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C₂²×C₅²×C₉×C₁₆ #72192551

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2211840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₅

Aliases

C₂²×C₅²×C₉×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂³×C₃×C₅²
socle, prime radical	C₂³×C₃×C₅²	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1176 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	C₂²×C₅²×C₉×C₃₂, C₂×C₄×C₅²×C₉×C₁₆, C₂³×C₅²×C₉×C₁₆
maximal normal subgroup of	C₂²×C₅²×C₉×C₃₂, C₂×C₄×C₅²×C₉×C₁₆, C₂³×C₅²×C₉×C₁₆
maximal quotient of	C₂²×C₅²×C₉×C₃₂, C₂×C₄×C₅²×C₉×C₁₆, C₂³×C₅²×C₉×C₁₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.