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C₄×C₃₇×C₅₉ #22576648

order	8732
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₉×C₂₉ (order 4176) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₉×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₇₃₂
abelian	C₄×C₃₇×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂	C₂×C₃₇×C₅₉
socle	C₂×C₃₇×C₅₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8732 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₇₃₂, D₁₇₄₆₄
Fitting subgroup of	C₄×C₅₉×C₃₇⋊C₃
maximal subgroup of	C₃×C₄×C₃₇×C₅₉, C₄×C₅₉×C₃₇⋊C₃, Dic₃×C₃₇×C₅₉, …
maximal normal subgroup of	C₃×C₄×C₃₇×C₅₉, C₄×C₅₉×C₃₇⋊C₃, C₈×C₃₇×C₅₉, …
maximal quotient of	C₃×C₄×C₃₇×C₅₉, Dic₃×C₃₇×C₅₉, C₈×C₃₇×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8732, 1);