Finite Group Databasebeta

← Prev (#72186443) Next (#72186445) →

C₂×C₃×C₄×C₃₁₁ #72186444

order	7464
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₃₁₁
multiplicative	(ℤ/9335)ˣ, (ℤ/11199)ˣ, (ℤ/14932)ˣ, (ℤ/18670)ˣ, (ℤ/22398)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₃₁₁
socle, prime radical	C₂²×C₃×C₃₁₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7464 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₃₁₁, C₃×C₄²×C₃₁₁, C₂²×C₃×C₄×C₃₁₁, …
maximal normal subgroup of	C₂×C₃×C₈×C₃₁₁, C₃×C₄²×C₃₁₁, C₂²×C₃×C₄×C₃₁₁, …
maximal quotient of	C₂×C₃×C₈×C₃₁₁, C₃×C₄²×C₃₁₁, C₂²×C₃×C₄×C₃₁₁, …
automorphism group of	C₅×C₁₈₆₇, C₃×C₃₇₃₃
outer automorphism group of	C₅×C₁₈₆₇, C₃×C₃₇₃₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.