Finite Group Databasebeta

← Prev (#72186571) Next (#72186573) →

C₅×C₈×C₁₉₁ #72186572

order	7640
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄×C₅×C₁₉ (order 3040) · Inn(G) = C₁ · Out(G) = C₂³×C₄×C₅×C₁₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₆₄₀
abelian	C₅×C₈×C₁₉₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₁₉₁
socle, prime radical	C₂×C₅×C₁₉₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7640 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₅₂₈₀, Dic₇₆₄₀
maximal subgroup of	C₅×C₁₆×C₁₉₁, C₂×C₅×C₈×C₁₉₁, C₃×C₅×C₈×C₁₉₁, …
maximal normal subgroup of	C₅×C₁₆×C₁₉₁, C₂×C₅×C₈×C₁₉₁, C₃×C₅×C₈×C₁₉₁, …
maximal quotient of	C₅×C₁₆×C₁₉₁, C₂×C₅×C₈×C₁₉₁, C₃×C₅×C₈×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.