Finite Group Databasebeta

← Prev (#72185261) Next (#72185263) →

C₂³×C₅×C₈×C₁₉ #72185262

order	6080
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3096576
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₅×C₈×C₁₉
multiplicative	(ℤ/18264)ˣ, (ℤ/18336)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₅×C₁₉
socle, prime radical	C₂⁴×C₅×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

676 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	C₂³×C₅×C₁₆×C₁₉, C₂⁴×C₅×C₈×C₁₉, C₂²×C₄×C₅×C₈×C₁₉, …
maximal normal subgroup of	C₂³×C₅×C₁₆×C₁₉, C₂⁴×C₅×C₈×C₁₉, C₂²×C₄×C₅×C₈×C₁₉, …
maximal quotient of	C₂³×C₅×C₁₆×C₁₉, C₂⁴×C₅×C₈×C₁₉, C₂²×C₄×C₅×C₈×C₁₉, …
automorphism group of	C₃×C₈×C₇₆₁, C₃×C₃₂×C₁₉₁
outer automorphism group of	C₃×C₈×C₇₆₁, C₃×C₃₂×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.