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C₈×C₃₁×C₄₁ #72188787

order	10168
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₅²×C₈ (order 4800) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₅²×C₈
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₁₆₈
abelian	C₈×C₃₁×C₄₁
multiplicative	(ℤ/10169)ˣ, (ℤ/20338)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃₁×C₄₁
socle, prime radical	C₂×C₃₁×C₄₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10168 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₁₆₈, D₂₀₃₃₆
maximal subgroup of	C₁₆×C₃₁×C₄₁, C₂×C₈×C₃₁×C₄₁, C₃×C₈×C₃₁×C₄₁, …
maximal normal subgroup of	C₁₆×C₃₁×C₄₁, C₂×C₈×C₃₁×C₄₁, C₃×C₈×C₃₁×C₄₁, …
maximal quotient of	C₁₆×C₃₁×C₄₁, C₂×C₈×C₃₁×C₄₁, C₃×C₈×C₃₁×C₄₁
automorphism group of	C₁₀₁₆₉
outer automorphism group of	C₁₀₁₆₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.