Finite Group Databasebeta

← Prev (#72185140) Next (#72185142) →

C₂×C₃×C₄×C₁₃×C₁₉ #72185141

order	5928
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₁₃×C₁₉
multiplicative	(ℤ/7415)ˣ, (ℤ/14830)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₁₃×C₁₉
socle, prime radical	C₂²×C₃×C₁₃×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5928 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₁₃×C₁₉, C₂×C₃×C₈×C₁₃×C₁₉, C₂²×C₃×C₄×C₁₃×C₁₉, …
maximal normal subgroup of	C₃×C₄²×C₁₃×C₁₉, C₂×C₃×C₈×C₁₃×C₁₉, C₂²×C₃×C₄×C₁₃×C₁₉, …
maximal quotient of	C₃×C₄²×C₁₃×C₁₉, C₂×C₃×C₈×C₁₃×C₁₉, C₂²×C₃×C₄×C₁₃×C₁₉, …
automorphism group of	C₅×C₁₄₈₃
outer automorphism group of	C₅×C₁₄₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.