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C₉×C₂₉×C₄₁ #24924167

order	10701
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₅×C₇×C₈ (order 6720) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₅×C₇×C₈
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₇₀₁
abelian	C₉×C₂₉×C₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₂₉×C₄₁
socle, prime radical	C₃×C₂₉×C₄₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10701 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₀₇₀₁
Fitting subgroup of	C₉×C₂₉×D₄₁, C₉×C₄₁×D₂₉, C₉×D₁₁₈₉, …
maximal subgroup of	C₂×C₉×C₂₉×C₄₁, C₉×C₂₉×D₄₁, C₉×C₄₁×D₂₉, …
maximal normal subgroup of	C₂×C₉×C₂₉×C₄₁, C₉×C₂₉×D₄₁, C₉×C₄₁×D₂₉, …
maximal quotient of	C₂×C₉×C₂₉×C₄₁, C₂₇×C₂₉×C₄₁, C₃×C₉×C₂₉×C₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10701, 1);