Finite Group Databasebeta

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C₂×C₃×C₄×C₂₅₁ #72185208

order	6024
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₂₅₁
multiplicative	(ℤ/6539)ˣ, (ℤ/13078)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₂₅₁
socle, prime radical	C₂²×C₃×C₂₅₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₂₅₁, C₃×C₄²×C₂₅₁, C₂²×C₃×C₄×C₂₅₁, …
maximal normal subgroup of	C₂×C₃×C₈×C₂₅₁, C₃×C₄²×C₂₅₁, C₂²×C₃×C₄×C₂₅₁, …
maximal quotient of	C₂×C₃×C₈×C₂₅₁, C₃×C₄²×C₂₅₁, C₂²×C₃×C₄×C₂₅₁, …
automorphism group of	C₁₃×C₅₀₃
outer automorphism group of	C₁₃×C₅₀₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.