebeta

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C₅×C₈×C₁₃×C₁₇ #72187689

order	8840
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₁₆ (order 3072) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₈₄₀
abelian	C₅×C₈×C₁₃×C₁₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₁₃×C₁₇
socle, prime radical	C₂×C₅×C₁₃×C₁₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8840 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₈₄₀, D₁₇₆₈₀
maximal subgroup of	C₅×C₁₃×C₁₆×C₁₇, C₂×C₅×C₈×C₁₃×C₁₇, C₃×C₅×C₈×C₁₃×C₁₇, …
maximal normal subgroup of	C₅×C₁₃×C₁₆×C₁₇, C₂×C₅×C₈×C₁₃×C₁₇, C₃×C₅×C₈×C₁₃×C₁₇, …
maximal quotient of	C₅×C₁₃×C₁₆×C₁₇, C₂×C₅×C₈×C₁₃×C₁₇, C₃×C₅×C₈×C₁₃×C₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.