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C₈₁×C₁₄₉ #27130487

order	12069
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7992
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₀₆₉
abelian	C₈₁×C₁₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃×C₁₄₉
socle, prime radical	C₃×C₁₄₉	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

10 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12069 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₀₆₉, C₂×D₁₂₀₆₉
maximal subgroup of	C₁₄₉×C₂₄₃, C₃×C₈₁×C₁₄₉, C₁₄₉×C₈₁⋊C₃, …
maximal normal subgroup of	C₁₄₉×C₂₄₃, C₃×C₈₁×C₁₄₉, C₁₄₉×C₈₁⋊C₃, …
maximal quotient of	C₁₄₉×C₂₄₃, C₃×C₈₁×C₁₄₉, C₂×C₈₁×C₁₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12069, 1);