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C₅×C₃₂×C₅₉ #72188201

order	9440
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₈×C₂₉ (order 3712) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₈×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₄₄₀
abelian	C₅×C₃₂×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₅×C₅₉
socle, prime radical	C₂×C₅×C₅₉	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9440 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₄₄₀, D₁₈₈₈₀
maximal subgroup of	C₅×C₅₉×C₆₄, C₂×C₅×C₃₂×C₅₉, C₃×C₅×C₃₂×C₅₉, …
maximal normal subgroup of	C₅×C₅₉×C₆₄, C₂×C₅×C₃₂×C₅₉, C₃×C₅×C₃₂×C₅₉, …
maximal quotient of	C₅×C₅₉×C₆₄, C₂×C₅×C₃₂×C₅₉, C₃×C₅×C₃₂×C₅₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.