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C₅×C₂₉×C₆₄ #72188079

order	9280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄²×C₇×C₁₆ (order 3584) · Inn(G) = C₁ · Out(G) = C₂×C₄²×C₇×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₂₈₀
abelian	C₅×C₂₉×C₆₄
multiplicative	(ℤ/9281)ˣ, (ℤ/18562)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃₂	C₂×C₅×C₂₉
socle, prime radical	C₂×C₅×C₂₉	C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

28 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9280 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₂₈₀, D₁₈₅₆₀
maximal subgroup of	C₅×C₂₉×C₁₂₈, C₂×C₅×C₂₉×C₆₄, C₃×C₅×C₂₉×C₆₄, …
maximal normal subgroup of	C₅×C₂₉×C₁₂₈, C₂×C₅×C₂₉×C₆₄, C₃×C₅×C₂₉×C₆₄, …
maximal quotient of	C₅×C₂₉×C₁₂₈, C₂×C₅×C₂₉×C₆₄, C₃×C₅×C₂₉×C₆₄
automorphism group of	C₉₂₈₁
outer automorphism group of	C₉₂₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.