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C₉×C₁₂₉₁ #26042492

order	11619
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7740
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₆₁₉
abelian	C₉×C₁₂₉₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₂₉₁
socle, prime radical	C₃×C₁₂₉₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11619 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₆₁₉
Fitting subgroup of	D₉×C₁₂₉₁, C₉×D₁₂₉₁, D₁₁₆₁₉, …
maximal subgroup of	C₂×C₉×C₁₂₉₁, D₉×C₁₂₉₁, C₉×D₁₂₉₁, …
maximal normal subgroup of	C₂×C₉×C₁₂₉₁, D₉×C₁₂₉₁, C₉×D₁₂₉₁, …
maximal quotient of	C₂×C₉×C₁₂₉₁, C₂₇×C₁₂₉₁, C₃×C₉×C₁₂₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11619, 2);