Finite Group Databasebeta

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C₄×C₅×C₉×C₆₇ #27130331

order	12060
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3168
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₀₆₀
abelian	C₄×C₅×C₉×C₆₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₅×C₆₇
socle, prime radical	C₂×C₃×C₅×C₆₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12060 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₀₆₀, D₂₄₁₂₀
maximal subgroup of	C₅×C₈×C₉×C₆₇, C₂×C₄×C₅×C₉×C₆₇, D₁₂₀₆₀, …
maximal normal subgroup of	C₅×C₈×C₉×C₆₇, C₂×C₄×C₅×C₉×C₆₇, D₁₂₀₆₀, …
maximal quotient of	C₅×C₈×C₉×C₆₇, C₂×C₄×C₅×C₉×C₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12060, 1);