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C₉×C₁₇×C₇₁ #24925859

order	10863
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₅×C₇×C₁₆ (order 6720) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₅×C₇×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₈₆₃
abelian	C₉×C₁₇×C₇₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₇×C₇₁
socle, prime radical	C₃×C₁₇×C₇₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10863 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₀₈₆₃
Fitting subgroup of	C₉×C₁₇×D₇₁, C₉×D₁₇×C₇₁, C₉×D₁₂₀₇, …
maximal subgroup of	C₂×C₉×C₁₇×C₇₁, C₉×C₁₇×D₇₁, C₉×D₁₇×C₇₁, …
maximal normal subgroup of	C₂×C₉×C₁₇×C₇₁, C₉×C₁₇×D₇₁, C₉×D₁₇×C₇₁, …
maximal quotient of	C₂×C₉×C₁₇×C₇₁, C₁₇×C₂₇×C₇₁, C₃×C₉×C₁₇×C₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10863, 1);