Finite Group Databasebeta

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C₈×C₂₉×C₄₁ #72188255

order	9512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₅×C₇×C₈ (order 4480) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₅×C₇×C₈
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₅₁₂
abelian	C₈×C₂₉×C₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₂₉×C₄₁
socle, prime radical	C₂×C₂₉×C₄₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9512 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₅₁₂, D₁₉₀₂₄
maximal subgroup of	C₁₆×C₂₉×C₄₁, C₂×C₈×C₂₉×C₄₁, C₃×C₈×C₂₉×C₄₁, …
maximal normal subgroup of	C₁₆×C₂₉×C₄₁, C₂×C₈×C₂₉×C₄₁, C₃×C₈×C₂₉×C₄₁, …
maximal quotient of	C₁₆×C₂₉×C₄₁, C₂×C₈×C₂₉×C₄₁, C₃×C₈×C₂₉×C₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.