Finite Group Databasebeta

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C₄×C₅×C₁₉×C₂₅ #72188229

order	9500
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 72000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

C₄×C₅×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₅²×C₁₉
socle, prime radical	C₂×C₅²×C₁₉	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

84 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	C₅×C₈×C₁₉×C₂₅, C₂×C₄×C₅×C₁₉×C₂₅, C₃×C₄×C₅×C₁₉×C₂₅
maximal normal subgroup of	C₅×C₈×C₁₉×C₂₅, C₂×C₄×C₅×C₁₉×C₂₅, C₃×C₄×C₅×C₁₉×C₂₅
maximal quotient of	C₅×C₈×C₁₉×C₂₅, C₂×C₄×C₅×C₁₉×C₂₅, C₃×C₄×C₅×C₁₉×C₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.