Finite Group Databasebeta

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C₂×C₄×C₅×C₃₁₁ #72190801

order	12440
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9920
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₅×C₃₁₁
multiplicative	(ℤ/18663)ˣ, (ℤ/24884)ˣ, (ℤ/37326)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅×C₃₁₁
socle, prime radical	C₂²×C₅×C₃₁₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12440 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₈×C₃₁₁, C₄²×C₅×C₃₁₁, C₂²×C₄×C₅×C₃₁₁
maximal normal subgroup of	C₂×C₅×C₈×C₃₁₁, C₄²×C₅×C₃₁₁, C₂²×C₄×C₅×C₃₁₁
maximal quotient of	C₂×C₅×C₈×C₃₁₁, C₄²×C₅×C₃₁₁, C₂²×C₄×C₅×C₃₁₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.