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C₉×C₁₃₀₃ #26043971

order	11727
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7812
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₇₂₇
abelian	C₉×C₁₃₀₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₃₀₃
socle, prime radical	C₃×C₁₃₀₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11727 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₇₂₇
Fitting subgroup of	D₉×C₁₃₀₃, C₉×D₁₃₀₃, D₁₁₇₂₇, …
maximal subgroup of	C₂×C₉×C₁₃₀₃, D₉×C₁₃₀₃, C₉×D₁₃₀₃, …
maximal normal subgroup of	C₂×C₉×C₁₃₀₃, D₉×C₁₃₀₃, C₉×D₁₃₀₃, …
maximal quotient of	C₂×C₉×C₁₃₀₃, C₂₇×C₁₃₀₃, C₃×C₉×C₁₃₀₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11727, 2);