Finite Group Databasebeta

← Prev (#72190811) Next (#72190813) →

C₂²×C₄×C₁₉×C₄₁ #72190812

order	12464
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 138240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₁₉×C₄₁
multiplicative	(ℤ/23385)ˣ, (ℤ/24944)ˣ, (ℤ/31180)ˣ, (ℤ/46770)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₁₉×C₄₁
socle, prime radical	C₂³×C₁₉×C₄₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12464 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₁₉×C₄₁, C₂×C₄²×C₁₉×C₄₁, C₂³×C₄×C₁₉×C₄₁
maximal normal subgroup of	C₂²×C₈×C₁₉×C₄₁, C₂×C₄²×C₁₉×C₄₁, C₂³×C₄×C₁₉×C₄₁
maximal quotient of	C₂²×C₈×C₁₉×C₄₁, C₂×C₄²×C₁₉×C₄₁, C₂³×C₄×C₁₉×C₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.