Finite Group Databasebeta

← Prev (#72185262) Next (#72185264) →

C₄³×C₅×C₁₉ #72185263

order	6080
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6193152
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

C₄³×C₅×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₅×C₁₉
socle, prime radical	C₂³×C₅×C₁₉	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

516 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₅×C₈×C₁₉, C₂×C₄³×C₅×C₁₉, C₃×C₄³×C₅×C₁₉, …
maximal normal subgroup of	C₄²×C₅×C₈×C₁₉, C₂×C₄³×C₅×C₁₉, C₃×C₄³×C₅×C₁₉, …
maximal quotient of	C₄²×C₅×C₈×C₁₉, C₂×C₄³×C₅×C₁₉, C₃×C₄³×C₅×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.