Finite Group Databasebeta

← Prev (#26044574) Next (#26044576) →

C₂×C₅×C₉×C₁₃₁ #26044575

order	11790
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3120
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₇₉₀
abelian	C₂×C₅×C₉×C₁₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅×C₁₃₁
socle, prime radical	C₂×C₃×C₅×C₁₃₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11790 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₇₉₀, D₂₃₅₈₀
Fitting subgroup of	C₅×C₉×Dic₁₃₁, C₉×Dic₅×C₁₃₁, C₉×Dic₆₅₅, …
maximal subgroup of	C₄×C₅×C₉×C₁₃₁, C₅×C₉×Dic₁₃₁, C₉×Dic₅×C₁₃₁, …
maximal normal subgroup of	C₄×C₅×C₉×C₁₃₁, C₅×C₉×Dic₁₃₁, C₉×Dic₅×C₁₃₁, …
maximal quotient of	C₄×C₅×C₉×C₁₃₁, C₂²×C₅×C₉×C₁₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11790, 1);