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C₇×C₉×C₁₆₉ #24922379

order	10647
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃³×C₄×C₁₃ (order 5616) · Inn(G) = C₁ · Out(G) = C₂²×C₃³×C₄×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₆₄₇
abelian	C₇×C₉×C₁₆₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₃	C₃×C₇×C₁₃
socle, prime radical	C₃×C₇×C₁₃	C₃×C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10647 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₀₆₄₇
Fitting subgroup of	C₇×C₉×D₁₆₉, C₉×D₇×C₁₆₉, C₉×D₁₁₈₃, …
maximal subgroup of	C₂×C₇×C₉×C₁₆₉, C₇×C₉×D₁₆₉, C₉×D₇×C₁₆₉, …
maximal normal subgroup of	C₂×C₇×C₉×C₁₆₉, C₇×C₉×D₁₆₉, C₉×D₇×C₁₆₉, …
maximal quotient of	C₂×C₇×C₉×C₁₆₉, C₇×C₂₇×C₁₆₉, C₃×C₇×C₉×C₁₆₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10647, 1);