Finite Group Databasebeta

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C₅×C₇×C₈×C₁₉ #72184635

order	5320
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃×C₄×C₉ (order 1728) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃×C₄×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₅₃₂₀
abelian	C₅×C₇×C₈×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₇×C₁₉
socle, prime radical	C₂×C₅×C₇×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₇×C₁₆×C₁₉, C₂×C₅×C₇×C₈×C₁₉, C₃×C₅×C₇×C₈×C₁₉, …
maximal normal subgroup of	C₅×C₇×C₁₆×C₁₉, C₂×C₅×C₇×C₈×C₁₉, C₃×C₅×C₇×C₈×C₁₉, …
maximal quotient of	C₅×C₇×C₁₆×C₁₉, C₂×C₅×C₇×C₈×C₁₉, C₃×C₅×C₇×C₈×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.