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C₂×C₉×C₁₃×C₂₅ #19154285

order	5850
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃²×C₄²×C₅ (order 1440) · Inn(G) = C₁ · Out(G) = C₂×C₃²×C₄²×C₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₅₈₅₀
abelian	C₂×C₉×C₁₃×C₂₅
multiplicative	(ℤ/5851)ˣ, (ℤ/11702)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃×C₅	C₂×C₃×C₅×C₁₃
socle	C₂×C₃×C₅×C₁₃	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₉×C₁₃×C₂₅, C₉×C₂₅×Dic₁₃, C₉×C₁₃×Dic₂₅, …
maximal normal subgroup of	C₄×C₉×C₁₃×C₂₅, C₉×C₂₅×Dic₁₃, C₉×C₁₃×Dic₂₅, …
maximal quotient of	C₄×C₉×C₁₃×C₂₅, C₂²×C₉×C₁₃×C₂₅, C₂×C₁₃×C₂₅×C₂₇, …
automorphism group of	C₅₈₅₁, C₂×C₅₈₅₁
outer automorphism group of	C₅₈₅₁, C₂×C₅₈₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 1);