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C₂×C₅²×C₉×C₁₉ #22555499

order	8550
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 51840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

C₂×C₅²×C₉×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃	C₂×C₃×C₅²×C₁₉
socle	C₂×C₃×C₅²×C₁₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₅²×C₉×Dic₁₉, C₅×C₉×C₁₉×Dic₅, C₅×C₉×Dic₉₅, …
maximal subgroup of	C₄×C₅²×C₉×C₁₉, C₅²×C₉×Dic₁₉, C₅×C₉×C₁₉×Dic₅, …
maximal normal subgroup of	C₄×C₅²×C₉×C₁₉, C₅²×C₉×Dic₁₉, C₅×C₉×C₁₉×Dic₅, …
maximal quotient of	C₄×C₅²×C₉×C₁₉, C₂²×C₅²×C₉×C₁₉, C₂×C₅²×C₁₉×C₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 37);