Finite Group Databasebeta

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C₄²×C₉×C₁₀₁ #72192673

order	14544
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 57600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₉×C₁₀₁
multiplicative	(ℤ/18185)ˣ, (ℤ/36370)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃×C₁₀₁
socle, prime radical	C₂²×C₃×C₁₀₁	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14544 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₈×C₉×C₁₀₁, C₂×C₄²×C₉×C₁₀₁
maximal normal subgroup of	C₄×C₈×C₉×C₁₀₁, C₂×C₄²×C₉×C₁₀₁
maximal quotient of	C₄×C₈×C₉×C₁₀₁, C₂×C₄²×C₉×C₁₀₁
automorphism group of	C₅×C₃₆₃₇
outer automorphism group of	C₅×C₃₆₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.