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C₈×C₂₃×C₅₉ #72189405

order	10856
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₁₁×C₂₉ (order 5104) · Inn(G) = C₁ · Out(G) = C₂⁴×C₁₁×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₈₅₆
abelian	C₈×C₂₃×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₂₃×C₅₉
socle, prime radical	C₂×C₂₃×C₅₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10856 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₈₅₆, D₂₁₇₁₂
maximal subgroup of	C₁₆×C₂₃×C₅₉, C₂×C₈×C₂₃×C₅₉, C₃×C₈×C₂₃×C₅₉, …
maximal normal subgroup of	C₁₆×C₂₃×C₅₉, C₂×C₈×C₂₃×C₅₉, C₃×C₈×C₂₃×C₅₉, …
maximal quotient of	C₁₆×C₂₃×C₅₉, C₂×C₈×C₂₃×C₅₉, C₃×C₈×C₂₃×C₅₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.