Finite Group Databasebeta

← Prev (#21418956) Next (#21418958) →

C₄×C₉×C₁₁×C₁₉ #21418957

order	7524
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃×C₅×C₉ (order 2160) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₅₂₄
abelian	C₄×C₉×C₁₁×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₃	C₂×C₃×C₁₁×C₁₉
socle	C₂×C₃×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7524 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₅₀₄₈, Dic₇₅₂₄
Fitting subgroup of	C₄×C₉×C₁₉×C₁₁⋊C₅
maximal subgroup of	C₄×C₅×C₉×C₁₁×C₁₉, C₄×C₉×C₁₉×C₁₁⋊C₅, C₉×C₁₁×C₁₉×Dic₅, …
maximal normal subgroup of	C₄×C₅×C₉×C₁₁×C₁₉, C₄×C₉×C₁₉×C₁₁⋊C₅, C₈×C₉×C₁₁×C₁₉, …
maximal quotient of	C₄×C₅×C₉×C₁₁×C₁₉, C₉×C₁₁×C₁₉×Dic₅, C₉×C₁₁×C₁₉×AGL(1,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 1);