Finite Group Databasebeta

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C₂×C₃×C₄×C₆₀₁ #72192598

order	14424
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₆₀₁
multiplicative	(ℤ/18035)ˣ, (ℤ/21639)ˣ, (ℤ/28852)ˣ, (ℤ/36070)ˣ, (ℤ/43278)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₆₀₁
socle, prime radical	C₂²×C₃×C₆₀₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₆₀₁, C₂×C₃×C₈×C₆₀₁, C₂²×C₃×C₄×C₆₀₁
maximal normal subgroup of	C₃×C₄²×C₆₀₁, C₂×C₃×C₈×C₆₀₁, C₂²×C₃×C₄×C₆₀₁
maximal quotient of	C₃×C₄²×C₆₀₁, C₂×C₃×C₈×C₆₀₁, C₂²×C₃×C₄×C₆₀₁
automorphism group of	C₅×C₃₆₀₇
outer automorphism group of	C₅×C₃₆₀₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.