Finite Group Databasebeta

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C₅×C₈×C₃₆₁ #72192606

order	14440
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄×C₉×C₁₉ (order 5472) · Inn(G) = C₁ · Out(G) = C₂³×C₄×C₉×C₁₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₄₄₀
abelian	C₅×C₈×C₃₆₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₁₉	C₂×C₅×C₁₉
socle, prime radical	C₂×C₅×C₁₉	C₄×C₁₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14440 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₄₄₀, D₂₈₈₈₀
Fitting subgroup of	D₁₄₄₄₀, Dic₇₂₂₀
maximal subgroup of	C₅×C₁₆×C₃₆₁, C₂×C₅×C₈×C₃₆₁, D₁₄₄₄₀, …
maximal normal subgroup of	C₅×C₁₆×C₃₆₁, C₂×C₅×C₈×C₃₆₁, D₁₄₄₄₀, …
maximal quotient of	C₅×C₁₆×C₃₆₁, C₂×C₅×C₈×C₃₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.