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C₂²×C₃²×C₁₁×C₁₉ #21419015

order	7524
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 51840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₃²×C₁₁×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7524 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂²×C₃²×C₁₉×C₁₁⋊C₅
socle of	C₂²×C₃²×C₁₉×C₁₁⋊C₅
maximal subgroup of	C₂²×C₃²×C₅×C₁₁×C₁₉, C₂²×C₃²×C₁₉×C₁₁⋊C₅, C₂×C₃²×D₅×C₁₁×C₁₉, …
maximal normal subgroup of	C₂²×C₃²×C₅×C₁₁×C₁₉, C₂²×C₃²×C₁₉×C₁₁⋊C₅, C₂×C₃²×C₄×C₁₁×C₁₉, …
maximal quotient of	C₂²×C₃²×C₅×C₁₁×C₁₉, C₂×C₃²×D₅×C₁₁×C₁₉, C₂×C₃²×C₄×C₁₁×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 59);