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C₉×C₃₁×C₄₃ #26046337

order	11997
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₉₉₇
abelian	C₉×C₃₁×C₄₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₃₁×C₄₃
socle, prime radical	C₃×C₃₁×C₄₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11997 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₁₉₉₇
Fitting subgroup of	C₉×C₃₁×D₄₃, C₉×C₄₃×D₃₁, C₉×D₁₃₃₃, …
maximal subgroup of	C₂×C₉×C₃₁×C₄₃, C₉×C₃₁×D₄₃, C₉×C₄₃×D₃₁, …
maximal normal subgroup of	C₂×C₉×C₃₁×C₄₃, C₉×C₃₁×D₄₃, C₉×C₄₃×D₃₁, …
maximal quotient of	C₂×C₉×C₃₁×C₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11997, 1);