Finite Group Databasebeta

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C₂²×C₅³×C₁₉ #72188233

order	9500
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 160704000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅³

Aliases

C₂²×C₅³×C₁₉

Subgroups

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

640 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅³×C₁₉, C₂³×C₅³×C₁₉, C₂²×C₃×C₅³×C₁₉
maximal normal subgroup of	C₂×C₄×C₅³×C₁₉, C₂³×C₅³×C₁₉, C₂²×C₃×C₅³×C₁₉
maximal quotient of	C₂×C₄×C₅³×C₁₉, C₂³×C₅³×C₁₉, C₂²×C₃×C₅³×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.