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C₅×C₁₆×C₅₉ #72184178

order	4720
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₂₉ (order 1856) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₄₇₂₀
abelian	C₅×C₁₆×C₅₉
multiplicative	(ℤ/4721)ˣ, (ℤ/9442)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₅₉
socle, prime radical	C₂×C₅×C₅₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₃₂×C₅₉, C₂×C₅×C₁₆×C₅₉, C₃×C₅×C₁₆×C₅₉, …
maximal normal subgroup of	C₅×C₃₂×C₅₉, C₂×C₅×C₁₆×C₅₉, C₃×C₅×C₁₆×C₅₉, …
maximal quotient of	C₅×C₃₂×C₅₉, C₂×C₅×C₁₆×C₅₉, C₃×C₅×C₁₆×C₅₉, …
automorphism group of	C₄₇₂₁, C₂×C₄₇₂₁
outer automorphism group of	C₄₇₂₁, C₂×C₄₇₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.