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C₃×C₅×C₈×C₇₁ #72187394

order	8520
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₄×C₅×C₇ (order 2240) · Inn(G) = C₁ · Out(G) = C₂⁴×C₄×C₅×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₅₂₀
abelian	C₃×C₅×C₈×C₇₁
multiplicative	(ℤ/8521)ˣ, (ℤ/17042)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₅×C₇₁
socle, prime radical	C₂×C₃×C₅×C₇₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8520 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₅₂₀, D₁₇₀₄₀
maximal subgroup of	C₃×C₅×C₁₆×C₇₁, C₂×C₃×C₅×C₈×C₇₁, C₅×C₈×C₉×C₇₁, …
maximal normal subgroup of	C₃×C₅×C₁₆×C₇₁, C₂×C₃×C₅×C₈×C₇₁, C₅×C₈×C₉×C₇₁, …
maximal quotient of	C₃×C₅×C₁₆×C₇₁, C₂×C₃×C₅×C₈×C₇₁, C₅×C₈×C₉×C₇₁, …
automorphism group of	C₈₅₂₁
outer automorphism group of	C₈₅₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.