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C₉×C₁₃₂₇ #26045935

order	11943
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7956
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₉₄₃
abelian	C₉×C₁₃₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₃₂₇
socle, prime radical	C₃×C₁₃₂₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11943 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₉₄₃
Fitting subgroup of	D₉×C₁₃₂₇, C₉×D₁₃₂₇, D₁₁₉₄₃, …
maximal subgroup of	C₂×C₉×C₁₃₂₇, D₉×C₁₃₂₇, C₉×D₁₃₂₇, …
maximal normal subgroup of	C₂×C₉×C₁₃₂₇, D₉×C₁₃₂₇, C₉×D₁₃₂₇, …
maximal quotient of	C₂×C₉×C₁₃₂₇, C₂₇×C₁₃₂₇, C₃×C₉×C₁₃₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11943, 2);