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C₉×C₁₃₂₁ #26045274

order	11889
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7920
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₈₈₉
abelian	C₉×C₁₃₂₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₃₂₁
socle, prime radical	C₃×C₁₃₂₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11889 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₈₈₉
Fitting subgroup of	D₉×C₁₃₂₁, C₉×D₁₃₂₁, D₁₁₈₈₉, …
maximal subgroup of	C₂×C₉×C₁₃₂₁, D₉×C₁₃₂₁, C₉×D₁₃₂₁, …
maximal normal subgroup of	C₂×C₉×C₁₃₂₁, D₉×C₁₃₂₁, C₉×D₁₃₂₁, …
maximal quotient of	C₂×C₉×C₁₃₂₁, C₂₇×C₁₃₂₁, C₃×C₉×C₁₃₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11889, 2);