Finite Group Databasebeta

← Prev (#72182788) Next (#72182790) →

C₂×C₄²×C₅×C₁₉ #72182789

order	3040
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 110592
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄²×C₅×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₅×C₁₉
socle, prime radical	C₂³×C₅×C₁₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅×C₈×C₁₉, C₄³×C₅×C₁₉, C₂²×C₄²×C₅×C₁₉, …
maximal normal subgroup of	C₂×C₄×C₅×C₈×C₁₉, C₄³×C₅×C₁₉, C₂²×C₄²×C₅×C₁₉, …
maximal quotient of	C₂×C₄×C₅×C₈×C₁₉, C₄³×C₅×C₁₉, C₂²×C₄²×C₅×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.