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C₂×C₉×C₁₉×C₂₅ #22555463

order	8550
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄×C₅×C₉ (order 2160) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₅₅₀
abelian	C₂×C₉×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃×C₅	C₂×C₃×C₅×C₁₉
socle	C₂×C₃×C₅×C₁₉	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8550 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₅₅₀, D₁₇₁₀₀
Fitting subgroup of	C₉×C₂₅×Dic₁₉, C₉×C₁₉×Dic₂₅, C₉×Dic₄₇₅, …
maximal subgroup of	C₄×C₉×C₁₉×C₂₅, C₉×C₂₅×Dic₁₉, C₉×C₁₉×Dic₂₅, …
maximal normal subgroup of	C₄×C₉×C₁₉×C₂₅, C₉×C₂₅×Dic₁₉, C₉×C₁₉×Dic₂₅, …
maximal quotient of	C₄×C₉×C₁₉×C₂₅, C₂²×C₉×C₁₉×C₂₅, C₂×C₁₉×C₂₅×C₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 1);