Finite Group Databasebeta

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C₈×C₃₁×C₄₃ #72189221

order	10664
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃²×C₅×C₇ (order 5040) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃²×C₅×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₆₆₄
abelian	C₈×C₃₁×C₄₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃₁×C₄₃
socle, prime radical	C₂×C₃₁×C₄₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10664 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₆₆₄, D₂₁₃₂₈
maximal subgroup of	C₁₆×C₃₁×C₄₃, C₂×C₈×C₃₁×C₄₃, C₃×C₈×C₃₁×C₄₃, …
maximal normal subgroup of	C₁₆×C₃₁×C₄₃, C₂×C₈×C₃₁×C₄₃, C₃×C₈×C₃₁×C₄₃, …
maximal quotient of	C₁₆×C₃₁×C₄₃, C₂×C₈×C₃₁×C₄₃, C₃×C₈×C₃₁×C₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.