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C₉×C₁₂₇₉ #26040241

order	11511
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7668
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₅₁₁
abelian	C₉×C₁₂₇₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₂₇₉
socle, prime radical	C₃×C₁₂₇₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11511 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₅₁₁
Fitting subgroup of	D₉×C₁₂₇₉, C₉×D₁₂₇₉, D₁₁₅₁₁, …
maximal subgroup of	C₂×C₉×C₁₂₇₉, D₉×C₁₂₇₉, C₉×D₁₂₇₉, …
maximal normal subgroup of	C₂×C₉×C₁₂₇₉, D₉×C₁₂₇₉, C₉×D₁₂₇₉, …
maximal quotient of	C₂×C₉×C₁₂₇₉, C₂₇×C₁₂₇₉, C₃×C₉×C₁₂₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11511, 2);