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C₂²×C₅×C₁₉×C₂₅ #72188232

order	9500
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 216000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₅×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅²×C₁₉
socle, prime radical	C₂²×C₅²×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

140 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×C₅×C₁₉×C₂₅, C₂³×C₅×C₁₉×C₂₅, C₂²×C₃×C₅×C₁₉×C₂₅
maximal normal subgroup of	C₂×C₄×C₅×C₁₉×C₂₅, C₂³×C₅×C₁₉×C₂₅, C₂²×C₃×C₅×C₁₉×C₂₅
maximal quotient of	C₂×C₄×C₅×C₁₉×C₂₅, C₂³×C₅×C₁₉×C₂₅, C₂²×C₃×C₅×C₁₉×C₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.