Finite Group Databasebeta

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C₄×C₅²×C₉×C₁₆ #72192547

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 737280
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄×C₅

Aliases

C₄×C₅²×C₉×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₈	C₂²×C₃×C₅²
socle, prime radical	C₂²×C₃×C₅²	C₂×C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

696 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅²×C₉×C₃₂, C₅²×C₈×C₉×C₁₆, C₂×C₄×C₅²×C₉×C₁₆
maximal normal subgroup of	C₄×C₅²×C₉×C₃₂, C₅²×C₈×C₉×C₁₆, C₂×C₄×C₅²×C₉×C₁₆
maximal quotient of	C₄×C₅²×C₉×C₃₂, C₅²×C₈×C₉×C₁₆, C₂×C₄×C₅²×C₉×C₁₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.