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C₄×C₉×C₁₅₇ #19150765

order	5652
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄×C₁₃ (order 1872) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₅₆₅₂
abelian	C₄×C₉×C₁₅₇
multiplicative	(ℤ/5653)ˣ, (ℤ/11306)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₃	C₂×C₃×C₁₅₇
socle	C₂×C₃×C₁₅₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5652 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅×C₉×C₁₅₇, C₉×Dic₅×C₁₅₇, C₉×AGL(1,𝔽₅)×C₁₅₇, …
maximal normal subgroup of	C₄×C₅×C₉×C₁₅₇, C₈×C₉×C₁₅₇, C₂×C₄×C₉×C₁₅₇, …
maximal quotient of	C₄×C₅×C₉×C₁₅₇, C₉×Dic₅×C₁₅₇, C₉×AGL(1,𝔽₅)×C₁₅₇, …
automorphism group of	C₅₆₅₃, C₂×C₅₆₅₃
outer automorphism group of	C₅₆₅₃, C₂×C₅₆₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5652, 1);